# Forthcoming articles

International Journal of Mathematics in Operational Research

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 International Journal of Mathematics in Operational Research (81 papers in press)  Regular Issues  Material Selection for multi tubular fixed bed reactor Fischer-Tropsch reactor (MFBR)   by Javier Martinez Abstract: The future of the fossil fuel supply is uncertain. For this reason, the transition from a fossil energy-based scenario to a bioenergy-based one is necessary for achieving the greenhouse gas emissions reduction and climate change targets. In this regards, multi-tubular fixed-bed Fischer-Tropsch reactor (MFBR) appears has an essential technology to improve and to reduce operation costs. For designing a MFBR, many studies have drawn upon computational fluid dynamics (CFD) for detailed evaluation of reaction systems. However, engineers usually define certain materials based on previous experiences and related studies, yet they neglect any preliminary selection of this procedure. This research use Multi-criteria decision making methods (MCDM) for the material selection of a MFBR. This project focuses on the selection of a proper material which fulfills the technological requirements for building the vessel and piping of a MFBR while costs reduction is considered as part of the analysis. The MCMD methods implemented are complex proportional assessment of alternatives with gray relations (COPRAS-G), operational competitiveness rating analysis (OCRA), a new additive ratio assessment (ARAS) and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) methods. The criteria weighting was performed by compromised weighting method, composed of analytic hierarchy process (AHP) and Entropy methods. The ranking results showed that ASME SA-106 and ASME SA-106 would be the best materials for the pipes and the vessel of a MFBR. Keywords: multi-criteria decision making methods; MCDM; material selection; multi tubular fixed bed reactor Fischer-Tropsch reactor; MFBR. An O (pnL) interior-point algorithm for PL(q) horizontal linear complementarity problems   by Hossein Mansouri Abstract: This paper presents a wide-neighborhood interior-point algorithm for\r\n $P_*(\\kappa)$ horizontal linear complementarity problem.\r\n The convergence analysis is shown for the introduced wide neighborhood of the central path by\r\n \\cite{Ai-Zhang} for monotone linear complementarity problem,\r\n and unifies the analysis for $\\m{N}_{\\infty}^-$ and $\\m{N}(\\tau,\\beta)$ wide neighborhoods.\r\n The Newton search directions are decomposed to the nonnegative and nonpositive parts,\r\n correspond to the parts of the right hand side.\r\n The achieved complexity bound is $O\\br{(1+4\\kappa)\\sqrt{n}\\log\\frac{n}{\\varepsilon}}$,\r\n which is the same as the best obtained bound for the monotone linear complementarity problems,\r\n except that it is multiplied by the factor $(1+4\\kappa)$, where $\\kappa$ is the handicap of the given problem. Keywords: Interior-point method; Horizontal linear complementarity problem; Wide neighborhood algorithm; Polynomial complexity. A Hierarchical Cellular Manufacturing System   by Seyed Hojat Pakzad-Moghaddam, Farhad Salehian, Seyed Esa Hosseini, Hassan Mina Abstract: Group technology proved to be advantageous in manufacturing a variety of products which have something in common. Cellular manufacturing is one of the most common and popular methods in order to take advantage of group technology. Cellular manufacturing helps the manufacturer to avoid surplus costs by bringing order to the whole manufacturing process. Of particular interest, applying Cellular Manufacturing Systems (CMSs) increases the efficiency of the applied transportation system by designing an efficient working floor. Controlling the amount of material handling, results in lower cost and energy required to transport materials/products. With this regard, hybrid cellular manufacturing systems are under consideration in the study at hand. Regarding a hybrid CMS, proper manufacturing systems such as (single machines, flow shops, job shops and open shops) are applied between and within cells to harmonize the whole manufacturing procedure. A special case of hybrid CMS, referred to as Hierarchical CMS (HCMS) is investigated in this paper. In a HCMS not only machines are placed in several interior cells, but also interior cells themselves must be located in exterior ones. Finally a Mixed Integer Non-Linear Programming (MINLP) mathematical model is presented and validated through numerical results. The aforementioned model is coded via GAMS IDE and solved by its well-known MINLP solver i.e. BARON. Keywords: Cellular manufacturing; Energy saving policy; Shop floor; Mathematical modeling. A Two-Phase Heuristic for Set Covering   by Salim Haddadi, Meryem Cheraitia, Abdellah Salhi Abstract: The set covering problem (SCP) is a well-known computationally intractable problem. We suggest here a two-phase heuristic to solve it. The first phase reduces substantially the size of the given SCP by removing some variables; the second phase applies a simple Lagrangian heuristic applied to the reduced problem. Construction and improvement heuristics are embedded in the Lagrangian solution approach. The construction heuristic provides good covers by solving small SCPs. The improvement heuristic inserts these covers into larger ones from which better covers are extracted, again by solving different but also small SCPs. The novelty lies in the reduction of the problem size by an effective variable-fixing heuristic, which, in practice, eliminates up to 95% of the variables of the problem without sacrificing the solution quality. Extensive computational and comparative results are presented. Keywords: Set Covering; Variable-fixing Heuristic; Greedy Heuristic with Regret; Lagrangian Heuristic. New generalized mixed vector variational-like inequalities with semi-$eta$-pseudomonotonicity   by Prashanta Majee, Chandal Nahak Abstract: In this paper, we introduce the concept of semi-$eta$-pseudomonotonicity for vector set-valued mappings. Using this concept, and utilizing KKM technique and Nadler's Lemma, we establish some existence results for the new generalized mixed vector variational-like inequality problem in reflexive Banach spaces. Our results are the extension and improvement of some of the results given by Plubtieng and Thammathiwat (J. Optim. Theory Appl. 162(2), 589-604, 2014). Few examples are given to justify our new findings. Keywords: New generalized mixed vector variational-like inequalities; semi-$eta$-pseudomonotonicity; Fan-KKM theorem; Nadler's result. Comparison between Linear Programming and Integer Linear Programming: A Review   by Mei Lee Sam, Adi Saptari, Mohd Rizal Salleh, Effendi Mohamad Abstract: This research discusses comparison of linear programming (LP) and integer linear programming (ILP). Both are used to seek for the optimal solution of a problem with the aim of minimizing cost or maximizing throughput with limited resources. LP allows having decimal solution, whereas ILP only allow integer. A review of literature of both programming was performed. LP and ILP have same formulation; it requires linear function for both objective and constraints. Two techniques to solve LP, simplex method and interior-point method were introduced. For ILP, available algorithms can be classified into exact algorithms and heuristic algorithms. Three criteria were used to evaluate the characteristics of LP and ILP techniques: time complexity, problem size and computational time. Simplex method is effective to solve small sized problems with less number of iteration while interior-point method was recommended for large sized problems due to its excellent performance and shorter computational time than simplex method. Exact algorithms is suitable for small sized problems and attain optimal solution in reasonable computational time. Meanwhile, heuristics outperform exact algorithms in solving large sized problem where it can obtain near optimal solution in an acceptable computational time. Heuristics are not guarantee obtain optimal solutions, compared to exact algorithms. Each technique has its own advantages. Keywords: linear programming;integer linear programming;computational time;problem’s size. Multi-objective unbalanced assignment problem with restriction of jobs to agents via NSGA-II   by Amiya Biswas, Asoke Kumar Bhunia, Ali Akbar Shaikh Abstract: In this paper, an approach based on genetic algorithm has beenproposed for solving multi-objective unbalanced assignment problems with restriction of job(s) to different agents which may arise due to the inability/ poor efficiency of performing certain jobs by some agents dealing with an additional constraint on the maximum number of jobs that can be performed by an agent. As the cost and time are considered as the most important factors for managerial decision in economic/ industrial establishments, so here the total cost of assignment of jobs to agents and the total time of completion of jobs by the agents are considered as the two prime objectives. This gives rise to an NP-hard 0-1 programming problem and to solve this problem, we have equipped NSGA-II with a newly developed crossover having the capability of repairing infeasible solution and two new mutation schemes. Also, for comparison of the results obtained from this algorithm, some other variants of this algorithm with existing crossover and mutation schemes have been considered.Finally, to illustrate the performance of proposed approach, a set of test problems have been solvedand the results have been analyzed for different variants of NSGA-IIand some potential future research directions has been discussed. Keywords: Multi-objective optimization,Unbalanced assignment problem; Genetic algorithm; Non-dominated sorting; Pareto-optimal solution. Efficient Near-Optimal Procedures for Some Inventory Models with Backorders-Lost Sales Mixture and Controllable Lead Time, under Continuous or Periodic Review   by Marcello Braglia, Davide Castellano, Dongping Song Abstract: This paper considers a number of inventory models with backorders-lost sales mixture, stockout costs, and controllable lead time. The lead time is a linear function of the lot size and includes a constant term that is made of several components. These lot-size-independent components are assumed to be controllable. Both single- and double-echelon inventory systems, under periodic or continuous review, are considered. To authors knowledge, these models have never been previously studied in literature. The purpose of this paper is to analyse and optimize these novel inventory models. The optimization is carried out by means of heuristics that work on an ad hoc approximation of the cost functions. This peculiarity permits to exploit closed-form expressions that make the optimization procedure simpler and more readily applicable in practice than standard approaches. Finally, numerical experiments investigate the efficiency of the proposed heuristics and the sensitivity of the developed models. Keywords: supply chain; inventory; logistics; lead time; stochastic; heuristics; optimization; joint economic lot size; stockout. Evaluation of Reordering Time in a Manufacturing Inventory Division   by NANDAKUMAR C D, SRINIVASAN S, SATHIYAMOORTHI R Abstract: In this paper, a production process is considered which requires two kinds of raw materials as inputs to make a product. The two kinds of raw materials are stored separately. During the time of crisis like non-availability of the raw materials due to scarcity or delayed delivery or for some other reasons, the reserve stocks are utilized to continue the production process, as a result; the level of reserve stocks would come down and finally may go void. This may result into production halt. To avoid this situation, a reorder is made to maintain the level of reserve inventory as soon as the reserve level touches a particular level called the threshold level. Using the shock model and cumulative damage process technique, a stochastic model is derived to find the threshold level or the time of reordering, which helps the production system to eliminate the holding cost on excessive raw materials and also the loss arising from the