A vehicle routing problem with time windows (VRPTW) is an important problem with many real applications in a transportation problem. The optimum set of routes with the minimum distance and vehicles used is determined to deliver goods from a central depot, using a vehicle with capacity constraint. In the real cases, there are other objective functions that should be considered. This paper considers not only the minimum distance and the number of vehicles used as the objective function, the customer’s satisfaction with the priority of customers is also considered. Additionally, it presents a new model for a bi-objective VRPTW solved by a revised multi-choice goal programming approach, in which the decision maker determines optimistic aspiration levels for each objective function. Two meta-heuristic methods, namely simulated annealing (SA) and genetic algorithm (GA), are proposed to solve large-sized problems. Moreover, the experimental design is used to tune the parameters of the proposed algorithms. The presented model is verified by a real-world case study and a number of test problems. The computational results verify the efficiency of the proposed SA and GA.

Multi-period models of portfolio selection have been developed in the literature with respect to certain assumptions. In this study, for the first time, the portfolio selection problem has been modeled based on mean-semi variance with transaction cost and minimum transaction lots considering functional constraints and fuzzy parameters. Functional constraints such as transaction cost and minimum transaction lots were included. In addition, the returns on assets parameters were considered as trapezoidal fuzzy numbers. An efficient genetic algorithm (GA) was designed, results were analyzed using numerical instances and sensitivity analysis were executed. In the numerical study, the problem was solved based on the presence or absence of each mode of constraints including transaction costs and minimum transaction lots. In addition, with the use of sensitivity analysis, the results of the model were presented with the variations of minimum expected rate of programming periods.

This paper considers the capacity determination in a closed-loop supply chain network when a queueing system is established in the reverse flow. Since the queueing system imposes costs on the model, the decision maker faces the challenge of determining the capacity of facilities in such a way that a compromise between the queueing costs and the fixed costs of opening new facilities could be obtained. We develop a De Novo programming approach to determine the capacity of recovery facilities in the reverse flow. To this aim, a mixed integer nonlinear programming (MINLP) model is integrated with the De Novo programming and the robust counterpart of this model is proposed to cope with the uncertainty of the parameters. To solve the model, an interactive fuzzy programming approach is combined with the hard worst case robust programming. Numerical results show the performance of the developed model in determining the capacity of facilities.

Banking industry has significant contribution in development of economies of developing countries. Most banks execute their operations through different branches. Therefore it is important to measure the relative efficiencies of these branches. Data envelopment analysis (DEA) is one of the most useful tools in measuring banks’ performance. The present paper aims to extract ranking pattern of banks based on performance evaluation using DEA analysis. In the present research, 120 bank branches of Bank Shahr in city of Tehran were selected and their efficiencies were evaluated using DEA technique. The results are discussed and compared with similar studies.

The single machine scheduling problem aims at obtaining the best sequence for a set of jobs in a manufacturing system with a single machine. In this paper, we optimize rewards in single machine scheduling in rewards-driven systems such that total reward is maximized while the constraints contains of limitation in total rewards for earliness and learning, independent of earliness and learning and etc. are satisfied. In mentioned systems as for earliness and learning the bonus is awarded to operators, we consider only rewards in mentioned systems and it will not be penalized under any circumstances. Our objective is to optimize total rewards in mentioned system by taking the rewards in the form of quadratic for both learning and earliness. The recently-developed sequential quadratic programming (SQP), is used by solve the problem. Results show that SQP had satisfactory performance in terms of optimum solutions, number of iterations, infeasibility and optimality error. Finally, a sensitivity analysis is performed on the change rate of the objective function obtained based on the change rate of the “amount of earliness for jobs (Ei parameter)”.

In this paper, a new robust approach is presented to handle demand uncertainty in cell formation and layout design process. Unlike the scenario based approaches, which use predefined scenarios to represent data uncertainty, in this paper, an interval approach is implemented to address data uncertainty for the part demands, which is more realistic and practical. The objective is to minimize the total inter- and intra-cell material handling cost. The proposed model gives machine cells and determines inter-and intra-cell layouts in such a way that the decision maker can control the robustness of the layout against the level of conservatism. An illustrative example is solved by CPLEX 10 to demonstrate the performance of the proposed method. The results reveal that when the level of conservatism is changed the optimal layout can vary, significantly.

Cell formation process is one of the first and the most important steps in designing cellular manufacturing systems. It consists of identifying part families according to the similarities in the design, shape, and presses of parts and dedicating machines to each part family based on the operations required by the parts. In this study, a hybrid method based on a combination of simulated annealing algorithm and dynamic programming was developed to solve a bi-objective cell formation problem with duplicate machines. In the proposed hybrid method, each solution was represented as a permutation of parts, which is created by simulated annealing algorithm, and dynamic programming was used to partition this permutation into part families and determine the number of machines in each cell such that the total dissimilarity between the parts and the total machine investment cost are minimized. The performance of the algorithm was evaluated by performing numerical experiments in different sizes. Our computational experiments indicated that the results were very encouraging in terms of computational time and solution quality.

In this paper, an integrated layout model has been considered to incorporate intra and inter-department layout. In the proposed model, the arrangement of facilities within the departments is obtained through the QAP and from the other side the continuous layout problem is implemented to find the position and orientation of rectangular shape departments on the planar area. First, a modified version of QAP with fewer binary variables is presented. Afterward the integrated model is formulated based on the developed QAP. In order to evaluate material handling cost precisely, the actual position of machines within the departments (instead of center of departments) is considered. Moreover, other design factors such as aisle distance, single or multi row intra-department layout and orientation of departments have been considered. The mathematical model is formulated as mixed-integer programming (MIP) to minimize total material handling cost. Also due to the complexity of integrated model a heuristic method has been developed to solve large scale problems in a reasonable computational time. Finally, several illustrative numerical examples are selected from the literature to test the model and evaluate the heuristic.

Over time, the number of unexpected earthy, oceanic and atmospheric events is rising each year. Hence, disaster management is considered as one of the most important scientific and practical issues in developed and developing countries. Therefore, in this study, we review and develop the problem of locating the emergency units with constraints including the number of available ambulances, limited budget for deployment of ambulances and the minimum acceptable level of covering. The proposed model improves the spatial queuing model (SQM) and Maximal Covering Location Problem (MCLP) by considering the cost of the deployment of the emergency units, which makes it closer to real-world conditions. Because the proposed model is NP-hard, the model is solved using three heuristics including Simulated Annealing (SA), Genetic Algorithm (GA) and a hybrid of both. The preliminary results indicate that the hybrid method had better performance to achieve the optimal or close to optimal solution.

In this paper, a new mathematical model in cellular manufacturing systems (CMSs) has been presented. In order to increase the performance of manufacturing system, the production quantity of parts has been considered as a decision variable, i.e. each part can be produced and outsourced, simultaneously. This extension would be minimized the unused capacity of machines. The exceptional elements (EEs) are taken into account and would be totally outsourced to the external supplier in order to remove intercellular material handling cost. The problem has been formulated as a mixed-integer programming to minimize the sum of manufacturing variable costs under budget, machines capacity and demand constraints. Also, to evaluate advantages of the model, several illustrative numerical examples have been provided to compare the performance of the proposed model with the available classical approaches in the literature.