International Journal of Mathematics in Operational Research (37 papers in press)
Material Selection through of Multi-Criteria Decisions Methods (MCDM) applied to a helical gearbox
by Javier Martinez, Julio Leguisamo, Chrytopher Vaca
Abstract: The aim of this study was to select the best material using the multi-criteria decision methods, obtaining the best results and the respective choice of material, optimising surface fatigue and increasing its resistance to wear applied to a gearbox. For which the multi-criteria decision methods were done to obtain an order or ranking of the set of alternatives. To obtain this ranking, the set of alternatives must be well defined, just as the criteria must be well determined. After using the multi-criteria, it was determined that the material chosen according to the ranking and is the third alternative that has relevant characteristics such as elastic limit, tensile strength and good thermal capacity. The entropy method applied to the weights helps avoid the subjectivity of the designer and make it conform to real parameters. According to the methods COPRAS, TOPSIS, PROMETHEE and VIKOR; the best material is the AISI 4140, due to the best mechanical and thermal properties. On the basis of the numerical results, it can be concluded that the proposed methods can deal with the problems of material selection with the dependence of criteria.
Keywords: Multi-criteria Methodology (MCDM). Material selection; weighting and classification factors; criteria dependence; helical gear.
A prospective multi attribute decision making based reliability allocation method using fuzzy linguistic approach and minimum effort function
by ANIRUDDHA SAMANTA, KAJLA BASU
Abstract: Reliability allocation has a great importance in the early design stage of a system. The result of this allocation directly affects the product's quality and robustness of the system. There are several reliability allocation techniques to allocate the target reliability. But these methods have several shortcomings. To overcome these shortcomings, a new allocation method considering future limiters depending upon the concept of prospective multi-attribute decision making (PMADM) has been proposed here. Also the fuzzy linguistic term sets, minimal variance OWGA weights and experts degree of orness have been combined to perform a more practical reliability allocation. Ultimately to recognise the nonlinear phenomenon for reliability and the element's potential for improvement, the proposed method takes an initiative to improve the initial target reliability using reliability growth effort function. An example of transceiver system is considered here to illustrate the efficiency and flexibility of the proposed approach to allocate the system reliability.
Keywords: Prospective multi attribute decision making (PMADM); Ordered Weighted Geometric Averaging Operator (OWGA); Reliability Allocation; Proportionality factor; Reliability growth effort function.
On the numerical solution of an inverse spectral problem with a singular potential
by Seyfollah Mosazadeh, Abdol Ali A. Neamaty, Maedeh Bagherzadeh
Abstract: This paper deals with the unique solvability of the inverse problem for second-order differential operators having a singular potential. It is shown that the coefficients of the differential operator can be determined from the spectral data. Then, we construct the theoretical bases and provide a numerical algorithm for solving the inverse problem of spectral analysis and finding the potential function. Finally, some numerical examples are considered to demonstrate the applicability of the algorithm.
Keywords: Inverse spectral problem?; ?singular potential?; ?spectral function?; ?numerical solution.
Maximal covering salesman problems with average traveling cost constrains
by Mohammad Mohammadi, Mostafa Dastmardi, Bahman Naderi
Abstract: We study the maximal covering salesman problem with the average travelling cost constraints (MCSPATCC) where the objective is to find a subset of customers with their tour so that the number of covered demand points is maximised. This paper presents a mathematical model to select a profitable subset of demand points to be covered. We also propose an effective heuristic algorithm with three elimination methods to remove unprofitable demand points. The proposed algorithm is based on the genetic algorithm (GA) hybridised with different local search strategies to solve this problem. Parameters of the algorithm are analysed for calibration by the Taguchi method. Extensive computational experiments, on a set of standard problems, have indicated the effectiveness of our algorithm.
Keywords: Covering salesman problem; maximum covering; genetic algorithm.
Multifactor modelling in asset management
by Tolulope Latunde
Abstract: A multifactor model of capital asset management is formulated from the perspective of investors, under the assumptions of hyperbolic absolute risk aversion, and employing the basic skills of mathematical modelling. The solution to a special case of problems in asset management is sought by formulating a continuous-time utility portfolio model satisfying some uncertainty criteria where investment is continuous, investors do not possess enough power to determine price and investors can borrow money for a given period of time at a particular interest rate. Thereafter, the model is solved analytical and the optimal values of control variables are derived using optimality conditions.