shortage of raw materials. Numerical illustrations are provided. Keywords: threshold level; reserve inventory; break down; random time points; depletion. A model for continuously degrading systems with outsourcing maintenance service   by Allen Tai Abstract: It is a common practice in industry that maintenance service is outsourced to external suppliers. In this paper, a model for a continuously degrading system is developed such that an optimal inspection-maintenance strategy can be derived. The model is capable of handling the situation when there is deferment of the maintenance services. Hence, the system manager can decide whether to stop system operation during the waiting time for the maintenance services. The system is subjected to two degradation sources: (i) the degradation due to the operation of the system and (ii) the degradation due to the operation environment. An optimal value of the inter-inspection time and an optimal maintenance threshold are then obtained by numerical methods such that the average availability of the system is maximized. Illustrative examples and some special cases are also provided. Keywords: Maintenance outsourcing; Degrading system; Periodic inspection; Availability. Proposing a New Mathematical Model and a Meta-heuristic Algorithm for Scheduling and Allocating Automated Guided Vehicle   by Mohammad Mehdi Tavakoli, Seyed Mojtaba Sajadi, Seyed Ali Sadeghi Aghili Abstract: One of the substantial things, which has been perceived more than ever by captains of industry in recent years is the necessity of earning competitive value. As a result, mechanization and enhancing the level of automation of the process has become one of the most fascinating issues to researchers. In this regard one of the most appealing systems to industries is flexible manufacturing systems which contribute to achievement of higher levels of automation in business environments. Since transportation plays an essential role in flexible production systems, Automated Guided Vehicle has been utilized to carry material in these systems in order to maintain the flexibility, increase the efficiency of production and distribution throughout the system. In this paper, a mathematical model for scheduling and allocating AVGs in the manufacturing process of a specific project is proposed and in the end, a heuristic algorithm is proposed and practiced to solve the model problem. Keywords: mathematical model; Automated Guided Vehicle (AGV); scheduling and allocation; NSGA II. On the multiserver retrial queues with negative arrivals.   by Nesrine Zidani, Natalia Djellab Abstract: The paper deals with an M/M/C/K retrial queue with exponential abandonments at which positive and negative customers arrive according to Poisson processes. This model is of practical interest: it can be used for analyzing the performance in call centers and e-mail contact systems. For model under investigation, we find the ergodicity conditions and also the approximate solution by using Finite Truncation and Value Extrapolation methods. We present some numerical results to examine the performance of Value Extrapolation method as well as the system performance. Keywords: abandonment; truncation; ergodicity condition; extrapolation; negative arrivals.DOI: 10.1504/IJMOR.2018.10005307  An imprecise-inventory model with PEND and SEND policy   by Barun Das, Dipak Barman Abstract: A continuous review economic order quantity (EOQ) model (with shortage)is modelled here. The inventory cost parameters are imprecise in nature. The model is developed for Partially Enforced Delay (PEND) and Strictly Enforced Delay (SEND) policies with lead time crashing cost. Here demand of the item is a linear function of selling price and usable lead time. For each policy, a set-up cost reduction technique has been applied to the model. More-over a statistical t-test has been used to compare the policies. We also present some numerical examples, sensitivity analysis and their discussions to stabilize the model. Keywords: Continuous review inventory policy; imprecise cost; controllable lead time; set up cost reduction; Fisher’s t-test. FINDING THE SHORTEST PATH BY ADHWARJEES ALGORITHM AND COMPARISON OF THIS POWERFUL METHOD WITH DIJKSTRA ALGORITHM   by DILIP KUMAR ADHWARJEE Abstract: The author introduces an algorithm for finding the shortest path which is more powerful method over all the existing method like Dijkstras algorithm. ADHWARJEES ALGORITHM is introduced to the readers for finding the shortest path The author gives few steps to find the shortest path. This method takes less standard time over DIJKSTRAS ALGORITM. First the Dijkstras method is explained in brief which is readily available in books. We will concentrate the new method of finding the shortest path. Adhwarjees algorithm does need no table to compute. Simple addition , subtraction & finding minimum , maximum can be done mentally & posted in the network itself. In the network the reader can see the minimum distance or time which requires to be found out. Keywords: Origin; Destination; Vertex; Shortest Path; minimum. On Optimization over the Integer Efficient Set in Fuzzy Linear Multicriteria Programming   by Ouiza Zerdani, Farida Achemine Abstract: The problem of optimizing a linear function over the efficient set of a multiobjective linear programming problem is an important field of research and has some applications in multiple objective decision making. The main difficulty of this problem is that its feasible domain is nonconvex and not described explicitly. The main purpose of this paper is to describe an efficient and finite new algorithm which provides a global R-optimal solution of the problem of optimizing a fuzzy linear function over the efficient set of a Fuzzy Multiobjective Integer Linear Programming (FMOILP) problem without having to search all integer R-Efficient solutions. All the parameters of the considered problem are characterized by trapezoidal fuzzy numbers. The proposed approach is based first on the concept of comparison of fuzzy numbers by using ranking function and on an extension of Jorges algorithm onto fuzzy numbers. Finally a numerical illustration is included for illustration. Keywords: Integer programming; Global optimization; Optimization over the efficient set; Ranking function; Trapezoidal fuzzy numbers.DOI: 10.1504/IJMOR.2018.10004946  Partial Backlogging EOQ Model with Trade-Credit Facility and Inflationary Environment   by Rahul Goel Abstract: In this article, an EOQ (economic order quantity) model for deteriorating items with trade-credit facility is presented. It is assumed that decay rate is two parameters Weibull distributed function of time. Demand rate of the products increases with time. Shortages are allowed and partially backlogged. The whole study is done in inflationary environment. A numerical assessment is done to exemplify the proposed model and sensitivity analysis with respect to the change in system parameters is also carried out. Keywords: EOQ; inventory; Weibull deterioration; shortages. AN APPLICATION OF MULTI LAYERED FUZZY ATTRIBUTED ROUGH SET IN STUDYING ORGANIZATIONAL CULTURE SYSTEM   by Praba Bashayam, Gomathi Ganesan, Vijaya Mani, Vageesh Mohan Abstract: In this paper, the concept of Rough set is introduced for an information system with multi layered weighted fuzzy attributes. The equivalence classes of the objects are formed using the fuzzy weight given to the objects in terms of these multi layered weighted fuzzy attributes. The weight of the Rough Set is also defined using the weight of its lower and upper approximations and also we defined an interval valued fuzzy set on the set of objects. This helps to study the behaviour of any system with complex attributes. These concepts are illustrated with a real time example. Keywords: Rough set; Information system; Lower Approximation; Upper Approximation; Equivalence classes.DOI: 10.1504/IJMOR.2018.10010379  Multi-objective optimization using genetic algorithm based clustering for multi- depot heterogeneous fleet vehicle routing problem with time windows   by Lahcene Guezouli, Samir Abdelhamid Abstract: Efficient routing and scheduling of vehicles has significant economic implications for both the public and private sectors. To this purpose, we propose in this study a decision support system which aims to optimize the classical Capacitated Vehicle Routing Problem by considering the existence of different vehicle types (with distinct capacities and costs) and multiple available depots, that we call the Multi-Depot Heterogeneous Vehicle Routing Problem with Time Window (MDHVRPTW) by respecting a set of criteria including: schedules requests from clients, the heterogeneous capacity of vehicles..., and we solve this problem by proposing a new scheme based on the application of the bio-inspired genetic algorithm heuristics and by embedding a clustering algorithm within a VRPTW optimization frame work, that we will specify later. Computational experiments with the benchmark test instances confirm that our approach produces acceptable quality solutions compared with the best previous results in similar problems in terms of generated solutions and processing time. Experimental results prove that our proposed genetic algorithm is effective in solving the MDHVRPTW problem and hence has a great potential. Keywords: Multi-depot vehicle routing problem; clustering; routing; scheduling; genetic algorithm; heterogeneous vehicle routing problem.DOI: 10.1504/IJMOR.2018.10008290  Designing an open-loop supply chain network for recyclable products: A case study   by Shiva Zandkarimkhani, Mohammad Mahdi Nasiri, Jafar Heydari Abstract: Recently because of the recycling policies and environmental issues, the combination of forward and reverse logistics have attracted lots of attention to itself. The current paper presents a designed open-loop supply chain network to reuse the returned goods. To this aim, a mixed integer linear model is proposed that minimizes the total cost. The proposed model determines the location of distribution centers, recycling centers, collection centers, disposal centers and also the quantity of the transferred product between levels. Finally, in order to investigate the effectiveness of the proposed model, it is implemented at one of Iranian Poly Ethylene Terephthalate (PET) product companies. Keywords: Supply chain management; Mathematical programming; Reverse logistics; open loop supply chain. Generate random variates using a newly introduced approximation to cumulative density of lower truncated normal distribution for Simulation Applications   by Mohammad Hamasha Abstract: The lower side truncated cumulative normal distribution and its inverse are approximated in simple functions, and random variates are explained how to be generated from the introduced approximation of the inverse. The introduced approximation is derived from Audaat and Alodat's model of approximating cumulative normal distribution. The accuracy of the introduced model and its inverse is investigated in term of maximum absolute error. The maximum absolute error of the introduced approximation is 0.003944 in the entire region. This level of maximum absolute error is the best comparing all other similar models to the best of authors knowledge. Keywords: Normal Distribution; Random Variate Generation; Cumulative Density Function; Upper and Lower Truncated Normal Distribution. Equilibrium behavioral strategies in an M/M/1 queue   by Sofiane Ziani, Fazia RAHMOUNE, Mohammed Said RADJEF Abstract: For an M/M/1 system, we analyze the strategic interactions of the social optimizer, the service provider and customers and their consequences on the system. The social optimizer chooses the type of information to make available to customers (make the system observable or unobservable), the service provider chooses the service rate with which he performs the service, and customers decide, according to the strategic choices of the first two agents, to use or not the system. As these agents are interacting in a common environment with respect to their objectives, we model the problem as a three-stage game between them. A resolution of the different stages will be made, which will give the overall solution to the considered problem, corresponding