QIAUJournal of Optimization in Industrial Engineering2251-990481820150701Bayesian Estimation of Shift Point in Shape Parameter of Inverse Gaussian Distribution Under Different Loss Functions112216ENMohammad SaberFallah NezhadDepartment of Industrial Engineering, Yazd University, Yazd, IranBatulRastiDepartment of Industrial Engineering, Yazd University, Yazd, IranJournal Article20140325In this paper, a Bayesian approach is proposed for shift point detection in an inverse Gaussian distribution. In this study, the mean parameter of inverse Gaussian distribution is assumed to be constant and shift points in shape parameter is considered. First the posterior distribution of shape parameter is obtained. Then the Bayes estimators are derived under a class of priors and using various loss functions. We assumed uniform, Jeffreys, exponential, gamma and chi square distributions as prior distributions. The squared error loss function (SELF), entropy loss function (ELF), linex loss function (LLF) and precautionary loss function (PLF), are used as loss functions. We attempt to find out the best estimator for shift point under various priors and loss functions. The proposed Bayesian approach can be adapted to any similar problem for shift point detection. Simulation studies were done to investigate the performance of different loss functions. The results of simulation study denote that the Jeffrey prior distribution under PLF has the most accurate estimation of shift point for sample size of 20, and the gamma prior distribution under SELF has the most accurate estimation of shift point for sample size of 50.http://www.qjie.ir/article_216_0e38aaddfc4c867549097412e3c72196.pdfQIAUJournal of Optimization in Industrial Engineering2251-990481820150701Designing Stochastic Cell Formation Problem Using Queuing Theory1326217ENParvizFattahiFaculty of Industrial Engineering, Bu-Ali Sina University, Hamedan, IranBahmanEsmailnezhadFaculty of Industrial Engineering, Bu-Ali Sina University, Hamedan, IranAmir SamanKheirkhahFaculty of Industrial Engineering, Bu-Ali Sina University, Hamedan, IranJournal Article20140121This paper presents a new nonlinear mathematical model to solve a cell formation problem which assumes that processing time and inter-arrival time of parts are random variables. In this research, cells are defined as a queue system which will be optimized via queuing theory. In this queue system, each machine is assumed as a server and each part as a customer. The grouping of machines and parts are optimized based on the mean waiting time. For solving exactly, the proposed model is linearized. Since the cell formation problem is NP-Hard, two algorithms based on genetic and modified particle swarm optimization (MPSO) algorithms are developed to solve the problem. For generating of initial solutions in these algorithms, a new heuristic method is developed, which always creates feasible solutions. Also, full factorial and Taguchi methods are used to set the crucial parameters in the solutions procedures. Numerical experiments are used to evaluate the performance of the proposed algorithms. The results of the study show that the proposed algorithms are capable of generating better quality solutions in much less time. Finally, a statistical method is used which confirmed that the MPSO algorithm generates higher quality solutions in comparison with the genetic algorithm (GA).http://www.qjie.ir/article_217_d4dca1000fff17aed673e148277b4cde.pdfQIAUJournal of Optimization in Industrial Engineering2251-990481820150701A Benders' Decomposition Method to Solve Stochastic Distribution Network Design Problem with Two Echelons and Inter-Depot Transportation2736218ENVahid RezaGhezavatiAssistant Professor, Faculty of Industrial Engineering, Islamic Azad University, South Tehran Branch, Tehran, IranJournal Article20140915 In many practical distribution networks, managers face significant uncertainties in demand, local price of building facilities, transportation cost, and macro and microeconomic parameters. This paper addresses design of distribution networks in a supply chain system which optimizes the performance of distribution networks subject to required service level. This service level, which is considered for each arbitrary request arriving at a distribution center (facility), has a (pre-specified) small probability of being lost. In this mathematical model, customer’s demand is stochastic that follows uniform distribution. In this model, inter-depot transportation (transportation between distributions centers (DCs)), capacities of facilities, and coverage radius restrictions are considered. For this restriction, each DC cannot service all customers. The aim of this model is to select and optimize location of plants and DCs. Also, the best flow of products between DCs and from plants to DCs and from DCs to customers will be determined. The paper presents a mixed integer programming model and proposed an exact solution procedure in regard to Benders’ decomposition method.http://www.qjie.ir/article_218_e1a41d4a23096a71f51652b1a3cb0894.pdfQIAUJournal of Optimization in Industrial Engineering2251-990481820150701A Mixed Integer Programming Formulation for the Heterogeneous Fixed Fleet Open Vehicle Routing Problem3746219ENMajidYousefikhoshbakhtAssistant Professor, Department of Mathematics, Faculty of Science, Bu-Ali Sina University, Hamedan, IranFrazadDidehvarAssistant Professor, Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, IranFarhadRahmatiAssociate Professor, Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, IranJournal Article20140127The heterogeneous fixed fleet open vehicle routing problem (HFFOVRP) is one of the most significant extension problems of the open vehicle routing problem (OVRP). The HFFOVRP is the problem of designing collection routes to a number of predefined nodes by a fixed fleet number of vehicles with various capacities and related costs. In this problem, the vehicle doesn’t return to the depot after serving the last customer. Because of its numerous applications in industrial and service problems, a new model of the HFFOVRP based on mixed integer programming is proposed in this paper. Furthermore, due to its NP-hard nature, an ant colony system (ACS) algorithm was proposed. Since there were no existing benchmarks, this study generated some test problems. From