Keywords: Multifactor; modelling; optimal control; optimality; uncertainty theory; capital asset management.
Hybrid Adaptive Memory Programming to optimize the multi-commodity many to many vehicle routing problem
by Jalel Euchi
Abstract: With the quick development of urban transport networks, the multi-commodity many to many variants of pickup and delivery vehicle routing problem (PDVRP) becomes more and more important. A critical issue is to solve this variant through optimisation techniques. We address a new variant of the multi-commodity many to many PDVRP (m-MMPDVRP). The m-MMPDVRP problem is when one or multi-commodities are collected from many sites to be transported to many destinations. In this problem, we assumed that all commodities share the same vehicle capacity during transportation. All vehicles are non-homogeneous and each commodity has to be stored separately during transportation. A new model is developed, based on multiple commodities. The objective is to generate an optimal path plan, ensuring that the demand for heterogeneous commodities can be satisfied by an arbitrary set of suppliers. We propose an adaptive memory-programming (AMP) technique based on the Scatter Search (SS). The solution quality of the suggested methodology is assessed and compared with the result presented in the previous works for the same instances. Numerical experimentation shows the distinction of the AMP with Scatter Search compared with other existing techniques; and establishing an efficient metaheuristic method for the m-MMPDVRP problem.
Keywords: Pick up and delivery;routing; adaptive memory; scatter search;many to many.
Chaos in a Fractional-Order Financial System
by Amirahmad Khajehnasiri, M. Afshar, Reza Ezzati
Abstract: In this paper, a fractional order financial system is proposed, and the complex dynamical behaviours of such a system are discussed by numerical simulations. We present a method for solving chaos in fractional-order financial system. Also, we derive the Hat function operational matrix of the fractional order integration and use it to solve the fractional-order financial system. To demonstrate the validity of the presented developments, three numerical simulations are given to verify the effectiveness of the proposed method.
Keywords: Chaos?; ?Hat functions?; ?Fractional calculus?; ?Block pulse function?; ?Operational matrix?; ?State space.
Transient behaviour of an M/Ek/1 queue with vacations, balking and control of admission during vacations
by A. Azhagappan, T. Deepa
Abstract: This paper studies the transient behaviour of an M/Ek/1 queueing model with single and multiple vacations, balking and control of admission during vacations. An arriving customer undergoes k exponential phases of service before leaving the system. Whenever the system becomes empty, the server starts vacation (single or multiple). All the arriving customers are not allowed to join the queue during vacations. That is, they are either permitted to join the queue or rejected. During the vacation period, the permitted arrivals may either join the queue or balk. Using the method of generating function, the transient system size probabilities are derived for the proposed model in terms of generalised modified Bessel function of the second kind. The system performance measures such as average and variance of system size, probability of system empty and server idle are also obtained. Numerical illustrations are presented to analyse the influence of the system parameters.
Keywords: The M/Ek/1 queue; Single and multiple vacations; Balking and control of admission during vacations; Generalized modified Bessel function; Time-dependent probabilities.
Manufacturing Procurement Cost Allocation as Dominant Factor under Limited Available Manufacturing Equipment Budget
by OLUWASEUN O. OJO, Basil O. Akinnuli, PETER K. FARAYIBI
Abstract: A production engineer as a decision maker has to setup a plan capable of meeting the needs of the customers and increasing company productivity and profitability knowing the challenges of a limited available budget for the equipment procurement. This work identified the strategic decisions required for machinery budget allocation which are: machines, accessories, spare-parts and miscellaneous costs for procurement. Strategic decisions data collected were statistically analysed pre-use for forecasting the allotted required amount for their procurement based on the limited available budget using conventional related models and; optimised the scenario using goal programming model because of its multi-criteria nature of problem. Using a developed software package Java programming language for its implementation. The predicted costs based on the available budget of N400,000,000 for the current year were: N119,975,000.00, N127,968,000.00, N134,965,000.00 and N33,491,500.00 while their goal targets were: N 119,975,000, N127,968,000, N577,655,000 and N1.1427
Keywords: cost allocation; manufacturing equipment; procurement; strategic decisions; optimisation; limited budget; goal programming; predicted costs; forecast; scenario.
