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"ABSTRAKIn this paper, we modelled a multi-product four-level integrated supply chain network problem consisting of a supplier, a producer, a wholesaler, and multiple retailers. The aims of this paper are both to find the number of optimum stockpiles in each level and the optimum period length such that the total cost of the chain is minimized while constraints such as limited procurement cost, limited space, and limited ordering cost are satisfied. Mentioned problem is a large non linear programming problem so a developed sequential quadratic programming (SQP) is used to solve the problem. Next, three numerical examples are solved in order to demonstrate the applicability of the proposed methodology and also to evaluate the performance of SQP. At the end, a sensitivity analysis is performed on the change rate of the integrated objective function obtained based on the change rate of the period length."

"This paper provides a developed mathematical model to derive the optimal integrated lot sizing in a multi-level supply chain with imperfect quality products. The developed mathematical model has a bi-objective function, with conflicting goals, minimizing the chain inventory costs and maximizing the chain total profit aided to find optimum policy for integrated lot sizing. We further actualize the problem by assuming multiple stochastic constraints. The mathematical formulation of the problem is stochastic, nonlinear, and large. In this regard, the interior point algorithm that is developed as more effective algorithm with less iteration is used for solving the recent convex nonlinear model. Numerical example shows that the developed interior point method is an efficient method with excellent performance in terms of the quality of the solution. Also, Sensitivity analysis shows that the developed interior point method is an efficient method with excellent performance in terms of the quality of the solution."

"ABSTRACTThis paper proposes a multi-product Vendor-Managed Inventory (VMI) supply chain inventory model by considering defective items. In this way, vendor purchases different kinds of products from a remote supplier and then delivers them to the retailer. On the other hand, delivered batches have some imperfect items while there is no access to the supplier to replace them. Consequently, there are two options to face imperfect items in order to satisfy the demand, buy or repair. Additionally, some innovations and contributions in this paper are Join Replenishment Policy, all units discount, different alternatives for shipping goods and backlogging shortage. They result in a novel VMI model that is as close as possible to the real world. Since, the proposed problem was NP-complete, two evolutionary algorithms are developed to solve it, Genetic Algorithm (GA) and imperialist Competitive Algorithm (ICA). After calibrating their main parameters by Taguchi approach, their performance is compared by solving numerical examples."