to the subgame perfect Nash equilibrium in behavioral strategies. A numerical analysis will be made where one can see the graphical solution of the game, comparisons and interpretationsrnwill be established. Keywords: Queueing; Reward-cost structure; Extensive form game; Behavioral strategy; Nash equilibrium. N-Policy for Redundant Repairable System with Multiple Types of Warm Standbys with Switching Failure and Vacation   by Ritu Gupta, Madhu Jain Abstract: This investigation is concerned with the reliability analysis of redundant repairable system which is supported by mixed standby and two repairmen who turn on according to a threshold N-policy failed. The first repairman never takes a vacation while the second repairman leaves for a vacation of random length when the number of failed components is less than N. The standby switching failure is taken into consideration to deal with real time redundant system. The concepts of degradation and common cause failure are incorporated. By developing Markov model, the transient queue size distribution and expressions for the system reliability, mean time to system failure and other performance measures are obtained. The sensitivity analysis is performed by taking numerical illustration. The model is also examined computationally by employing neuro-fuzzy technique based on adaptive network-based fuzzy interference system (ANFIS) to compute the system descriptors. Using supervised learning process, the comparison between approximate results and analytical results are made. Keywords: Reliability; N-policy; Standby switching failures; Server vacation; Neuro fuzzy technique. Numerical approach to the uniqueness solution of Von-Karman evolution   by Oudaani Jaouad Abstract: The purpose of this paper is to give some theoretical and numerical analysis approach, for local generalized and weakly uniqueness solution, to the models with interior dissipation and clamped boundary conditions of Von-Karman evolution, without rotational inertia and nonlinear internal dissipation. For approached the uniqueness solution we use the scheme of finite difference method. Keywords: Von-Karman evolution; Rotational inertia (α ≥ 0); finite difference method; Noncoupled method.DOI: 10.1504/IJMOR.2018.10011949  A Unified Approach for Optimal Release, Patching and Testing Time of a Software   by P.K. Kapur, Ompal Singh, A.K. Shrivastava Abstract: The ever growing consumers expectations for innovative and reliable software products within no time have driven developers to reframe the whole development process accordingly. Rigorous testing is required before release to provide highly reliable software to the customer so that users face less failures during operational phase. Although, efficient testing ensures reliable software but costs a lot to developer in terms of higher testing and market opportunity cost. Also, due to stiff market competition and risk of delaying release, now a days software firms are releasing their product early and continue testing to fix the remaining number of bugs in the operational phase by providing patches. A Patch is a small program to fix the bugs. But continuing testing to provide patches for better product experience to users is also not economical from firms point of view. Hence it is important to determine the optimal time for releasing, patching and stop testing the software. In this paper we present a unified framework of optimal policy to determine optimal software release, patching time and testing stop time, to minimize overall testing cost. Proposed cost model is validated on a real life software failure data set of Tandem Computers. Keywords: Modeling; Patch; Release; Software Reliability; Software updating; Software testing; Unified Approach. A model for supplier evaluation and selection based on integrated interval-valued intuitionistic fuzzy AHP-TOPSIS approach   by Hossein Sayyadi Tooranloo, Arezoo Sadat Ayatollah, Asiyeh Iranpour Abstract: Todays, in the global market are confronted with short-lifecycle products or highly demanding customers that calls a lot of focus on supply chain. Among the activities of the supply chain, activities of effective purchasing are as most important activity to proper selection of suppliers. Since of Supplier evaluation and selection problem is a multi-criteria decision making problem that is along with high degree of ambiguity and uncertainty in the real world decision makings. Since of information of real world decision-makings are often imprecise and expressed with verbally terms therefore the fuzzy sets theory can be effectively used to solve such problems. This paper first provides an overview on the supplier evaluation and selection problem, and then presents a decision making model that is integrates interval-valued intuitionistic fuzzy AHP (IVIF- AHP) and interval-valued intuitionistic fuzzy TOPSIS (IVIF-TOPSIS) to solve such problems, and in the end, provides a numerical example to demonstrate the use of proposed approach. Keywords: supplier selection; AHP; TOPSIS; interval-valued intuitionistic fuzzy. A Forward with Backward Inventory Policy Algorithm for Non-Linear Increasing Demand and Shortage Backorders   by Ririn Diar Astanti, Huynh Trungh Luong, Hui Ming Wee, The Jin Ai Abstract: The traditional inventory policies have been developed for constant demand processes. In reality, demand is not always stable; it might have an increasing pattern. In this paper, a forward with backward inventory policy algorithm is developed to determine the operational parameters of an inventory system with a non-linear increasing demand rate, shortage backorders and a finite planning horizon. Numerical experiments are also conducted to compare the results with the existing techniques and to illustrate the applicability of the proposed technique. Keywords: Inventory; non-linear increasing demand pattern; shortage backorders; forward with backward inventory policy algorithm. Measuring the Productivity Changes with Double Frontiers Data Envelopment Analysis for Two-stage processes   by Ali Mohtashami, Alireza Alinezhad, Mohammad Javad Nasiri Sadeghloo Abstract: The purpose of this paper is to develop an output oriented methodology with constant return to scale (CRS) assumption for calculating productivity changes by using double frontier (optimistic and pessimistic) data envelopment analysis (DEA) simultaneously for two-stage processes. Measuring the productivity changes with Malmquist productivity index (MPI) via double frontiers DEA with single process has been defined by Wang and Lan (2011) as a geometrically average of optimistic and pessimistic point of views to generate an aggregate MPI. In order to develop and modify the previous studies, in this paper we have proposed a method to modify Wang and Lan (2011) aggregate MPI and also extend it to two-stage process which we refer to the double frontiers two-stage DEA (DFTDEA). It should be mentioned that the proposed model of this paper measures the MPIs distance functions for two individual stages and whole process for both DEA different points of view by the traditional DEA models and supposed relational models in output oriented CCR models, respectively. Therefore, the identified double frontiers two-stage DEA (DFTDEA-based MPI) is more realistic and comprehensive than the conventional optimistic or pessimistic DEA-based MPI individually. Subsequently, the proposed approach is examined to five Iranian commercial banks over the 5-years period (2009-2013). Keywords: Data envelopment analysis; Two-stage; Double Frontier; Malmquist productivity index. Promotional effort and quality sensitive two echelon production inventory model with partial backlogging   by Brojeswar Pal Abstract: This study deals with the modeling aspect of a two echelon imperfect production system in presence of the promotional effort of the retailer. The production cost of the system varies with both the ordering lot size and quality of product, and the demand of the product depends on the quality of the product. The inventory level for the manufacturer starts with shortages and new production and the inventory level for the retailer also begins with shortages and new product lot. The cycle ends for both the players with also backlogged inventory. The backlogging rate for each of the player is dependent on waiting time. The behavior of the model under integrated system is analyzed. In the decentralized structure, retailer Stackelberg model are also discussed. The sensitivity of the key parameters is examined to test feasibility of the model. Finally, a numerical example is provided to investigate the proposed model. Keywords: Imperfect production inventory model; promotional effort; quality; partially backlogging. 1 Introduction. A New Short Term Energy Price Forecasting Method based on Wavelet Neural Network   by Farshid Keynia, Azim Heydari Abstract: A Wavelet Neural Network (WNN) is proposed for Short-Term Price Forecasting (STPF) in electricity markets. Back propagation algorithm is used for training the Wavelet Neural Network for prediction. Weights in the back propagation algorithm are usually initialized with small random values. If the random initial weights happen to be far from a suitable solution or near a poor local optimum, training may take a long time or get trapped in the local optimum. In this paper, we show that WNN has acceptable prediction properties compared to other forecasting techniques. We investigated proper weight initializations of WNN, and proved that it attains a superior prediction performance. Finally, we used a two-step correlation analysis algorithm for feature selecting. This algorithm selects the best relevant and non-redundant input features for WNN. Our model is examined for MCP prediction of the Spanish market and LMP forecasting in PJM (Pennsylvania, New Jersey, and Maryland) market for the year 2002 and 2006 respectively. Keywords: Adaptive wavelet neural network; Electricity market; Location marginal price; Short term price forecasting. Second Order Duality for Variational Problem Via Efficiency of Higher Order   by Promila Kumar, Bharti Sharma Abstract: A mixed type second order dual of a multiobjective variational problem has been considered. Notion of generalized second order (F,ρ,θ,m)-invexity is introduced which is utilized to obtain duality results using efficiency of higher order as optimality criteria. Generalized second order (F,ρ,θ,m)-invexity assumptions broadens the domain of the problem, whereas efficiency of higher order leads to stronger results. Keywords: Second order duality; Variational problem; Efficiency of higher order. Joint replenishment model of both-ways and one-way substitution among products in Fixed Time Horizon   by Raghu Nandan Giri, Shyamal Kumar Mondal, Manoranjan Maiti Abstract: A general joint replenishment model (JRM) has been developed for two substitutable products with different demand structures depending on their prices and availabilities over the time cycle. When both products are available, the demand of a substitute product deceases against its own price and increases with the other's price. When one product is out of stock, a portion of demand of the stock-out product goes to the available product. The model is formulated to determine the optimal order quantities and total profits for different scenarios are determined using the classical optimization method and parametric study. The optimal criteria for maximum profit is outlined and the model is illustrated numerically. Some sensitivity analyses with different substitution ratios are performed and some interesting conclusions have been derived. Keywords: Joint replenishment model; Substitutable products; Degree of substitution; Fixed time horizon. Developing an integrated decision making model in supply chain under demand uncertainty using genetic algorithm and network data envelopment analysis   by Sara Nakhjirkan, Farimah Mokhatab Rafiei, Ali Husseinzadeh Kashan Abstract: Nowadays, organizations have recognized the importance of supply chain performance improvement and coordination and integration of supply, production, distribution and inventory operations. They have found out that achieving the competitive advantages requires more focus on supply chain integration (Mina et al., 2014). Since organizations are combined with each other as a network of supply and distribution, the ineffectiveness (such as less operation capacity) and inefficiencies (higher costs) have been more highlighted and the importance of integration has become more specific. This research describes a four echelon supply chain including supplier, producer, distribution and customer levels. Whole scheduling and decision makings are performed by producer. The considered problem is a location routing inventory problem (LIRP). Supply chain integration and demand uncertainty are considered to generate a proper model for the problem. An integrated mathematical model is presented and a set of problems are randomly generated and solved using GAMS software to validate the model. The results show that by increasing the dimensions of the problems the solution times increase exponentially; this represents the complexity of the problem. Therefore, a heuristic genetic algorithm base on network data envelopment analysis selection method is proposed. To evaluate the effectiveness of this proposed algorithm, a set of problems with various dimensions are solved by utilizing this method and three other selection methods. Obtained results are compared by Wilcoxon test which represents proposed algorithms effectiveness. Keywords: Supply chain network; Location-inventory-routing problem; Genetic Algorithm; NDEA. A New Optimal Multi-product (Q, R, SS) Policy with Multivariate Markov Stochastic Demand Forecasting Model   by Jie Chen, Zhixiang Chen Abstract: Multi-product inventory control is a challenging problem. Since its complexity in computation, many prior studies simplify the modeling conditions to assume that the demands are independent. In this paper, we consider a multi-product inventory system with stochastic demands which have multivariate Markov transition characteristics. We first study the demand transition process based on multivariate Markov theory, and construct a multivariate Markov demand model to forecast the stochastic demands of multiple products. Then, we propose a new optimization model of inventory decision for multi-product under the multivariate Markov demand transition pattern. By solving the optimal solution of the model, we propose an optimal (Q, R, SS) policy to decide the ordering quantity Q, ordering point R, and safety stock SS. At last, we use a numerical example to demonstrate the application feasibility and efficiency of the proposed method. Keywords: Demand forecasting; stochastic demand; multi-product inventory system; multivariate Markov model; optimal (Q; R; SS) policy. Optimal Strategy for an Inventory Model Based on Agile Manufacturing under Imperfect Production Process   by Himani Dem, S.R. Singh, Leena Parasher Abstract: This paper presents a production inventory model over infinite planning horizon with manufacturing process producing both perfect as well as imperfect items. Demand is stock dependent for perfect quality items and for imperfect items it depends on the reduction rate of selling price and the amount of imperfect production. The Production rate is a function of demand. Reliability of the manufacturing system is assumed to be exponentially decreasing function of time. The objective is to determine the optimal policy for production system which maximizes the total profit subject to some constraints under consideration. The results are discussed with a numerical example to illustrate the theory. The effects of important parameters on decision policy are also analysed through sensitivity analysis. Keywords: Imperfect production; Agile/ volume flexible manufacturing system; Stock dependent demand; Reduction rate. A fuzzy rough integrated multi-stage supply chain inventory model with carbon emissions under inflation and time-value of money   by Soumita Kundu, Tripti Chakrabarti Abstract: Growing consciousness about environment compel governments across nations to enact legislation to reduce the greenhouse gas emission from industries. Recently, many investigations have been done on supply chain model imposing carbon regulation policies. But the effect of inflation and time value of money are overlooked. Here, we extended our research by considering the concept of inflation and time value of money in fuzzy rough environment where the cost coefficient are taken as trapezoidal fuzzy rough variables. In order to obtain optimistic and pessimistic equivalent of fuzzy rough objective function we use fuzzy rough expectation operator based on trust measure theory. Optimal inventory replenishment policy is obtained by using interior point algorithm in MATLAB R2013a and sensitivity analysis is also presented to explore the effect of changes in carbon tax , net discount rate of inflation and optimistic -pessimistic parameter on the optimal solution. Keywords: Integrated supply chain; Shipment; Inflation; Greenhouse gas emission; Emissions tax;Fuzzy rough variable. A two level supply chain model with trade credit and imperfect production process   by UDAYAKUMAR RAMASAMY, GEETHA KRITHIVASAN Abstract: In this article, we discuss a production-distribution inventory model with a single-vendor and single buyer for defective items. The production process is imperfect and the items are inspected by a complete inspection process. Trade credit is offered by the supplier, who encourages the retailer to buy more products. The lead time is controllable. The lead time crashing cost is considered to be an exponential function of lead time. Two models are proposed in this article. In the first model, the lead time demand is allowed to follow a normal distribution and another model is framed with distribution free lead time demand. Also, the vendors setup cost is reduced by an added cost. The objective of this work is to frame the model under imperfect production process and delay in payment and to investigate the impact of product defective rate on the expected total cost of the integrated system. The optimal values of order quantity, lead time, setup cost and the number of shipments from vendor to the buyer are found such that the total expected cost of the system is minimized. Efficient computational algorithms for both the models are designed to find the optimal solution. Managerial insights are obtained with the help of numerical example and sensitivity analysis. Keywords: Supply chain; Setup cost; Controllable Lead time; Trade credit;. Large deviations for the overflow level of G/G/1 queues in series.   by Karol Rosen Abstract: We present a result characterizing the large deviations behavior of the total overflow level in a cycle starting with zero customers for a system of G/G/1 queues in series. We also present large deviations results for the total overflow level as seen by a random customer and in stationarity. We prove that the large deviations behavior of the total overflow level for all three distributions, in a cycle, as seen by a random customer and in stationarity, have the same decay rate. We find the most likely path to have overflow in the system. Based on those results we propose a state-independent importance sampling algorithm. We also give conditions under which that algorithm is asymptotically efficient. By means of numerical simulation, we provide evidence of the advantages of this algorithm. Keywords: Large deviations; G/G/1 queues in series; rare event simulation; importance sampling; exponential twist; Palm distribution; stationary distribution. An M^[X]/G(a,b)/1 queueing system with Server breakdown and Repair, Stand-by server and Single vacation.   by Ayyappan G. Govindan, Karpagam S Abstract: In this paper, we discuss a Non-Markovian batch arrival general bulk service single server queueing system with server breakdown and repair, single vacation and stand-by server. The main server may breakdown at any time during service with exponential rate alpha and in such a case the main server immediately goes for a repair which follows exponential distribution with rate eta and the service to the current batch of customers is interrupted. Such a batch of customers is transferred to the stand-by server who starts service to that batch of customers afresh. If the system size becomes less than a before main servers repair completion, then the stand-by server decides to stay in the system and starts service to the next batch only when the queue size reaches at least a. At the instant of repair completion, if the stand-by server is busy then the service to the batch of customers is interrupted and that batch of customers is transferred to the main server who starts service to that batch of customers afresh. Suppose at the instant of service completion if the queue length is less than a then the main server goes for a vacation. Otherwise, if he finds at least a customers waiting for service, say xi, then he serves a batch of size min (xi,b) customers, where b greater than or equal to a. Suppose at the instant of repair completion or at the instant of vacation completion if the system size is less than a then the main server stays in the system and waits for the next batch of arriving customers. The probability generating function of queue size at an arbitrary time and some performance measures of the system are derived. An extensive numerical result for a particular case of the model is illustrated. Keywords: General bulk service; Single vacation; Stand-by server; Non-Markovian queue; Breakdown and Repair. Work planning optimization in ports. A simplex application   by Iñigo L. Ansorena Abstract: This paper presents an optimization of the work plan at the gate of Barcelona Container Terminal (also known as TCB). The optimization problem is formulated in accordance with the average traffic flow as a Linear Programming (LP) problem. Constraints of the LP problem are based on the data collected at the gate of TCB. The LP problem is solved by simplex algorithm and the solution includes: First, the value of the objective function (that is the feasible solution that minimizes the number of clerks at the gate throughout a day); and second, the value, contribution to the objective, reduced cost, and range of optimality for each decision variable. Once the optimal solution has been achieved a sensitivity analysis is developed. The methodological procedure presented in this paper is general enough to be applied to any other container terminal. Keywords: Barcelona; container terminal; gate; linear programming; simplex. Prioritizing Vulnerabilities using ANP and Evaluating their Optimal Discovery and Patch Release Time   by Yogita Kansal, P.K. Kapur, Uday Kumar, Deepak Kumar Abstract: Risk assessment and management are the necessary actions performed by software developing organizations to ensure the continuity of the product in case of vulnerabilities. Clustering vulnerabilities on the basis of its behavior and properties is one of the approaches made by the experts as discussed in Common Weakness Enumeration that provides a hierarchy of vulnerabilities. Although vulnerability classification does not able to provide a solution as developers are still not able to decide which vulnerability class should be tackled first. Thus, a method for filtering and identifying a vulnerability class whose occurrence potential is high is needed by an organization to patch their software in timely manner. In this paper, our first step is to filter the most frequently observed vulnerability type/class through a multi-criteria decision making that involves dependency among various criteria and feedback from various alternatives, known as Analytic network process. We will also formulate a cost model so as to provide a solution to the developers facing high revenue debt because of the occurrence of highly exploited vulnerabilities belonging to the filtered group. The cost model involves the cost of identifying vulnerabilities, patching vulnerabilities, cost of testing the patches and cost of risk mitigation. The main aim of formulating the cost model is to evaluate the optimal discovery and patch release time such that the total developers cost could be minimized which is subject to risk constraints. To illustrate the proposed approach, reported vulnerabilities of Google chrome with high exploitability potential have