Order Six Generalized Hybrid Block Method for the Solution of Third Order Initial Value Problems
by Raft Abdelrahim
Abstract: In this article, a generalise two step method with two off step points that gives better approximate solution for third order IVP of ODEs is examined. Method of collocation and interpolation is used where approximated power series is considered as basis function. The stability properties of the method is established and the method is applied to variety of test problems. The results generated proved the superiority of the new method over existing methods in terms of error.
Keywords: Hybrid method; Block method; Third order differential equation; power series; Two off step points.
Desert Sparrow Optimization Algorithm for Permutation Flowshop Scheduling Problems
by Sameer Sharma, Meenakshi Sharma, Dr Manisha Sharma
Abstract: Permutation flowshop scheduling problems (PFSSP) with an objective to minimise the total elapsed time (makespan), are typically NP-hard in nature. Many heuristics and metaheuristics have been designed and developed to optimise makespan in flowshop scheduling environment. Better quality of metaheuristic approach depends on solution obtained by heuristic. In this paper, a nature inspired heuristic based on the biological characteristics of desert sparrow is proposed to optimise makespan in flowshop environment. The cooperative task allocation nature of desert sparrow is the basis to find the best initial feasible solution. Computational analysis depicts that proposed heuristic gives significantly better results than referred heuristics for the considered problem.
Keywords: Flowshop scheduling; Desert sparrow optimization; constructive heuristic; Makespan.
Intelligent sensor impact on predictive maintenance program costs
by Maurizio Faccio, Soukaina Sadiki, M. Ramadany, S. Boutahari, D. Amgouz
Abstract: In this work, we develop a simulation study based on economic optimisation to compare the economical impact of two maintenance policies, traditional failure maintenance policy with predictive maintenance policy that utilises intelligent network sensor information. The simulation study established in this work compare tow maintenance strategies: predictive maintenance and failure-based maintenance, in order to compare when it is less expensive to maintain the equipment before it breaks down using intelligent network sensors than to replace it after its breakdown, to sum up, if it is profitable to implement this new technology. Also with this proposed approach, the decision maker could be in the position to decide on a most appropriate economical framework for the optimum cost, based on the comparison between breakdown cost and the cost of sensors. The method can be used by companies to make a decision when considering implementing remote monitoring. To illustrate the use and the advantages of the proposed maintenance policy, a numerical example is investigated.
Keywords: Intelligent network sensors; condition based predictive maintenance; Reliability; cost optimization.
Keynesian Resurgence: Financial Stimulus And Contingent Claims Modelling
by Sovan Mitra, Ephraim Clarke, Octave Jokung
Abstract: Since the commencement of the Global Financial Crisis, a worldwide resurgence in applying Keynesian modelling has occurred, and has been cited as a major factor in averting a worldwide economic depression. A key aspect of Keynesian modelling is that governments gain contingent claims on firms in exchange for financial stimulus. However, there exist few mathematical finance models examining Keynesian modelling, stimulus modelling and the valuation of such government contingent claims. In this paper we provide a new mathematical finance framework for modelling firms and financial stimulus under a Keynesian framework; we apply a stochastic differential equation model, rather than the standard time series models. Our model incorporates fundamental concepts of Keynesian modelling and Keynesian stimulus, which is a new characteristic to current financial models. We model the government's contingent claim on the firm as a real call option, and derive a closed form solution for the value of this option which takes into account firm stimulus. We also derive a solution for the minimum firm value required to exercise the option. We conduct numerical experiments for different firm equilibrium values, firm values, economic cycles and analyse the impact on option and stimulus values.
Keywords: financial crisis; stimulus; options; contingent claims; Keynes; Geometric Ornstein-Uhlenbeck.
Stability of the Optimal Distribution for the Searching Effort to find the Markovian Targets by using Fuzzy Maximum Discounted Effort Reward Search: Case of the Cooperative Search Techniques
by Alaa Alzulaibani
Abstract: The aim of this paper is to study the stability of the optimal distribution for the searching effort to detect two related Markovian targets by using multiple cooperative searchers. This effort, at each fixed number of time intervals, is a random variable with a normal distribution. The optimal solution (which makes the discounted effort reward with fuzzy parameter maximum) is obtained from solving a fuzzy stochastic optimisation problem. Rather than presenting an algorithm that shows the stability of the optimal distribution of an effort, we study more interesting special cases of located spider landmines and unrestricted effort. Two illustrative examples of Markovian and randomly located spider landmines are discussed.
Keywords: probability theory; stability of the optimal search; fuzzy stochastic optimisation problem; Markovian targets.
