International Journal of Mathematics in Operational Research (44 papers in press)
Selection of materials by multi-criteria methods applied to the side of a self-supporting structure for light vehicles
by Javier Martinez, Juan Carlos Rocha, Edilberto LLanes, Rodger Salazar
Abstract: The selection of materials is an important stage in the design and development of products, but considering the enormous amount of materials available on the market that have different properties and characteristics, defining suitable and ideal alternatives is a difficult task. Within the automotive area there is a tendency to develop vehicles with greater efficiency and capacity, keeping aside the economic implications without underestimating the functionality of the materials. The use of multi-criteria methods (MCDM) allows the establishment of a reliable selection methodology, due to the interaction between each of the criteria with statistical methods that converge in a single solution. The methodology used in this study was based on the application of MCDM methods, and the comparison between them to determine a convergence in the alternatives of greater potential for the structural section of vehicles. Four methods were evaluated: TOPSIS, COPRAS, VIKOR, PROMETHEE II, obtaining that for all the methods the best material corresponds to the Martensitic Steel YS1200, being this the most appropriate one when fulfilling structural requirements, as well as providing a reduction of weight and price.
Keywords: Lateral structure; weighting method; multi-Criteria method; MCDM; Material selection.
New class of estimators of the population mean using the known population median of the study variable
by Dinesh K. Sharma, S.K. Yadav, Kate Brown
Abstract: In this paper, we propose an improved class of estimators of the population mean using the population median of the study variable. We study the properties of the sampling distribution of the proposed class of estimators up to the approximation of order one. Different values of the two characterising constants in the new estimators affect the mean squared error (MSE) of the proposed family of estimators. Finding the optimum values of the constants to minimise the MSE of the suggested class of estimators provides the least MSE of the recommended family for these optimal values of the characterising scalars. We compare the proposed family of estimators with other competing estimators of the population mean. The theoretical findings are justified with an empirical example and reveal that the proposed class of estimators performs more efficiently than other competing estimators of the population mean under a simple random sampling without replacement (SRSWOR) scheme.
Keywords: Main variable; known variable; ratio estimators; bias; MSE; efficiency.
A robust bi-objective programming approach to environmental closed-loop supply chain network design under uncertainty
by Zahra Homayouni, Mir Saman Pishvaee
Abstract: Imposition of strict environmental protection acts and the imperative need of the best possible allocation of resources have given birth to the concept of low carbon logistics. Environmental laws force the manufacturers to extend their existing supply chains to form a closed-loop supply chain (CLSC) through the setup of an efficient recovery system. In this paper, a multi-objective robust optimisation model is proposed for the design of CLSC network under uncertainty. First, a deterministic bi-objective mixed integer linear programming (BOMILP) model is developed for designing a CLSC network. Then, the robust counterpart of the proposed BOMILP is presented to cope with the real-world uncertainty. The first objective aims to maximise the total profit generated in the CLSC network and the second objective minimises the environmental pollution of the CLSC network. The proposed bi-objective model is solved using a multi-choice goal programming (MCGP) approach.
Keywords: Closed-loop supply chain; Environmental issues; Robust optimization; Multi-choice goal programming.
Sion's minimax theorem and Nash equilibrium of symmetric three-players zero-sum game
by Yasuhito Tanaka, Atsuhiro Satoh
Abstract: About a symmetric three-players zero-sum game we will show the following results. A modified version of Sions minimax theorem with the coincidence of the maximin strategy and the minimax strategy are proved by the existence of a symmetric Nash equilibrium. The existence of a symmetric Nash equilibrium is proved by the modified version of Sions minimax theorem with the coincidence of the maximin strategy and the minimax strategy. Thus, they are equivalent. However, without the coincidence of the maximin strategy and the minimax strategy there may exist an asymmetric equilibrium in a symmetric three-players zero-sum game.
Keywords: three-players zero-sum game; Nash equilibrium; Sion's minimax theorem.