been examined at its source level. Keywords: Vulnerability; Multi Criteria Decision Making; Analytic Network Process; Optimization; Patches. Use of a Sine Cosine Algorithm Combined with Simpson Method for Numerical Integration   by Mohamed Abdelbaset, Yongquan Zhou, Ibrahim Mohamed Abstract: The Sine Cosine Algorithm (SCA) is one of the most recent nature-inspired meta-heuristic optimization algorithm, which the mathematical model based on sine and cosine functions. SCA has validated excellent performance in solving continuous problems and engineering optimization problems. In this paper, we propose a new algorithm that encompasses the features of Sine Cosine Algorithm and Simpson method (SCA-SM). The proposed procedure consists of two phases: in the first phase, the of Sine cosine algorithm are used to find the optimal segmentation points on the integral interval of an integrand. In the second phase, the approximate integral value of the integrand is then calculated by a Simpson method. Numerical simulation results show that the algorithm offers an effective way to calculate numerical value of definite integrals, and it has a high convergence rate, high accuracy and robustness. Keywords: Sine cosine algorithm; meta-heuristics; optimization; Simpson method; numerical integration. Robust and Stable flexible job shop scheduling with random machine breakdowns: Multi-objectives genetic Algorithm approach   by Seyed Mojtaba Sajadi, Azar Alizadeh, Mostafa Zandieh Abstract: In this paper, robust and stable scheduling for a flexible job-shop problem with random machine breakdowns has been discussed. A two-stage genetic algorithm is used to generate the predictive schedule. The first stage optimizes the primary objective, which minimizes the makespan, where all data is considered to be deterministic with no expected disruptions. The second stage optimizes two objectives, makespan and stability, function in the presence of random machine breakdowns. For the second stage two different versions of multi-objective genetic algorithm, non-dominated sorting genetic algorithm II and non-dominated ranking genetic algorithm, is used. A simulator is proposed to simulate random machine breakdowns. An experimental study and analysis of variance is conducted to study the results of each multi-objective algorithm and breakdown simulator. The results of their comparison indicate that, non-dominated ranking genetic algorithm (NRGA) performs better and also shows a significant difference between various repair times in the proposed breakdown simulator. Keywords: Flexible job-shop scheduling problem; Machine breakdowns; Robustness; Stability. Production Inventory Model of Deteriorating Items with Holding Cost, Stock, and Selling Price with Backlog   by Bani Mukherjee, Dharamender Singh Abstract: This paper deals production inventory model with stock-dependent and selling price dependent demand. Demand rate is linearly increasing with stock and time, decreasing with a selling price of the item. Shortages are allowed and partially back ordered at the rate of decreasing waiting time of next replenishment. This model is classified as the deterioration rate is constant, and holding cost-based as constant. The model is solved numerically and analytically by minimizing the total inventory cost and maximizes the total profit at the last sensitivity analysis has been performed to show the nature of model in every parameter on the optimum solution. We have presented a solution-search procedure to find the preservation technology and optimal production time. Keywords: deterioration; inventory; preservation technology; production; shortage. An EPQ model in the perspective of Carbon emission reduction.   by Sudipta Sinha, Nikunja Mohan Modak Abstract: One of the major reasons behind the abnormal increase of temperature of the Earth is the uncontrollable emission of of the production houses. Industrialists are very much interested to enhance their profit only instead of greater interest of the society at large. The present paper devices to put in place an economic production quantity (EPQ) model reckoning the aspects of carbon emission and carbon trading. In the model production house or a firm house has to pay compulsory tax for carbon emission and in addition to that it incurs a penalty cost or carbon buying cost if the quantity of emitted carbon exceeds the permissible limit alloted to it. But, side by side, the manufacturer or producer is also able to earn revenue by the way of carbon trading (Cap & Trade policy) if it can control carbon emission within the permissible limit. Plantation of trees can effectively mitigate the effect of emission. Finally, some numerical examples are given to illustrate the validity and feasibility of the proposed model and comparison of result between with and without plantation are provided in tabular form. The problems are solved by the software Mathematica-7. Comprehensive sensitivity analysis of various parameters has also been carried out. Keywords: EPQ; Carbon emission; Carbon trading; Cap and trade; Penalty Tax; Plantation. Steady state analysis of system size based balking in M/Mb/1 queue   by Gopal Gupta, Anuradha Banerjee Abstract: In this paper we consider a single server Poisson queue where customers are served in batches of fixed size. The inter arrival time and the service time are considered to be exponentially distributed. The customers upon arrival may decide to join the system or not to join the system by observing the system length. They may join or balk the system with certain probability. Using probability generating function method we obtain the closed form expression for steady state queue length distribution, expected system (queue) length and expected waiting time of a customer in the system (queue). Finally, several numerical results are discussed in the form of table and graphs to explore the sensitivity of system parameters on key performance measures. Keywords: Balking; Bulk service queue; Fixed batch size; Probability generating function method; Steady state. Single-vendor multi-buyer integrated inventory system for multi-item   by R. Uthayakumar, M. Ganesh Kumar Abstract: In this paper, a single-vendor multi-buyer supply chain system is considered in which several products. The demand of this supply chain for each product is a stochastic variable and its assumed to follow a normal distribution. The lead time of receiving products from vendor to buyer is a variable which controllable by adding extra cost. During the consumption period, the shortages are allowed and they are completely backlogged in the next replenishment. The production process is assumed to be imperfect, i.e., all the finished products need not consumable, so the buyer implements a screening process to separate the defective and non-defective items and the vendor pay warranty cost for each defective item to the buyer. We investigated the Economic Order Quantity (EOQ), lead time and number of shipments such that total cost of the supply chain have been minimized. Numerical illustration and sensitivity analysis are given to show the applicability of the proposed methodology in real-world supply chain problems. Keywords: Controllable lead time; defective items; economic order quantity; inspection; integrated model; process quality. An Inventory Model for Deteriorating Items with Time and Price Dependent Demand and Shortages Under the effect of Inflation.   by Sumit Saha, Nabendu Sen Abstract: Variation of demand with time and price is one of the major concerns in any inventory system.. Several studies report situations where demand varies with time and price separately. A few researchers have considered the joint effect of demand with price and time on optimal solutions. Thus, a suitable inventory policy in this regard is always sought for. The paper presents an inventory model with selling price and time dependent demand, constant holding cost and time dependent deterioration. In this model, shortages are assumed to be partially backlogged. It is designed keeping in mind to optimize total inventory cost under the effect of inflation. For the solution of the model, an algorithm is proposed and illustrated with numerical values of system parameters. The optimal results are also presented graphically. Finally, sensitivity analysis is performed for different parametric values of system parameters. Keywords: Time and price dependent demand; Deterioration; Partial backlogging; Maximum life time of item; Inflation. Ensure Optimum Profit using Linear Programming a Product-Mix of Textile Manufacturing Companies   by Gera Workie, Abebaw Bizuneh, Senait Asmelash Abstract: An optimum profit is to be guaranteed for a rapidly changing manufacturing situation when the best product mix is produced. The product mix determination problem involves determining the optimal level of different products given a set of capacity limitations. This paper addresses a tool in operations research for determining the optimal allocation of limited resources in order to maximize profit. One of the methods widely used is linear programming, which has been proven to be a very powerful tool in making managerial decisions in a manufacturing plant about maximizing net profit. Fortunately, having well-formulated model, linear programming solution software packages help to determine the best combination of available resources. This paper considers a textile industrial unit in Ethiopia as a case study. In this company, held resources, product volumes, amount of resources required to produce single item and profit per unit of each manufactured goods have been collected. The data gathered was used to estimate the parameters of the linear programming model. The model was solved using Excel Solver software. The findings of the study show that the profit of the company can be improved by 11.8% (= (66850232.79-59793841.91/59793841.91)) if linear programing technique is used. This can be considered as a remarkable profit improvement. In addition, actual resource utilization can be significantly improved by adopting linear programing method. Keywords: Excel solver; Linear programming; Optimal profit; Product mix; Textile Manufacturing. A Class of Always Pooling Shrinkage Testimators for the Weibull Model   by Zuhair Al-Hemyari Abstract: Utilizing the prior information or additional information from the past in new estimation processes has been receiving considerable attention in the last few decades - as such appears from the list of the references of this paper. It may worth mentioning that the shrinkage testimators were developed orginally for the purpose of utilizing the prior information or additional prior information in new estimation problems. Most of the literature of the shrinkage testimators of the paramneters are either based on complete or censored data schemes and in single stage or double stage sampling.rnIn this paper, we have developed a general class of shrinkage testimator, and because it always uses the prior value, is called the always pooling shrinkage testimator (APST) for any parameter or distribution and two special cases, i.e. two testimators of the shape parameter of the Weibull model are studied. The expressions of bias, risk, risk ratio, relative efficiency, region and shrinkage weight function are derived.The simulation study has been developed and has revealed that the proposed cases have lower risk for the interval than the classical and existing testimators. The comparisons, recommendations, disscusions and limitations are provided in this paper.rn Keywords: always pooling; shrinkage; Weibull failure model; shape parameter; censored data;bias ratio; relative risk. New model for improving discrimination power in DEA based on dispersion of weights   by Ali Ebrahimnejad, Shokrollah Ziari Abstract: One of the difficulties of Data Envelopment Analysis(DEA) is the problem of deficiency discrimination among efficient Decision Making Units(DMUs) and hence, yielding large number of DMUs as efficient ones. The main purpose of this paper is to overcome this inability. One of the methods for ranking efficient DMUs is minimizing the Coefficient of Variation (CV) for inputs-outputs weights, which, was suggested by Bal et al.