The Supplier-retailer Optimal Replenishment Decisions Under a Two-level Trade Credit Model with Shortage for Deteriorating Items
by Zohreh Molamohamadi, N. Ismail, Zulkiffli Leman, Norzima Zulkifli, Anvarjon Ahmedov
Abstract: This paper establishes an integrated inventory model of a supplier and a manufacturer under a two-level trade credit contract. The manufacturer's inventory model follows the economic production quantity model and the produced items follow exponentially deterioration rate and price-dependent demand. Shortages are allowed for the manufacturer and are completely backlogged to the next period. Traditional inventory system and one-level trade credit are also concluded as special cases of the developed two-level trade credit model and the supply chain performance under these three policies are compared. The formulated models aim at helping the supply chain decision makers to determine the best delay strategy and find the optimal values for replenishment policy and the manufacturer's selling price in order to maximise the supply chain total net profit. The results have been then validated with a numerical example and the effect of various parameters on the optimal solution is finally studied by performing sensitivity analysis.
Keywords: inventory management; trade credit; permissible delay in payment; deterioration; backorder.
AN EPQ MODEL FOR DELAYED DETERIORATING ITEMS WITH RELIABILITY CONSIDERATION AND QUADRATIC DEMAND
by Dari Sani, Sani Babangida
Abstract: In this paper, an EPQ model for delayed deteriorating items is developed where the demand before deterioration sets in is assumed to be different from that after deterioration sets in. There are three stages for the inventory system as follows: 1) the production build-up stage (0 ? t ? L1); 2) stage before deterioration sets in (L1 ? t ? L2); 3) stage after deterioration sets in (L3 ? t ? L). It is also assumed that the unit cost of production is directly proportional to the process reliability and inversely proportional to the rate of demand and shortages are not allowed. A numerical example is given to illustrate the developed model and sensitivity analysis carried out on the example to see the effect of parameter changes.
Keywords: EPQ; Quadratic Demand; Reliability; Delayed Deterioration.
Modelling and analysis of a discrete-time GI^X/Geom/1/K queue with N threshold policy
by Karabi Sikdar
Abstract: This paper presents modelling and analysis of a discrete-time GIX/Geom/1/K queueing system (where K is the capacity of the system) with N threshold policy for the early arrival system (EAS). The server is turned off when the system is vacant and checks the queue length every time for an arrival of a batch. As soon as the queue length reaches a pre-specified value N(1 ? N ? K), the server turns on and serves continuously until the system becomes vacant. We obtain the steady state system length distributions at pre-arrival, arbitrary and outside observer's epochs using the combination of the supplementary and the imbedded markov chain techniques. Various performance characteristics like average number of users in the queue/system, blocking probabilities of users (first-, an arbitrary- and last-user of an arriving batch) and average waiting time are obtained analytically with numerical analysis. The numerical analysis data are presented in graphical format for blocking probabilities under different buffer size values.
Keywords: Batch arrival; Discrete-time queue; Finite-buffer; Threshold policy.
Batch Arrival Poisson Queue with Breakdown and Repairs
by Sundar Rajan Balasubramanian, Ganesan V, Rita Samikannu
Abstract: This paper considers a single server bulk arrival queuing system in which the services performed in two different stages. The server must provide the two services simultaneously. The server may opt for vacation at the end of each second stage service of the unit. The system is subjected to repair due to random breakdown and the system demands two types of repairs. When the service of any unit interrupted due to breakdown, it goes back to the head of the queue. The processes used in this system are distributed according to some designed statistical distributions. The expected number of units in the system has been obtained.
Keywords: Bulk arrival; Breakdown; vacation; repairs; mean queue size.
A multi-objective model to allocate multiple facilities at proposed locations in the multi-floor organization, using an improved genetic algorithm. Case Study: Isfahan Governorate
by Mehdi Safaei, Meisam Nassrollahi
Abstract: The impressive role in the proper design of facility layout on productivity cannot be simply overlooked. So far, many models of the genetic algorithm have been introduced to solve such problems. The common approach of all these methods is to eliminate unacceptable answers. But given that unacceptable responses also have positive characteristics that can have a positive effect on next-generation fitness, this positive character can be exploited. In the multi-objective and multi-scale model presented, graded punishment is intended for such solutions, but will benefit from their positive features. Finally, the effectiveness of this method was evaluated by studying a case study. The results confirm the model's ability to improve the existing conditions. The main application of this model, in multi-layered organizations, is the allocation of several facilities to one location, depending on its capacity. It is also used to design workshop facility layouts.