A Hybrid Direction Algorithm for Solving a Convex Quadratic Problem
by Mohand Ouamer Bibi, Nacira Ikheneche, Mohand Bentobache
Abstract: In this paper, we propose a new algorithm for solving convex quadratic programming problems with bounded variables. Instead of using the standard direction of the adaptive method, which is constructed by minimising only the linear part of the objective function increment, we will suggest a new descent direction, called hybrid direction. This latter is constructed by minimising a quadratic part of the increment. Furthermore, we define a quantity called optimality estimate from which we derive sufficient and necessary conditions of optimality. On the basis of this new concept, we construct an algorithm for solving convex quadratic programs. In order to compare our method with the active-set method implemented in MATLAB, numerical experiments on randomly generated test problems are presented.
Keywords: Convex quadratic programming; Adaptive method; Bounded variables; Hybrid direction; Optimality estimate; Numerical experiments.
Holistically addressing uncertainty in group decision-making: the case of a
by Lanndon A. Ocampo, Eppie Clark, Anthony Shun Fung Chiu, Raymond Tan
Abstract: This paper presents a methodology that holistically captures the uncertainty of judgment in 'quasi-collaborative' group decision-making in the context of the analytic hierarchy/network process. The proposed method is motivated mainly by the two uncertainty approaches that seemingly diverge in literature: the simulation approach and the fuzzy set theory (FST) approach. In the proposed method, FST is used to handle the judgmental uncertainty of individual decision-maker while simulation addresses randomness and uncertainty when individual judgments are aggregated as a group decision. An illustrative problem is presented in this paper along with a numerical experiment that attempts to compare the efficacy of the proposed methodology with existing methods. Results show that the method is more capable of handling uncertain group decisions through simulation runs and it can perform sensitivity analysis which is essential in testing robustness of judgment results. Finally, the proposed method can identify non-expert member of the group.
Keywords: analytic hierarchy process; analytic network process; simulation; fuzzy set theory; sensitivity analysis.
A DECENTRALIZED MULTI-OBJECTIVE SUSTAINABLE SUPPLY CHAIN MODEL UNDER INTUITIONISTIC FUZZY ENVIRONMENT
by Murshid Kamal, Srikant Gupta, Irfan Ali
Abstract: This paper uses the fuzzy goal programming approach with different kinds of membership functions like linear, exponential, parabolic, hyperbolic and quadratic membership; for solving the multi-objective sustainable supply chain (MOSSC) problem under the intuitionistic fuzzy environment. The primary objective is to maximise the minimum value of the membership function so the preferred compromise solution can achieve to the MOSSC problem. By attaining this preferred compromise solution, the optimum order quantity allocation to each supplier can also be determined. Additionally, a situation even has been considered where the decision maker tries to control the optimum order quantity and search for another satisfactory solution, for this, he uses the membership function. A case study of the sustainable supply chain has been used to show the usefulness of the proposed work.
Keywords: Multi-objective Optimization; Sustainable Supply Chain; Supplier Selection Problem; Fuzzy Goal Programming; Intuitionistic Fuzzy Number.
On the distribution of an infinite-buffer queueing system with versatile bulk-service rule under batch-size-dependent service policy: M/G^(a,Y)_n/1
by Sourav Pradhan
Abstract: Batch-service queues have a wide range of noteworthy applications in wireless telecommunication to deal with the multimedia type of data, manufacturing systems, group testing procedure, etc. The knowledge of both the queue and server content distributions helps the system designer to evaluate the efficiency of the queueing system in a better way. We analyse a single server infinite-buffer batch-size-dependent service queue with Poisson arrival and versatile batch-service rule. Based on supplementary variable technique, a bivariate probability generating function, the entire spectrum of new contributions, of queue content and number in a served batch at departure epoch is derived. Moreover, we perceive the complete queue and server content distribution at departure as well as arbitrary epochs. The utility of analytical results is illustrated by the inclusion of some numerical examples, which also includes the investigation of multiple zeros.
Keywords: Batch-service; Versatile-bulk-service; Batch-size-dependent; Multiple roots; Queueing; Server content.
Evaluation the Branches of Iran Insurance Corporation based on Data Envelopment Analysis-Free Disposal Hull in the Presence of Weight Restrictions
by Mohammad Reza Fathi, Hossein Safari, Abdol Hossein Jafarzadeh
Abstract: This study reviews the concepts of performance evaluation in the insurance industry based on data envelopment analysis. In this study to deal with the problems that exists in conventional DEA model, a new DEA model is introduced and applied based on FDH and weight restrictions to evaluate Insurance Corporation branches. In this study, non-parametric frontier technologies for data analysis are mainly discussed. It combines several models with non-parametric frontier technology to suggest a new model for analysing the data. This paper is based on a combination of the two frontier technology, DEA and free disposal hull. As it is mainly based on DEA and benchmarking based on DEA. The proposed method was successfully conducted in a case study about Iran Insurance Corporation; secondly, the paper depicts the insurance company evaluation process through a DEA model, while allowing for incorporating the preferences of decision maker. According to result, 26 branches are efficient and achieved efficiency score is equal to 1.