(2008). In this paper, we introduce a nonlinear model for ranking efficient DMUs based on modifying of the model suggested by Bal et al. and then we convert the nonlinear model proposed into a linear programming form. The motivation of this work is to linearize the existing nonlinear model which has the computational complexity. Keywords: Data Envelopment Analysis (DEA); Ranking; Extreme efficient; Dispersion of weights. Evaluating Fuzzy Risk Based On a New Method of Ranking Fuzzy Numbers Using Centroid of Centroids   by Phani Peddi Abstract: This paper describes a method to rank fuzzy numbers based on centroid of centroids of fuzzy numbers and emphasizes the use of the subjectivity of the decision makers view point, such as optimistic or pessimistic. Using the decision makers view point and index of modality, a ranking index of each fuzzy number is calculated which serves as a criterion for ranking fuzzy numbers. The proposed fuzzy ranking method is used to analyse the fuzzy risk involved in manufacturing products by different companies, where the probability of failure of a product is represented by a fuzzy number. The proposed method is more flexible than the existing methods as it takes into consideration the degrees of confidence of decision makers opinion in both the stages. Keywords: Fuzzy numbers; Centroid points; Index of optimism; Index of modality; Fuzzy risk analysis. Design Optimization of cost of the Pressure Vessel through MatLab and Simulation through ANSYS   by Elizabeth Amudhini STEPHEN, Chrsitu Nesam David, Joe Ajay Abstract: The objective functions used in Engineering Optimization are complex in nature with many variables and constraints. Conventional optimization tools sometimes fail to give global optima point. Very popular methods like Genetic Algorithm, Pattern Search, Simulated Annealing, and Gradient Search are useful methods to find global optima related to engineering problems. This paper attempts to use new non-traditional optimization algorithms which are used to find the minimum cost of designing a pressure vessel to obtain global optimum solutions. The cost, number of iterations and the total elapsed time to complete the problems are all compared using these ten non-traditional optimization methods. The validation is done through simulation using Ansys. Keywords: Pattern search ; Simulate annealing; Pattern search; GODLIKE; Cuckoo search; Firefly algorithm; Flower pollination; Ant lion optimizer; Gravitational search algorithm; Multi-verse optimizer; Simulation Ansys. Geolocation of electric bikes recharging stations: city of Quito study case   by Geovanna Villacreces, Javier Martinez Abstract: The aim of this research was to implement a Geographical Information System with multi-criteria decision making methods, to select the most feasible location to install electric bikes recharging stations in the city of Quito. For this purpose, the technique for the order of preference by similarity to ideal solution and weighted overlay have been used. In addition, the analytic hierarchy process method was developed to calculate the weights of the criteria. In addition, a standardization process was performed, which consists on establishing an overall performance index to evaluate the results. Finally, the Pearson correlation coefficient was used to analyze mutual correspondence between multi-criteria decision making methods. The results Pearson correlation coefficient indicate that the two selected multi-criteria decision making methods provided similar results. In this context, the methods analyzed covers which similar solutions and indicated that the multi-criteria decision making methods are a powerful tool to select ideal locations for electric bikes recharging stations. Keywords: Optimization location; e-bikes; geographic information systems (GIS); multi-criteria decision making (MCDM) methods. Analysis of Bulk Queue with Additional Optional Service, Vacation and Unreliable Server   by Charan Jeet Singh, Sandeep Kaur, Madhu Jain Abstract: The present investigation deals with the performance analysis of group input queueing system with unreliable server. The server is capable of rendering essential as well as -optional services. After getting essential service, the customer may choose any one of the available optional services if required. The server has choice either to avail the vacation for the short period after completion of the service or may continue to provide the service to other customers. The server may fail at any instant of the essential/optional service and undergoes for repair immediately. The queueing model is developed by introducing the supplementary variables corresponding to elapsed setup time, service time, repair time and vacation duration for obtaining the queue size distribution. The maximum entropy principle is employed to determine the approximate results of the system state probabilities and the waiting time of the customers in the queue. The numerical simulation and sensitivity analysis are performed by taking the numerical illustration to study the effect of system parameters on the various performance measures and cost function. Keywords: Bulk queue; Unreliable server; Repair; Essential service; Optional service; Vacation; Supplementary variable. Resource Portfolio Problem under Relaxed Resource Dedication Policy in Multi-mode Multi-project Scheduling   by Umut Beşikçi, Ümit Bilge, Gündüz Ulusoy Abstract: The most common approach in the multi-project scheduling literature considers resources as a common pool shared among all projects. However, different resource management strategies may be required for different problem environments. We present the Relaxed Resource Dedication (RRD) policy, which prevents the sharing of resources among projects but allows resource transfers when a project starts after the completion of another one. We treat the case where the available amounts of resources -namely, the capacities- are decision variables subject to a limited budget. This capacity planning problem, called the Resource Portfolio Problem, is investigated under the RRD policy employing both renewable and nonrenewable resources with multiple modes of usage. A mixed integer linear programming model to minimize total weighted tardiness is proposed. To obtain some benchmark solutions for this hard problem, the branch and cut procedure of ILOG CPLEX is modified by customized branching strategies, feasible solution generation schemes and valid inequalities. Keywords: Multi-mode Resource Constrained Multi-project Scheduling;Resource Dedication; Resource Portfolio Allocation; Branch and Cut. On Phase type Arithmetico-Geometric Process and its application to deteriorating systems with warranty   by Sarada Yedida, R. Shenbagam Abstract: This research article makes an attempt to introduce phase type arithmetico-geometric process and illustrate its applicability to a deteriorating system with fixed warranty. Properties, renewal function, second moment and variance of the underlying counting process are derived analytically and supplemented numerically in the case of three distributions: Exponential, Erlang distribution of order 3 and Coxian distribution of order 2. Sensitivity analysis and graphical illustrations are provided to highlight the effect of various cost parameters on the expected warranty cost by means of the Exponential and Erlang distribution of order 2. Keywords: phase type distribution; arithmetico-geometric process; fixed warranty. Parameter Estimation for Partially Observed Linear Stochastic System   by Chao Wei Abstract: This paper is concerned with the problem of parameter estimation for partially observed linear stochastic system. The state estimator is obtained by using continuous-time Kalman linear filtering theory. The likelihood function is given based on the innovation theorem and Girsanov theorem, the parameter estimator and error of estimation are derived. The strong consistency of the parameter estimator and the asymptotic normality of the error of estimation are proved by applying ergodic theorem, maximal inequality for martingale, Borel-Cantelli lemma and the central limit theorem for stochastic integrals. Keywords: Linear stochastic system; parameter estimation; state estimation; strong consistency; asymptotic normality. Analysis of Batch Arrival Bulk Service Queue with Additional Optional Service Multiple Vacation and Setup Time   by G. Ayyappan, T. Deepa Abstract: This paper studies an M[x]/G(a,b)/1 queueing system with additional optional service, multiple vacation and setup time. After completing the first service, the customers may opt for the second service with probability or leave the system with probability . After completing a bulk service, if the queue size is less than a', then the server leaves for a vacation of random length. When he returns from the vacation, if the queue length is still less than a', he leaves for another vacation and so on. This process continues until he finds at least a' customer in the queue. After a vacation, if the server finds at least a' customer waiting for service, he requires a setup time 'G' to start the service. After this setup he serves a batch of customers (). Using supplementary variable technique, the probability generating function of the queue size, expected queue length, expected waiting time, expected busy period and expected idle period are derived. Numerical illustrations are presented to visualize the effect of system parameters. Keywords: Batch arrival; Bulk service; Additional optional service; Multiple vacation; Setup time. Comments on the Polynomial formulation and heuristic based approach for the k-Travelling Repairman Problem   by Imdat Kara, Bahar Y. Kara Abstract: The paper Polynomial formulation and heuristic based approach for the k-Travelling Repairman Problem claims to present the first polynomial formulation for the k-travelling repairman problem (k-TRP). We first make some corrections on this formulation and we show that the first polynomial size formulation for k-TRP is the one proposed by Kara et al. (2008). Keywords: Repairman problem; k-Traveling Repairman problem; minimum latency problem; delivery man problem. Solution of Fuzzy Multi Objective Generalized Assignment Problem   by Supriya Kar, Aniruddha Samanta, Kajla Basu Abstract: In this paper, Multi Objective Generalized Assignment Problem (MOGAP) with fuzzy parameters has been solved using three different approaches. Here we consider three objective functions which are to be minimized. In the first approach, weighted sum method has been used and the problem is converted into a single objective one and then solved by Extremum Difference Method (EDM) to get the optimal assignment. In the second one, Modified Fuzzy Programming Technique (MFPT) has been used for the same problem. Application of linear and exponential membership functions give comparative results with the goal that the better alternative can be obtained. The third one describes Multi Objective Genetic Algorithm (MOGA) to find the solution surface and the Pareto Optimal front including the optimal assignment. The methods are demonstrated by a suitable numerical example. Keywords: FMOGAP; EDM; MFPT; MOGA. A Cryptosystem Based on Chaotic Maps and Factoring Problems   by Nedal Tahat, Eddie Esmail, Ashraf Aljammal Abstract: A cryptosystem allows a sender to send any confidential or private message using a receiver's public key and the receiver next confirms the integrity and validity of the received message using his own secret key. Cryptosystem algorithms can be categorized based on the type of security suppositions, for example discrete logarithm, factorization, and elliptic curve hard problems, which are all currently believed to be unsolvable in a reasonable time of period. Recently, cryptosystems based on chaotic maps have been proposed. Due to some subtle and close relationship between the properties of traditional cryptosystems and chaotic-based systems, the idea of using chaotic in cryptography has received a great deal of attention from many cryptographys researchers. Therefore, to enhance system security, we explore the implementation of a cryptosystem algorithm based on both cryptographic and chaotic system characteristics. We also provide security against known cryptographic