Keywords: Genetic Algorithm; Basic Layout Model; Fitness Function; Objective Function; Mutation; Crossover.
Hermite-Hadamard and Fejer type integral inequalities for Harmonic Convex (Concave) fuzzy mappings
by MINAKSHI PARIDA, Sunita Chand
Abstract: In this paper the Hermite Hadamard and Fejer type integral inequalities for harmonic convex (H-convex) and harmonic concave (H-concave) fuzzy mappings have been studied by using ranking value function. Furthermore, Hermite Hadamard inequality via Sugeno fuzzy integral has been given for H-concave fuzzy mappings. Moreover, the upper bound of the Sugeno fuzzy integral has been obtained for the H-concave fuzzy mapping by using ranking value function and the results have been justified with suitable examples.
Keywords: Fuzzy numbers; H-convex (H-concave) fuzzy mappings; Hermite-Hadamard inequality; Fejer type inequality; Sugeno fuzzy integral.
Solving generalized intuitionistic fuzzy 1-median problem on tree networks with a new ranking method
by Fahimeh Baroughi, Akram Soltanpour, Behrooz Alizadeh
Abstract: The 1-median location problem on a tree T is to find a vertex v* on T that minimise the sum of the weighted distances from all vertices to the vertex v*. In this paper, we investigate the 1-median location problem on tree networks with generalised intuitionistic fuzzy weights. We first resent a new method for comparing generalised fuzzy numbers and then develop it for generalised intuitionistic fuzzy numbers. The proposed method for ranking generalised fuzzy numbers can also effectively rank real numbers. These methods are able to rank the generalised trapezoidal fuzzy numbers and generalised trapezoidal intuitionistic fuzzy numbers in linear times. Then numerical examples are given to compare the proposed methods with other existing methods. Finally, we apply our ranking method to solve the 1-median location problem on a tree network with generalised trapezoidal intuitionistic fuzzy vertex weights and then we show that the problem is solvable in linear time.
Keywords: Ranking function; Generalized fuzzy numbers; Generalized intuitionistic fuzzy numbers; Location problem; 1-median.
MODIFIED VACATION POLICY FOR UNRELIABLE RETRIAL QUEUES WITH DELAYED REPAIR
by Shweta Upadhyaya, Chetna Kushwaha
Abstract: This paper deals with the analysis of MX/G/1 retrial queue with impatient customers, modified vacation policy and Bernoulli feedback. When the incoming customer finds the server busy, on vacation or in the state of breakdown, he joins the virtual queue called retrial orbit, otherwise the service is provided to the customer which is at the head of the queue. The service is provided in phases where first is compulsory service and remaining services are optional. When the system becomes empty, server leaves for the vacation of arbitrary length and can take at most J number of vacations. When server comes back from the vacation and finds at least one customer in the queue, he starts providing services to the customer. Supplementary variable technique is used to derive the system size distribution.
Keywords: MX/G/1 retrial queue; multi-optional services; server breakdown; delayed repair; modified vacation policy; system size.
NEW FAMILY OF ESTIMATORS FOR POPULATION MEAN USING REGRESSION-CUM-RATIO EXPONENTIAL ESTIMATORS
by Dinesh K. Sharma, S.K. Yadav, Cem Kadilar
Abstract: Sampling is inevitable whenever the population is vast, and one estimates the population mean rather than to calculate it. This article improves the estimation for the population mean of the primary variable through a new ratio-cum-exponential ratio family of estimators. The estimation properties, mainly bias and mean squared errors (MSE), are studied up to an approximation of order one for the suggested family. We make a comparison of the suggested family of estimators with the existing competing estimators of the population mean of the main variable in theory. In this way, the efficiency conditions for the suggested family are obtained. These conditions are satisfied in practice using the numerical example.
Keywords: Main variable; supplementary variable; ratio-cum-exponential estimators; bias; MSE; efficiency.
