Forthcoming articles


International Journal of Mathematics in Operational Research


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International Journal of Mathematics in Operational Research (65 papers in press)


Regular Issues


  • On Optimization over the Integer Efficient Set in Fuzzy Linear Multicriteria Programming   Order a copy of this article
    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   Order a copy of this article
    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.

    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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.
    DOI: 10.1504/IJMOR.2018.10014392
  • A model for supplier evaluation and selection based on integrated interval-valued intuitionistic fuzzy AHP-TOPSIS approach   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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.   Order a copy of this article
    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.   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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.   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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.   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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.

    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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 eciency 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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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.

  • The Efficiency of Greedy Best Response Algorithm in Road Traffic Assignment   Order a copy of this article
    by Lahna Idres, Mohammed Said Radjef 
    Abstract: In this work, we investigate the problem of the integer road traffic assignment. So, we model the interaction among the road users sharing the same origin-destination pair, as a symmetric network congestion game. We focus on Rosenthals results to guarantee the existence of a Pure Nash Equilibrium (PNE). Then, we study the behaviour of an algorithm based on Greedy Best Response (GBR) in finding PNE. In previous studies, the efficiency of GBR to compute a PNE of a symmetric network congestion game in series-parallel networks is proved. In ourwork, another approach is used to demonstrate its efficiency in more general networks. It is shown that the non-series parallel networks can be classed into two types. The conditions that make GBR succeeds for each type is then drawn. The advantage of GBR-algorithm is that provides a better approximation of the equilibrate assignment, since it is integer.
    Keywords: Road traffic assignment; Congestion Game; Nash Equilibrium; GBR-Algorithm.

  • A New Ranking Technique On Heptagonal Fuzzy Numbers to Solve Fuzzy Transportation Problem   Order a copy of this article
    by Malini Ramki 
    Abstract: In this work a general fuzzy transportation problem model is discussed and proposed a new ranking procedure to the heptagonal fuzzy numbers using which convert any fuzzy valued transportation problem to a crisp valued transportation problem which then could be solved using the MODI method. The proposed method serves as an efficient method in ranking Heptagonal fuzzy numbers which is illustrated through a numerical example. The purpose of this paper is to give a new ranking index to rank fuzzy numbers effectively. Fuzzy numbers cannot be easily ordered as ordinary real numbers. Several proposals have addressed this problem, each with some drawbacks and limitations. This paper renounces to the idea of finding a universal ordering method for fuzzy numbers.
    Keywords: Heptagonal Fuzzy numbers; Fuzzy Transportation Problem.

  • Using a multi-criteria decision making approach to select the optimal freeway rout (Case Study: Isfahan Shiraz Freeway)   Order a copy of this article
    by Jalil Heidary Dahooie 
    Abstract: Road construction problems are one of the important factors in countries. The reason for this is the effective role of road transportation in economic development. Considering the high cost of constructing and repairing freeways, principled and optimal design is one of the most important steps in creating a transport infrastructure, especially freeways. On the other hand, the effects of multiple variables and parameters on the decision making process to determine the optimal route have made this choice a difficult and specialized issue for decision-makers. In this regard, this paper aims to select the optimal variant route for Isfahan Shiraz freeway using multi- attribute decision-making approaches. For this purpose, in the first stage, by reviewing the literature and organizing a panel of experts, the indices for evaluation of the optimal variant route have been extracted. In the following, in order to weight and select the optimal variant route, the extended dynamic fuzzy GRA method is used. The results show that road longevity, views of the NGOs, route integrity and ease of tracking are identified as the highest-weighted criteria in the prioritization of the route variant. To evaluate the validity of the results of the GRA method, the problem is examined by using the, COPRAS-IVIF, ARAS-IVTF, WASPAS-IVIF,TOPSIS-IVIF and Multimoora-IVIF methods. Also, Route 3 that takes priority over others is also chosen, in practice, as the main basis for the work.
    Keywords: Variant route Selection; Freeway; Multi Attribute Decision Making (MADM); dynamic fuzzy GRA.

  • On differentiable harmonic univex fuzzy mappings and its applications to fuzzy mathematical programming problem   Order a copy of this article
    by Minakshi Parida, Sunita Chand 
    Abstract: In this paper, harmonic preunivex (H-preunivex) and harmonic preunicave (H-preunicave) fuzzy mappings have been introduced and several interesting results have been obtained related to generalized convexity. By using the concept of differentiability with H-preunivex and H-preunicave fuzzy mappings, harmonic univex (H-univex) and harmonic unicave (Hunicave) fuzzy mappings have been obtained respectively. Furthermore, H-univex and pseudo H-univex fuzzy mappings have been applied to study the sufficient optimality conditions and the duality results for Harmonic univex fuzzy programming problem (HUFP). Moreover, KKT conditions for the HUFP have been studied by using the H-univex fuzzy mappings. Suitable examples have been given to illustrate the results.
    Keywords: Fuzzy optimization; H-preunivex; H-preunicave; H-univex; H-unicave; Fuzzy mappings; Sufficient optimality conditions; Duality results.

  • Solid Transportation Problem under Fully Fuzzy Environment   Order a copy of this article
    by Abhijit Baidya, Uttam Kumar Bera 
    Abstract: Transportation policy seeks to improve agency freight and cargo management and enhance sustainable, efficient and effective transportation operations. In this paper, the profit maximization solid transportation problem under fully fuzzy environment is formulated. In this model formulation the unit transportation costs, purchasing costs, loading costs, unloading costs, selling prices, fixed charges, availabilities, demands, conveyance capacities, vehicle weight and volume capacities, desired total budget are considered as fuzzy in nature. When items are transported from sources to destinations, then due to bad road condition, hilly region etc. few items should be damaged. The unknown quantities those are transported from source to destination with different mode of conveyances are also considered as fuzzy. Also, an additional new constraint on the complete budget at each destination is imposed. Five new approaches are proposed to defuzzify the fully fuzzy model. The nearest interval approximation is used to convert the fully fuzzy model into its equivalent interval form. The interactive fuzzy satisfying technique and different interval approaches are used to determine the crisp equivalent of the objective function and constraints of the proposed model. The reduced deterministic model was solved using generalized reduced gradient techniques (GRG technique). A numerical example is provided to illustrate the model and methodology and finally, the obtained results are compared.
    Keywords: Fully fuzzy solid transportation problem; complete budget constraint; interval approaches; nearest interval approximation; interactive fuzzy satisfying technique.