Keywords: Insurance; performance evaluation; non-parametric analysis; DEA; data envelopment analysis; FDH; free disposal hull; benchmarking; weight restrictions; discernment power.
Mathematical Modelling and Performance Analysis of Single Server Queuing System
by E. Mamatha, S. Saritha, Chandra Sekhar 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.
Transient analysis of multi-server Markovian queueing system with synchronous multiple working vacations and impatience of customers
by Vijaya Laxmi Pikkala
Abstract: In this paper, we study an infinite capacity multi-server Markovian queue with synchronous multiple working vacations, balking and reneging. It is assumed that customers may balk and/or renege with some probability if all the c servers are busy serving customers either during the regular busy period or working vacation period. The reneging times follow an exponential distribution. The system is modeled by a quasi-birth-death process and the transient-state probabilities of the model are obtained in the Laplace domain using matrix geometric method.
Keywords: Multi-server; multiple working vacations; Balking; Reneging; Transient-state probabilities; Matrix geometric method; Truncation method; Laplace transform.
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.
Reliability Analysis of Different Systems Using Triangular Multi-Fuzzy Sets
by Eman Elghamry, Medhat Eldamcese, Mohamed 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.
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.
Analysis of Parameter Selection for Solar Radiation Prediction and Global Solar Radiation Prediction Model using Polynomial Regression
by PRAKASH MARIMUTHU, Chinnamuthu P, 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; ANOVA; 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 J. UDAYAGEETHA, Ayyappan G, SOMASUNDARAM B
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.
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.
Analyzing interval and multi-choice bi-level programming for Stackelberg game using intuitionistic fuzzy programming
by Sankar Kumar Roy, Sumit Kumar Maiti
Abstract: The aim of this paper is to provide a computational algorithm for solving interval-valued and multi-choice bi-level programming for Stackelberg game using intuitionistic fuzzy approach. It also includes the cost parameters of upper and lower-level objective functions corresponding to interval numbers and multi-choice types while the parameters of constraints are intuitionistic fuzzy numbers. The interval-valued and multi-choice types objective functions are converted into deterministic form using interval programming and a general transformation technique respectively. Again, the intuitionistic fuzzy parameters of constraints are reduced to an interval by taking expected value of intuitionistic fuzzy number. A conflicting nature between the objective functions is resolved with the help of intuitionistic fuzzy programming by considering nonlinear degree of membership and non-membership functions respectively. The resultant max-min problem is solved with LINGO 15.0 iterative scheme. The developed algorithm is illustrated by an application example and Pareto optimality test is performed as well. The conclusions and an outlook of future study are described at last.
Keywords: Bi-level programming; Interval programming; Multi-choice programming; Intuitionistic fuzzy programming; Pareto-optimal.
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.
Numerical methods for first order uncertain stochastic differential equations
by Justin Chirima, Eriyoti Chikodza, Senelani Dorothy Hove-Musekwa
Abstract: Uncertain stochastic calculus is a relatively new sub discipline of mathematics. This branch of mathematical sciences seeks to develop models that capture aleatory and epistemic features of generic uncertainty in dynamical systems. The growth of uncertain stochastic theory has given birth to a novel class of differential equations called uncertain stochastic differential equations (USDEs). Exact and analytic solutions to this family of differential equations are not always available. In such cases, numerical analysis provides a gateway to approximate solutions. This paper examines a Runge-Kutta method for solving USDEs. Before examining and applying the Runge-Kutta method, the paper states and proves the existence and uniqueness theorem. The Runge-Kutta method is then applied to solve an American call option pricing problem. This numerical algorithm proves to be effective and efficient because it produces almost the same results as compared to Chen's analytic formula and the classical Black-Scholes model.
Keywords: Runge-Kutta; call option; uncertainty; aleatory; epistemic.