Towards a Performance Analysis of Composite Web Services using Petri Nets.
by BERNINE Nassima, Nacer Hassina, Djamil Aissani, Hassan Alla
Abstract: The proliferation of web services-based applications, collaboration, interoperability between companies, and more generally demands of web services over the internet are major challenges in the design of performance evaluation in web services discovery and composition. It is required for the web services providers to analyse the performance related to the satisfaction of clients requests. This paper presents an analytical model based on Petri Nets, for evaluating the performance of a web services system where requests and web services follow an exponential server. The arrival process of the users requests and web services follows a Poisson distribution. When the web services finish the service, they join the queue. This model follows a Poisson distribution, it is based on Petri Nets. We use an analytical method for solving the model. Furthermore, we compute the system's response time, and the average number of clients in the system in terms of the arrival rate of clients requests. We find the limit number of clients in the system from which it begins to be saturated.
Keywords: Performances analysis; Requests; Web services composition; Petri Net.
Optimal 3-Dimensional Search Model to Find the Underwater Randomly Hidden Target
by Mohamed El-hadidy, Mohamed El-Fakharany
Abstract: The searcher's path for finding a 3-dimensional underwater randomly located target like a black box for the air plan crash is studied. The searcher moves along slinky-turn-spiral curve and starts its motion from a known point (X?,Y?,Z?). We focus on the geometry features such as curvature and torsion of the search path for the target position that has a known distribution. The searcher is desired to search in an optimal manner by obtaining the optimal values of the curvature and the torsion that minimize the expected time for detecting the target. An illustrative example has been given to demonstrate the applicability of this technique.
Keywords: Optimal search theory; Trivariate normal distribution; Slinky-Turn-Spiral; Geometry features.
Activity couple with interdependent durations: Serial, parallel or partly overlapping scheduling?
by Baruch Keren, Gregory Gurevich, Zohar Laslo
Abstract: This paper explores a problem of a hammock (sub-project) with two remaining activities, both eligible for execution. The activities can be scheduled in a serial mode, a parallel mode, or a partly overlapping mode. Each activity has alternative execution-modes that are related to the amount of budget allocated. We assume an interdependency between the activity time-cost tradeoffs functions that are defined differently if the activities are scheduled separately, or if their schedule is overlapping. The aim is to determine, in the context of different objective functions and budget constraints, the optimal scheduling of the activities, with the appropriate allocation of budget to the activities. The paper presents a deterministic time-cost tradeoffs model that takes into account the interdependency between the activity durations and enables decision makers to meet the above aim. Extension of the model and the analysis for the case where the activity durations are stochastic, are also examined.
Keywords: Project schedule; overlapping; time-cost tradeoff; duration interdependencies; stochastic durations.
Energy analysis of adobe performance as a housing construction material in Ecuador
by Luis Felipe Godoy Vaca, Javier Martinez Gomez
Abstract: For housing construction design in Ecuador, mechanical characteristics of constructive materials are highly prioritised instead of thermal considerations. In this sense, promoting the use of local materials with good energy efficient features appears as a suitable solution. As a consequence, in this article, energy performance of adobe is analysed in household energy performance. For this purpose, the following steps were taken: thermal characterisation of adobe (thermal conductivity). Adobe is obtained from quarries located in Pichincha province, Ecuador and its conductivity was the major thermal parameter tested. The research was carried out by means of experimental and statistical techniques. In addition, a strong state of the art review is presented, considering national and international standards. Finally, field tests show that adobe reaches an average conductivity around 0.22 W/m K. This value tends to increase due to the density of the sample and the technique used during the manufacture process. In addition, some studies demonstrate that by using adobe, for instance, on the frontage of a building, thermal comfort improves in some regions of the country, and energy consumption is reduced by 10%.
Keywords: Energy performance; housing; thermal conductivity; adobe.
Multistep Crossover Genetic Algorithm for Bi-criteria Parallel Machine Scheduling Problems
by Sameer Sharma, Mehak Chadha, Harpreet Kaur
Abstract: This paper propounds the bi-criteria scheduling problem with identical parallel machines, volatile due dates and processing times. A robust and simple structured nature inspired approach has been applied for minimisation of maximum tardiness as the primary and the number of tardy jobs as the secondary criteria. The optimal values of both criteria are evaluated on the trot confined with a constraint that optimal value of secondary criteria does not infringe the primary criteria in the opposite sense of the requirement. To unfold such kind of NP hard optimisation problems, genetic algorithm (GA) has shown a great advantage in solving the combinatorial optimisation problems in view of its characteristic that has high efficiency and is the best fit for practical application. In this paper, a multi-step crossover fusion operator of genetic algorithms (MSXF) has been introduced and applied to a set of randomly generated problems of different sizes. The results obtained are correlated with the other crossover operators. Computational results show that MSXF operator outperforms all the most every time on randomly generated problems analogous to the parameter under consideration.
