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We develop an inventory model to determine optimal ordering policy under permissible delay in payment by considering demand rate to be stock dependent. Mathematical models are derived under two different cases: credit period being greater than or equal to cycle time for settling the account, and credit period being less than or equal to cycle time for settling the account. The results are illustrated with numerical examples. Sensitivity analysis is given for the proposed model.

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This paper proposes a robust model for optimizing collaborative reverse supply chains. The primary idea is to develop a collaborative framework that can achieve the best solutions in the uncertain environment. Firstly, we model the exact problem in the form of a mixed integer nonlinear programming. To regard uncertainty, the robust optimization is employed that searches for an optimum answer with nearly all possible deviations in mind. In order to allow the decision maker to vary the protection level, we used the "budget of uncertainty" approach. To solve the np-hard problem, we suggest a hybrid heuristic algorithm combining dynamic programming, ant colony optimization and tabu search. To confirm the performance of the algorithm, two validity tests are done firstly by comparing with the previously solved problems and next by solving a sample problem with more than 900 combinations of parameters and comparing the results with the nominal case. In conclusion, the results of different combinations and prices of robustness are compared and some directions for future researches are suggested finally.

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Air defense is a crucial area for all naval combat systems. In this study, we consider a warship equipped with an air-defense weapon that targets incoming threats using surface-to-air missiles. We define the weapon scheduling problem as the optimal scheduling of a set of surface-to-air missiles of a warship to a set of attacking air threats. The optimal scheduling of the weapon results in an increase in the probability of successful targeting of all incoming threats. We develop a heuristic method to obtain a very fast and acceptable solution for the problem. In addition, a branch and bound algorithm is developed to find the optimal solution. In order to increase the efficiency of this algorithm, a lower bound, an upper bound and a set of dominance rules have been developed. Using randomly generated test problems, the performance of the proposed solution approaches is analyzed. The results indicate that in all practical situations, the branch-and-bound algorithm is able to solve the problem optimally in less than a second.

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A multi-periodic, multi-echelon green supply chain network consisting of manufacturing plants, potential distribution centers, and customers is developed. The manufacturing plants can provide the products in three modes including production in regular time, production in over time, or by subcontracting. The problem has three objectives including minimization of the total costs of the green supply chain network, maximization of the average safe inventory levels of the manufacturing plants and the distribution centers and minimization of the environmental impacts of the manufacturing plants in producing, holding and dispatching the products and also the environmental impacts of the distribution centers in holding and dispatching the products. The problem is first formulated as a mixed-integer mathematical model. Then, in order to solve the model, the augmented weighted Tchebycheff method is employed and its performance in producing the Pareto optimal solutions is compared with the goal attainment method.

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The hub location problems (HLP) constitute an important class of facility location problems that have been addressed by numerous operations researchers in recent years. HLP is a strategic problem frequently encountered in designing logistics and transportation networks. Here, we address the competitive multiple allocation HLP in a duopoly market. It is assumed that an incumbent firm (the leader) is operating an existing hub network in a market and an entrant firm (the follower) tries to enter the market by locating its own hubs aiming at capturing as much flow as possible from the leader. The customers choose one firm based on the service level (cost, time, distance, etc.) provided by the firm. We formulate the problem from the entrant firm’s point of view and propose an efficient tabu search based solution algorithm to solve it. Computational experiments show the capability of the proposed solution algorithm to obtain the optimal solutions in short computing times.

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Over five decades have passed since the first wave of robust optimization studies conducted by Soyster and Falk. It is outstanding that real-life applications of robust optimization are still swept aside; there is much more potential for investigating the exact nature of uncertainties to obtain intelligent robust models. For this purpose, in this study, we investigate a more refined description of the uncertain events including (1) event-driven and (2) attribute-driven. Classical methods transform convex programming classes of uncertainty sets. The structural properties of uncertain events are analyzed to obtain a more refined description of the uncertainty polytopes. Hence, tractable robust models with a decent degree of conservatism are introduced to avoid the over-protection induced by classical uncertainty sets.

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A genetic algorithm is proposed to optimize a tree-structured power distribution network considering optimal cable sizing. For minimizing the total cost of the network, a mixed-integer programming model is presented determining the optimal sizes of cables with minimized location-allocation cost. For designing the distribution lines in a power network, the primary factors must be considered as maximum allowable electrical flow in cables, permitted length of cables, maximum permitted voltage drops, and balance of load. The relationship between rates of electric current and cable sizes with consideration of constraints such as voltage drops and length are our essential data. To create a network with a minimum number of arcs and no closed loop such that all the nodes are covered, a minimum spanning tree technique is utilized. Here, we solve the problem using a genetic optimization algorithm and apply the offered approach to a real problem. By comparing the two extracted results from the proposed approach and an exact method, effectiveness of the genetic algorithm for optimization of power distribution network is shown. To demonstrate the validity of the offered model, a case study in Tehran power distribution company in Iran is made.

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We present a stochastic dynamic programming approach with Markov chains for optimal control of the forest sector. The forest is managed via continuous cover forestry and the complete system is sustainable. Forest industry production, logistic solutions and harvest levels are optimized based on the sequentially revealed states of the markets. Adaptive full system optimization is necessary for consistent results. The stochastic dynamic programming problem of the complete forest industry sector is solved. The raw material stock levels and the product prices are state variables. In each state and at each stage, a quadratic programming profit maximization problem is solved, as a subproblem within the STDP algorithm.

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This paper considers the optimization problem of scheduling jobs with identical sizes on a single batch processing machine. The jobs are divided into some incompatible families where each family contains the jobs with the same processing times and the jobs from different families could not proceed in the same batch. Our optimization problem has two objectives. The first objective is minimizing the weighted number of tardy jobs regarding the due dates of jobs given by customers. The second one aims to minimize operations costs by finding the schedules with the minimum electrical cost consummation under the Time-of-Use tariff policy. A two-objective mixed integer programming mathematical programming is proposed to find optimal solutions for small-size instances of the problem. To solve the medium and large-scale size of the problem, two meta-heuristic algorithms NSGA-II and MOPSO are proposed. The Computational experiments results show that two solution algorithms are capable to find near-optimal solutions at a reasonable computational time. The MOPSO algorithm generate more diverse solutions in less computational time comparing with NSGA II algorithm. But the quality of the solutions obtained by NSGA II algorithm are superior to the ones obtained by MOPSO.