attacks and discuss the performance analysis of the developed system. Keywords: Cryptography; Cryptosystem; Factorization; Chaotic maps. A Matheuristic Approach for the Split Delivery Vehicle Routing Problem: An Efficient Set Covering-Based Model with Guided Route Generation Schemes   by Nurul Huda Mohamed, Said Salhi, Gabor Nagy, Nurul Akmal Mohamed Abstract: The Split Delivery Vehicle Routing Problem (SDVRP) is a relaxed version of the classical VRP where customers can be visited more than once. The SDVRP is also applicable for problems where one or more of the customers require a demand larger than the vehicle capacity. Constructive heuristics adapted from the parallel savings and the sweep methods are first proposed to generate a set of solutions which is then used in the new and more efficient set covering-based formulation which we put forward. An effective repair mechanism to remedy any infeasibility due to the set covering problem is presented. A reduced set of promising routes is used in our model, instead of the original set of routes, proposing and using well defined reduction schemes. This set covering-based approach is tested on large data sets from the literature with encouraging results. In brief, 7 best solutions including ties are found among the 137 SDVRP instances. Keywords: split deliveries; vehicle routing; set covering; hybrid method; matheuristic. Exact Stationary Solution for a Fluid Queue Driven by an M/M/1 Queue with Disaster and Subsequent Repair   by Vijayashree K.V., Anjuka A Abstract: This paper deals with the stationary analysis of a fluid queueing model driven by an M/M/1 queue subject to disaster and subsequent repair. Further, arrivals are allowed to join the background queueing model during the period of repair at a slower rate as compared to the arrivals during regular busy period of the server. Such a model was analysed earlier by Sherif. I. Ammar cite{sherif}, however the model formulation and hence the main results are found to be incorrect. In this paper, the assumptions are suitably modified to ensure correctness, detailed mathematical analysis is carried out to find an explicit analytical expression for the buffer content distribution. The underlying system of differential difference equations that govern the process are solved using Laplace transform and generating function methodologies. Closed form expressions for the joint steady state probabilities of the state of the background queueing model and the content of the buffer are obtained in terms of modified Bessel function of the first kind. Keywords: Generating function;Laplace Transform;Steady State Probabilities;Buffer Content Distribution. Inventory model for deteriorating items with incremental holding cost under partial backlogging   by Sanjay Singh, Seema Sharma, Shiv Raj Pundir Abstract: The present paper deals with an inventory model for deteriorating items with dynamic demand. Shortages are allowed and partially backlogged. The demand has been considered as the function of inventory level during storage period and function of time during shortage period. Storage period is divided into n distinct time periods. In practice, longer storage period requires additional specialized equipment and facilities to keep the products away from deterioration. So, it is assumed that holding cost is increasing step function. The model has been discussed for n arbitrary distinct time periods of storage time and a numerical example has been solved for n = 1 and 2. The sensitivity analysis has been performed in order to examine the effect of various costs and parameters on optimal policy. Keywords: Inventory; Holding cost; Deterioration; Partial backlogging. A STUDY ON MX/G(a,b)/1 QUEUE WITH SERVER BREAKDOWN WITHOUT INTERRUPTION AND CONTROLLABLE ARRIVALS DURING MULTIPLE ADAPTIVE VACATIONS   by E. Rameshkumar Abstract: In this paper, a queueing system in which the server follows multiple adaptive vacations, server breakdown without interruption and closedown time with controllable arrival is considered. In a single server model, after completion of a bulk service, if there is no breakdown with probability (1- ѱ) and queue length is greater than or equal to a, then the bulk service continues, otherwise, the server performs closedown work. At the end of bulk service, if there is a breakdown occurs with probability (ѱ), then the server performs renovation process. After a renovation process, if the queue length is greater than or equal to a, then he performs bulk service otherwise the server is doing closedown work and the server avails a vacation of random length. At the end of a vacation, if the queue length is less than a, then the server takes at most M vacations successively. After M vacations, if the queue length is still less than a, then the server remains in the system till the queue length reaches a. However, the customers enter the service station with probability p (0 ≤ p ≤1) during multiple adaptive vacations. At a vacation, service and dormant period completion epoch, if the queue length ξ, is at least a customers, then the server serves a batch of min(ξ, b) customers, where b ≥ a. The Probability Generating Function (PGF) of queue size and performance measures are obtained and cost model is developed. The wide-range of algebraic results for the various particular cases is obtained. Keywords: multiple adaptive vacation; closedown times; server breakdown; renovation times; controllable arrival. Minimizing Vehicle Distribution Duration Considering Service Priority   by Dimitra Alexiou Abstract: A Vehicle Routing Problem (VRP) is dealt with, where a fleet of vehicles serve (distribution/pickup) a given subset of demand locations in an urban network. A service time priority degree is given to a subset of demand locations. The aim of this paper is to find the least possible overall service time for vehicles to all the demand locations and particularly those that have a high degree of priority. The problem is dealt with in the context of graph theory and a corresponding method is proposed. The paper incorporates a numerical example of the proposed method. Keywords: distribution; graph theory; vehicle routing; priority service; network. Modelling and Analysis of Two-Unit Hot Standby Database System with Random Inspection of Standby Unit   by Amit Manocha, Gulshan Taneja, Sukhvir Singh, Rahul Rishi Abstract: Stochastic model for a two-unit hot standby database system comprising of one operative (primary unit) and one hot standby unit has been developed. The primary unit acts as production unit which is synchronized with hot standby unit through online transfer of archive redo logs. Data being saved in the primary unit gets simultaneously stored in the hot standby unit. Different modes of failure of primary database have been considered. To avoid loss of data, random inspection of the standby unit is carried out by a database administrator (DBA) to see as to whether redo log files are created/updated in standby unit or not. The repair of the failed unit and creation/updation of redo log files are also done by the DBA. The system is analyzed using semi-Markov process and regenerative point technique. Mathematical expressions for various performance measures of the system have been obtained along with cost-benefit analysis of the system. Numerical analysis has been done to validate the derived results. Bounds for various parameters have also been obtained with regard to profitability of the system. Keywords: database system; hot standby; random inspection; semi-Markov process; regenerative point technique; stochastic modelling; measures of system effectiveness; cost-benefit analysis; profitability; bounds. A Hybrid Metaheuristics Approach for a Multi-Depot Vehicle Routing Problem with Simultaneous Deliveries and Pickups   by Sonu Rajak, P. Parthiban, R. Dhanalakshmi Abstract: Multi-Depot Vehicle Routing Problem with Simultaneous Deliveries and Pickups (MDVRPSDP) is a variant of classical Vehicle Routing Problem (VRP), which has often encountered in real-life scenarios of transportation logistics; Where, vehicles are required to simultaneously deliver the goods and also pick-up some goods from the customers. The current scenario importance of reverse logistics activities has increased. Therefore it is necessary to determine efficient and effective vehicle routes for simultaneous delivery and pick-up activities. MDVRPSDP, which is very well-known Non-deterministic Polynomialhard (NP-hard) and Combinatorial Optimization (CO) problem., which, requires metaheuristics to solve this type of problems. In this context, this article presents a hybrid metaheuristic which combines Simulated Annealing (SA), Ant Colony Optimization (ACO) and along with long-arc-broken removal heuristic approach for solving the MDVRPSDP. The preliminary results show that the proposed algorithm can provide good solutions. Keywords: K-means Clustering; Vehicle routing problem; Simulated annealing; Ant colony optimization; Long-arc-broken removal heuristic. A modified two-step method for solving interval linear programming problems   by Mehdi Allahdadi Abstract: In this paper, we propose a new method for solving interval linear programming (ILP) problems. For solving the ILP problems, two important items should be considered: feasibility (i.e., solutions satisfy all constraints) and optimality (i.e., solutions are optimal for at least a characteristic model). In some methods, a part of the solution space is infeasible (i.e., it violates any constraints) such as the best and worst cases method (BWC, proposed by Tong in 1994) and two-step method (TSM, proposed by Huang et al. in 1995). In some methods, the solution space is completely feasible, but is not completely optimal (i.e., some points of the solution space are not optimal) such as modified ILP method (MILP, proposed by Zhou et al. in 2009) and improved TSM (ITSM, proposed by Wang et al. in 2014). Firstly, basis stability for the ILP problems is reviewed. Secondly, the solving methods are analyzed from the point of view of the feasibility and optimality conditions. Later, a new method which modifies the TSM by using the basis stability approach is presented. This method gives a solution space that is not only completely feasible, but also completely optimal. Keywords: Basis stability; Feasibility; Interval linear programming; Optimality; TSM. Effects Of Product Reliability Dependent Demand In An EPQ Model Considering Partially Imperfect Production   by J.K. Dey Abstract: In this article, an economic production quantity (EPQ) model with partially imperfect production system has been considered where both perfect and imperfect quality items are produced and demand has been assumed as a function of selling price, reliability of the product and advertisement. In fact, every manufacturing sector wants to produce only perfect quality items to maximize his profit but due to long run process several kinds of problem like labor, machinery, technology etc. arise and therefore, system becomes out of control state and consequently it produces both perfect and imperfect quality items simultaneously. Perfect quality items are ready for sale but imperfect quality items are reworked at a cost to become perfect one. Reworking cost, reliability of the product and reliability parameter of the manufacturing system can be improved by introducing the time dependent development cost and also by improving the quality of the raw material used in the production system. Under such circumstances, a profit function has been developed and maximized by optimizing the reliability parameter of the manufacturing system, reliability of the product and duration of production. Finally, the model has been illustrated with some numerical examples exploring the sensitivity analysis with respect to some parameters to illustrate the feasibility of the model. Keywords: Inventory; Imperfect production; Production time; Reliability parameter; Product reliability. A new approach for solving fully fuzzy linear programming problem   by Sapan Das, Diptiranajan Behera, Tarni Mandal Abstract: This paper presents the limitations of Kumar and Kaur [1] for solving a FullyrnFuzzy Linear Programming (FFLP) problem. And accordingly to overcomernthese limitations a new