Keywords: Bi-criteria; Scheduling; Tardiness; Due dates; Genetic algorithm.
Existence of Optimal N-Slinky-Turn-Spiral Search Paths for Finding N-Dimensional Brownian Target
by Mohamed El-hadidy
Abstract: This paper presents more effective search technique for finding the N-dimensional Brownian target in N-dimensional space by using N-searchers. Each searcher moves along slinky-turn-spiral curve and starts its motion from the origin. An adaptive geometric features such as curvature and torsion of each searching path to meet the target is proposed. Rather than showing the existence of finite and optimal search paths, we find these optimal search paths which minimize the expected value of the first meeting time between one of the searchers and the target based on its geometric characteristics and features. A simulation study has been discussed to demonstrate the applicability of this technique.
Keywords: Optimal search theory; geometric features; N-Dimensional Brownian target; expected value of the first meeting time.
On solving linear programming problem by duality approach in neutrosophic environment.
by Tuhin Bera, N.K. Mahapatra
Abstract: This paper extends the concept of crisp linear programming problem by adopting the coefficients in objective function, technical coefficients, the right hand side coefficients and the decision variables as single valued triangular neutrosophic numbers (Svtrn number) which is a special type of neutrosophic set. This modified concept is here called neutrosophic linear programming problem (Nlp problem).To develop this notion, a ranking function is newly constructed from geometrical concept first. Then the validity of existing crisp results are tested by means of ranking function in this new environment. An attempt is also taken to solve an Nlp problem by duality approach. For that, an efficient algorithm is developed by obeying the properties of ranking function. Finally, this proposed algorithm is demonstrated to solve a real life problem and some special cases are also illustrated by numerical examples.
Keywords: neutrosophic set; single valued triangular neutrosophic number; neutrosophic linear programming problem; duality.
Searching for Multiple Equivalent Predictors from Oral Squamous Cell Carcinoma Dataset Using Statistically Equivalent Signature Algorithm
by R. Dhanalakshmi, Utkarsh Khaire
Abstract: Selecting highly predictive features from the high dimensional dataset is a formidable task. The existing feature selection algorithms available today is not dealing with multiple equally predictive subsets of features. We strongly believe that there are other subsets of features as well, which can give equivalent predictive accuracy as that of state-of-the-art algorithms. Statistically equivalent signature (SES) is one such feature selection algorithm, which is centered on constraint-based learning of Bayesian networks. Other feature selection algorithms return only a single set of features of maximum predictive accuracy, while SES returns multiple subsets of features of predictive accuracy. These subsets are similar to the maximum predictive feature set given by state-of-the-art algorithms. The proposed model selects equivalent subsets of features from Oral Squamous Cell Carcinoma (OSCC) dataset with the help of SES. OSCC is microarray dataset of oral cancer of very high dimensionality (50 samples, 41000 features).
Keywords: High Dimensional Dataset; Statistically Equivalent Signature; Oral Squamous Cell Carcinoma; Microarray; K-Nearest Neighbor; Support Vector Machine; Neural Networks.
A dynamic DEA model for resource allocation
by Seaid Ghobadi
Abstract: In this paper we discuss the inverse Data Envelopment Analysis (DEA) in framework of dynamic DEA. This discussion is based on extending the non-radial Enhanced Russell Measure (ERM) model to framework of dynamic DEA. Also, necessary and sufficient conditions are established to characterizing dynamically efficient paths using dynamic ERM-model. Simultaneous estimation of input and output levels are studied using ERM-model under inter-temporal dependence assumption. Necessary and sufficient conditions for simultaneous estimation of input and output levels are introduced based on Pareto solutions of multiple-objective linear programming problems. In addition, the performance of the proposed method is illustrated through an example in banking sector.
Keywords: Data Envelopment Analysis (DEA); Inverse DEA; Dynamic DEA; Multiple Objective Linear Programming (MOLP); Enhanced Russell Measure (ERM).