the comparison with the results of exact algorithm, the proposed algorithm showed that it can provide better solutions within a comparatively shorter period of time.http://www.qjie.ir/article_219_ebb2cd520ac0626659d9b38e3b93b4d1.pdfQIAUJournal of Optimization in Industrial Engineering2251-990481820150701Vendor Managed Inventory of a Supply Chain under Stochastic Demands4760220ENTaherehPoorbagheriMSc, Department of Industrial & Mechanical Engineering, Islamic Azad University, Qazvin Branch, Qazvin, IranSeyed TaghiAkhavan NiakiProfessor, Department of Industrial Engineering, Sharif University of Technology, Tehran, Iran0000-0001-6281-055XJournal Article20140706In this research, an integrated inventory problem is formulated for a single-vendor multiple-retailer supply chain that works according to the vendor managed inventory policy. The model is derived based on the economic order quantity in which shortages with penalty costs at the retailers` level is permitted. As predicting customer demand is the most important problem in inventory systems and there are difficulties to estimate it, a probabilistic demand is considered to model the problem. In addition, all retailers are assumed to share a unique number of replenishments where their demands during lead-time follow a uniform distribution. Moreover, there is a vendor-related budget constraint dedicated to each retailer. The aim is to determine the near optimal or optimal order quantity of the retailers, the order points, and the number of replenishments so that the total inventory cost of the system is minimized. The proposed model is an integer nonlinear programming problem (NILP); hence, a meta-heuristic namely genetic algorithm (GA) is employed to solve it. As there is no benchmark available in the literature to validate the results obtained, another meta-heuristic called firefly algorithm (FA) is used for validation and verification. To achieve better solutions, the parameters of both meta-heuristics are calibrated using the Taguchi method. Several numerical examples are solved at the end to demonstrate the applicability of the proposed methodology and to compare the performance of the solution approaches.http://www.qjie.ir/article_220_af763f026d9854687e7c787637a9b049.pdfQIAUJournal of Optimization in Industrial Engineering2251-990481820150701Modelling and Scheduling Lot Streaming Flexible Flow Lines6170221ENBahmanNaderiAssistant Professor, Department of Industrial Engineering, Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, IranMehdiYazdaniAssistant Professor, Department of Industrial Engineering, Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, IranJournal Article20140708Although lot streaming scheduling is an active research field, lot streaming flexible flow lines problems have received far less attention than classical flow shops. This paper deals with scheduling jobs in lot streaming flexible flow line problems. The paper mathematically formulates the problem by a mixed integer linear programming model. This model solves small instances to optimality. Moreover, a novel artificial bee colony optimization is developed. This algorithm utilizes five effective mechanisms to solve the problem. To evaluate the algorithm, it is compared with adaptation of four available algorithms. The statistical analyses showed that the proposed algorithm significantly outperformed the other tested algorithms.http://www.qjie.ir/article_221_7d75c0446265f8fb6bdad41e3c734819.pdfQIAUJournal of Optimization in Industrial Engineering2251-990481820150701Modelling Integrated Multi-item Supplier Selection with Shipping Frequencies7178222ENAbolfazlKazemiFaculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, IranDanialEsmaeili AliabadiFaculty of engineering and natural science, Sabanci university, Istanbul, TurkeyJournal Article20111012There are many benefits for coordination of multiple suppliers when single supplier cannot satisfy buyer demands. In addition, buyer needs to purchase multiple items in a real supply chain. So, a model that satisfies these requests has many advantages. We extend the existing approaches in the literature that assume all suppliers need to be put on a common replenishment cycle and each supplier delivers exactly once in a cycle. More specifically, inspired by approaches that perform well for the Economic Lot Scheduling Problem, we assume an integer number of times a supplier can ship available items in an overall replenishment cycle. Because of complexity issue, a new approach based on genetic algorithm is employed to solve the presented model. Results depict that new model is more beneficial and practical. http://www.qjie.ir/article_222_63fcd714427d3737db53379a219bad3b.pdfQIAUJournal of Optimization in Industrial Engineering2251-990481820150701A Benders Decomposition Method to Solve an Integrated Logistics Network Designing Problem with Multiple Capacities7993223ENNadiehSodagariMSc, Faculty of Industrial & Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, IranAhmadSadeghiAssistant Professor, Faculty of Industrial & Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, IranJournal Article20140111In this paper, a new model is proposed for the integrated logistics network designing problem. In many research papers in this area, it is assumed that there is only one option for the capacity of each facility in the network. However, this is not a realistic assumption because generally there may be many possible options for the capacity of the facility that is being established. Usually the cost of establishing a facility depends on its capacity. Moreover, of the majority of the research done in the field of logistics network designing problem only a limited number of options for product recovery is addressed. Specifically, in most of the research papers only one option, i.e. remanufacturing, has been considered. Therefore, a mathematical formulation with multiple options for capacities and product recovery is addressed in this research to obviate this gap. Afterwards a benders decomposition method is developed to efficiently solve the problem. The computational results introduce several random generated problems to be solved with benders algorithm and demonstrate that this algorithm can efficiently solve the proposed model.http://www.qjie.ir/article_223_81f03ffea2a52facade501e5ec0a88a1.pdf