method has been proposed by using the rankingrnfunction. We have considered a FFLP problem with mixed constraints whererndecision variables are represented by non-negative fuzzy numbers. Triangularrnconvex normalized fuzzy sets are considered for the analysis. To illustraternthe applicability and eciency of the proposed method various numericalrnexamples have been solved and obtained results are discussed. Keywords: Fully fuzzy linear programming; fuzzy optimal solution; triangularrnfuzzy numbers; ranking function. MAP/PH(1),PH(2)/2 Finite Retrial Inventory System with Service Facility, Multiple Vacations for Servers   by Suganya Chokkalingam, Sivakumar B Abstract: In this paper, we consider a retrial $(s, S)$ inventory system with multiple server vacations for two heterogeneous servers. We have assumed that the customers arrive according to a Markovian arrival process and two parallel servers who provide heterogeneous phase type services to customers. The lead times for the orders are assumed to have independent and identical exponential distributions. The vacation times of both servers are assumed to be independent and identically distributed exponential random variables. The arriving customer who finds both servers are busy or both servers are on vacation, joins an orbit of finite size. These orbiting customers retry for their demand after a random time, which is assumed to be exponential distribution. The joint probability distribution of the inventory level, the number of customers in the orbit and the server status is obtained in the steady state. Some important performance measures are obtained and the optimality of an expected total cost rate is shown through numerical illustration. Keywords: service facility; heterogeneous servers; multiple vacations; retrial customers. Generalized Linear Search Plan for a D-Dimensional Random Walk Target   by Mohamed El-hadidy Abstract: In this paper, we present a mathematical search model that studies the generalized linear search plan for detecting a d-dimensional random walk target. The target will be met one of n searchers where each searcher starts its motion from any point rather than the origin on n-disjoint real lines in ℝⁿ. Rather than, finding the conditions that show the finiteness of this search plan, we study the existence of the optimal search plan that minimizes the expected value of the first meeting time between one of the searchers and the target. Keywords: Linear search method; d-dimensional random walk; finite search plan;rnoptimal search plan; semi continuous mapping. A Boundary-point LP Solution Method and Its Application to Dense Linear Programs   by Chanaka Edirisinghe, William Ziemba Abstract: This paper presents a linear programming solution method that generates a sequence of boundary-points belonging to faces of the feasible polyhedron. The method is based on a steepest descent search by iteratively optimizing over a two-dimensional cross section of the polyhedron. It differs from extreme point algorithms such as the simplex method in that optimality is detected by identifying an optimal face of the polyhedron which is not necessarily an extreme point. It also differs from the polynomial-time methods such as the ellipsoid algorithm, or projective scaling method that avoids the boundary of the feasible polyhedron. Limited computational analysis with an experimental code of the method, EZLP, indicates that our method performs quite well in total solution time when the number of variables and the density of the constraint matrix increase. Keywords: Linear programming; steepest descent; orthogonal projections. An EOQ inventory model for deteriorating items with time-dependent deterioration rate, ramp-type demand rate and shortages   by Trailokyanath Singh, Pandit Jagatananda Mishra, Hadibandhu Pattanayak Abstract: This paper presents an economic order quantity (EOQ) model for deteriorating items having time proportional deterioration rate, time dependent ramp-type demand rate and shortages. Shortages are allowed to occur in the inventory system and completely backlogged. The ramp-type demand rate is deterministic and varies with time up to a certain point and then becomes constant. The three-parameter Weibull distribution rate indicates the change in deterioration rate with respect to time and takes into account of the items which are already deteriorated while receiving into an inventory system as well as items those might start deteriorating in future. To start with, the model is developed for shortages, but is also valid for the seasonal items and newly launched high tech products like computers, laptops, mobile phones and automobiles, etc. The purpose of this study is to develop an optimal policy, so that the average total cost is minimised by optimising the procurement time point. Furthermore, the solution procedure and the numerical example are provided to illustrate the proposed model. Finally, sensitivity analysis of the various parameters on optimal solution is carried out. Keywords: deteriorating items; economic order quantity; EOQ; ramp-type demand; shortages; time-dependent deterioration rate.DOI: 10.1504/IJMOR.2018.10008489  Bias-correction in DEA efficiency scores using simulated beta samples: an alternative view of bootstrapping in DEA   by Parakramaweera Sunil Dharmapala Abstract: Bootstrapping of DEA efficiency scores came into being under the criticism that DEA input/output data may contain random error, and as a result the efficient frontier may be warped by statistical noise. Since the publication of the seminal paper by Simar and Wilson (1998), several researchers have carried out bootstrapping the DEA frontier, re-computing the efficiency scores after correcting the biases and developing confidence intervals for bias-corrected scores. We view bias-correction in DEA efficiency scores from a different perspective by randomising the efficiency scores that follow underlying beta distributions. In a step-by-step process, using the simulated beta samples, we show how to correct the biases of individual scores, construct confidence intervals for the bias-corrected mean scores and derive some statistical results for the estimators used in the process. Finally, we demonstrate this method by applying it to a set of banks. Keywords: data envelopment analysis; DEA; assurance regions; AR; order statistics; beta distribution; bias-correction; simulation.DOI: 10.1504/IJMOR.2018.10011877  Duality for non-differentiable multi-objective semi-infinite programming for higher order invex functions   by Promila Kumar, Jyoti Abstract: This paper deals with non-differentiable multi-objective semi-infinite programming problem. It is a problem of simultaneous minimisation of finitely many scalar valued functions subject to an arbitrary (possibly infinite) set of constraints. Non-differentiability enters, due to the square root of a quadratic form which appears in the objective functional. Concept of efficiency of order m has been extended to the above stated problem. In order to study this new solution concept, the notion of ρ-invexity of order m is also proposed which is utilised to establish sufficient optimality conditions for the non-differentiable multi-objective semi-infinite programming problem. Mond-Weir type of dual is proposed for which weak, strong and strict converse duality theorems are established. Keywords: optimality; duality; semi-infinite programming; non-differentiable programming; ρ-invexity of order m.DOI: 10.1504/IJMOR.2018.10011878  Testing the fractional integration parameter revisited: a fractional Dickey-Fuller test   by Ahmed Bensalma Abstract: The main scope of this paper is to provide how to extend the standard Dickey-Fuller test (1979) by taking into account the fractional case. Such extension has already been discussed by Dolado et al. (2002). In this paper, we show, in the first step, that the fractional Dickey-Fuller test proposed by Dolado et al. is useless in practice. In the second step we show how to extend adequately the standard framework of Dickey-Fuller test to take into account the fractional case by using the usual test statistics and the usual asymptotic distributions (Phillips, 1987). Such extension can be very useful in practice. Through a simulation study, we show the good performance of the test in terms of size and power. Finally, in order to show how to use the new testing procedure, the test is applied to the well-known Nelson and Plosser data. Keywords: fractional integration; fractional unit root; Dickey-Fuller; unit root test; fractional Dickey-Fuller test.DOI: 10.1504/IJMOR.2018.10011879  Approximating service-time distributions by phase-type distributions in single-server queues: a strong stability approach   by Yasmina Djabali, Boualem Rabta, Djamil Aïssani Abstract: Phase-type queueing systems are used to approximate queues with general service-time distributions. In this work, we provide by means of the strong stability method, the mathematical justification of the approximation method by phase-type distributions that is already used in several works. We consider the approximation of M/G/1 queueing system by a M/PH/1 system, where PH refers to a hyperexponential H2 or a hypoexponential HOE2 distribution depending on the value of the coefficient of variation of the original distribution. We prove the robustness of the underlying Markov chain in each case and estimate an upper bound of the deviation of the stationary vector, resulting from the perturbation of the service-time distribution. We provide numerical examples and compare the perturbation bounds obtained in this paper with the estimates of the real deviation of the stationary vector obtained by simulation. Keywords: queueing systems; phase-type distributions; perturbation; sensitivity analysis; strong stability; quantitative estimates; perturbation bounds.DOI: 10.1504/IJMOR.2018.10005095  On logarithmic fixed-charge transportation problem   by Debiprasad Acharya, Manjusri Basu, Atanu Das Abstract: The fixed-charge transportation problem (FCTP) is still a challenging problem in the field of mathematical programming. In this paper, we consider fixed-charge transportation problem with logarithmic objective function. In the absence of any suitable algorithm to obtain the solution of this type of nonlinear transportation problem, we discuss the advantage of polynomial approximation. There exists a major difference between the two problems that the variables in the polynomial transportation problem have no upper bound but in the logarithmic transportation problem they are bounded. Using the expansion of logarithm we show the resemblance between the structural behaviour of linear and fixed-charge transportation problems. We illustrate a numerical example in support of the developed method. Keywords: transportation problem; fixed cost; logarithm modelling.DOI: 10.1504/IJMOR.2018.10011880  A mathematical investigation of Rao diversity coefficients among the communities according to species morphometry and species taxonomy   by Kenneth Barroga Abstract: Although Rao diversity coefficient (Rao DIVC) is sensitive to the differences among species, a gap still remains in investigating how the communities are affected when the dissimilarity among the species are in terms of its morphometry and taxonomy. I studied the effect of using species taxonomic classification and species morphometrical traits in the computation of Rao DIVC in assessing diversity of ecological communities. I utlised the Mahalanobis distance for measuring the variation of species morphometry. As for species taxonomy, I employed the method by Warwick and Clarke (1995). When the calculated Rao DIVCs, double principal coordinate analysis and co-inertia analysis outputs were compared, I discovered that Rao DIVCs accounting species morphometry (Rsm) and species taxonomy (Rst) yielded different results and interpretation. Rsm clearly showed more the variation among communities but contributed less in the analysis, whereas Rst showed more clearly the clusters between the communities which make the interpretation easier. Keywords: double principal coordinate analysis; DPCoA; Mahalanobis distance; Rao diversity coefficient; Rao DIVC; co-inertia analysis; COIA.DOI: 10.1504/IJMOR.2018.10011881