Mathematical modelling and performance analysis of single server queuing system - eigenspectrum
by E. Mamatha, S. Saritha, C.S. Reddy, P. Rajadurai
Abstract: Classical queuing theory is playing vital role to study and analyse the performance analysis of real-time servicing systems, production inventory and manufacturing systems, telecommunication systems, modern information and communication technology systems and computing sector. In recent decays, bounded and immeasurable queues have been intensively studied; due to its attractive mathematical features with wide spread applicability. Such a system describes units of work, e.g., particles or customers, arriving at a resource, that stay present for some random duration that is independent of other customers. The aim of this paper is to evaluate the performance measures with a single server queuing system. Mathematical model has been developed to study the probability live time of the server using algebraic eigenproperties. These models are indispensable in real-time systems, manufacturing and communication queuing systems, including wireless networks, mobility, and randomly arriving traffic.
Keywords: Markov process; server live probability; latent values and vectors; matrix geometric approach; single server queuing system.
Analysis of parameter selection for solar radiation prediction and global solar radiation prediction model using polynomial regression
by Prakash Marimuthu, P. Chinnamuthu, R. Jeyapaul
Abstract: Solar irradiance is available in abundance and can be harvested to satisfy ever-growing energy demand. Installation of photovoltaic (PV) solar panels at any desired location is not often economically feasible and hence prediction of solar radiation is crucial. Relative humidity and temperature at a specific location Chumukedima, Nagaland (latitude 25.86 N, longitude 93.75 E) in India have been used for the present study along with the solar irradiance outcome. Significant parameter contributing towards the solar radiation outcome is derived with the help of design of experiments (DOE) and analysis of variance (ANOVA). Polynomial regression model is developed to predict the solar irradiation. From the results obtained, it is evident that the humidity contributes more towards the solar irradiation prediction.
Keywords: solar radiation; analysis of variance; ANOVA; design of experiment; DOE; polynomial regression.
Analysis of non-pre-emptive priority retrial queueing system with two-way communication, Bernoulli vacation, collisions, working breakdown, immediate feedback and reneging
by G. Ayyappan, J. Udayageetha, B. Somasundaram
Abstract: In this study, we investigate a single server priority retrial queueing system including two-way communication, collision, working breakdown, repair, immediate feedback, Bernoulli vacation and reneging. Incoming requests (calls) appear at the service station according to a compound Poisson process. During the idle time, the server can make an outgoing call with an exponentially distributed time. The incoming call that identifies the server occupied will join an orbit or collide with the call currently in service. The server renders the service following a non-pre-emptive priority service rule. The server takes a Bernoulli vacation. The server may become inactive due to normal breakdown and the call currently in service will get the remaining service at a moderate service rate. The repair process starts instantly. After the completion of service, vacation and repair the server is in an idle state. We allow reneging to happen at the orbit. Using the supplementary variable technique, the stability condition is derived.
Keywords: priority queueing systems; two-way communication; retrial queue; working breakdown; collisions; Bernoulli vacation.
Reliability analysis of different systems using triangular multi-fuzzy sets estimated by statistical data
by E. El-Ghamry, M. El-Damsece, M. Shokry
Abstract: In this paper, the multi-fuzzy sets and its arithmetic operations are first introduced briefly then we describe an idea of using multi-fuzzy sets approach to reliability analysis of different types of unrepairable fuzzy systems as series, parallel, series-parallel and parallel-series systems consist of independent components. The knowledge about causes and effects of failures is usually described with large uncertainty content so the reliability of each component can be represented by triangular multi-fuzzy set. Each multi-fuzzy set is estimated by using the concept of confidence interval that calculated based on statistical data taken from random samples of each component. A numerical example is given to demonstrate the applicability of the multi-fuzzy sets in different structural engineering systems and the results were drawn by using MAPLE software program.
Keywords: reliability; multi-fuzzy set; confidence interval; statistical data.
Optimal service rates of a perishable inventory system with service facility
by N. Sangeetha, B. Sivakumar
Abstract: This paper studies a continuous-review perishable inventory system with service facility. We consider a finite capacity inventory system with Markovian arrivals and exponentially distributed service times. The inventory is replenished according to an (s, S) policy and the lead times follow phase type distribution. The life time of each item is assumed to be exponential. By controlling the service rate at each instance of time, we can minimise the total expected cost rate. We formulate this model as a semi Markov decision problem. The stationary optimal policy is computed using linear programming algorithm and the results are illustrated numerically.
Keywords: inventory control; Markovian arrivals; (s, S) ordering policy; control of service rates; semi Markov decision process.