Material selection using multi-criteria decision making methods for geomembranes
by Cristhian Chingo, Javier Martínez-Gómez, Ricardo A. Narváez C.
Abstract: The present work aims to be a useful information about the novel MCDM methods applied on geomembranes in order to select the best alternative for construction. Qualitative and quantitative information will be used to do the best choice. AHP method is used to calculate the weight (importance) of the different criteria which uses the subjective information to assign numeric values among 0 and 1, being better weights with values near to 1. COPRAS-G, OCRA, TOPSIS, VIKOR, EXPROM II and ORESTE methods are applied as MCDM methods in order to perform the more accurate selection using relevant information about the features of different materials. These methods use the weight obtained by AHP for ranking the best alternative, whose result contains subjective and objective information. Finally, all methods are standardised with a unique equations template, which makes it easier to understand all of them in subsequent applications.
Keywords: geomembranes; multi-criteria decision making; MCDM; qualitative; quantitative; standardised; weight.
An M[X]/G(a, b)/1 queue with unreliable server, second optional service, closedown, setup with N-policy and multiple vacation
by G. Ayyappan, M. Nirmala
Abstract: Batch arrival bulk service queueing system has been effectively used to model many real life systems like production, manufacturing, transportation as well as telecommunication. Characteristic like second optional service, service interruption, closedown time, multiple vacation, setup time with N policy, etc. have been respectively considered in such models. So far, no comprehensive combination of these characteristics have been reported in the literature. This paper deals with the analysis of a non-Markovian batch arrival bulk service queue with a general combination of all the above mentioned characteristics.
Keywords: general bulk service; unreliable server; closedown; multiple vacation; setup with N-policy; optional service.
Transient solution of an M/M/∞ queue with system's additional tasks and impatient customers
by R. Sudhesh, A. Azhagappan
Abstract: This paper studies the impatient behaviour in an infinite server queue with additional tasks assigned to the system. Whenever the system becomes empty, the system as a whole is assigned a secondary task of duration U whose distribution is exponential. Any arrival during the period U becomes impatient due to the unavailability of service facility. Each individual waiting customer activates an independent impatience timer of duration T which is exponentially distributed. When the system comes back after the completion of U, before T expires, the waiting customers are simultaneously taken for service and they leave the system after the completion of service. If T expires before the completion of task U, the customers abandon the system and never to return. The transient system size probabilities of this model are derived explicitly for both single and multiple task cases. The time-dependent mean and variance of system size are also derived. Further, numerical simulations are also presented to analyse the effect of system indices.
Keywords: infinite server queue; single and multiple tasks; impatient customers; transient probabilities.
Data analytics for relative ranking of factors to optimise blood bank supply chain
by J. Arul Valan, E. Baburaj, P. Parthiban
Abstract: Healthcare systems are supported by blood service operations. Restricted usage limit of 21 days and stochastic nature of demand against the supply are the challenges in the field and results in complex situations. The paper focuses on the model mentioned for which a regionalised blood banking system is considered. Typically, it consists of hospitals, regional blood banks, in addition to central blood banks. The 20 factors that influence is weighed and raked using multiple criterion decision making (MCDM) methods. Interpretive structural modelling (ISM) gives the influence of a factor on another and determines weights. Fuzzy-TOPSIS is used to quantify the qualitative values systematically and rank the alternatives. The relative ranking enables to identify best alternative. The procedure for a single central blood bank executed may be extended to similar central blood banks. Supply chain optimisation of perishable products is possible with the framework proposed, with suitable modifications.
Keywords: influencing factors; relative ranking; interpretive structural modelling; ISM; fuzzy TOPSIS.
An application of bilevel optimisation to the waste collection centres location problem
by Massimiliano Caramia, Mattia Dalla Costa
Abstract: In this paper, we show an application of bilevel programming to the problem of locating waste collection centres inside a municipal area. In our study, the latter problem possesses a hierarchical structure, i.e., there are two decision makers, one of which acts as a leader and the other behaves as a follower. Therefore, we exhibit a bilevel optimisation program able to capture this hierarchy and propose an iterative algorithm to solve the problem. This solution proposal is then tested on data derived from a real scenario. Experimental results reveal that the approach is effective in this kind of decision problems.
Keywords: bilevel programming; facility location; waste collection.