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In this study, a vendor-managed inventory model is developed for a single-vendor multiple-retailer single-warehouse (SV-MR-SV) supply chain problem based on the economic order quantity in which demands are stochastic and follow a uniform probability distribution. In order to reduce holding costs and to help balanced on-hand inventory cost between the vendor and the retailers, it is assumed that all inventory is held at a central warehouse with the lowest cost among the parties. The capacity of the central warehouse is limited. The objective is to find the warehouse replenishment frequency, the vendor\'s replenishment frequency, the order points, and the order quantities of the retailers such that the total inventory cost of the integrated supply chain is minimized. The proposed model is a mixed integer nonlinear programming problem (MINLP); hence, a genetic algorithm (GA) is utilized to solve this NP-hard problem. The parameters of the GA are calibrated using the Taguchi method to find better solutions. Some numerical illustrations are solved at the end to demonstrate the applicability of the proposed methodology and to evaluate the performance of the solution method.

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In this study, a bi-objective model for integrated planning of production-distribution in a multi-level supply chain network with multiple product types and multi time periods is presented. The supply chain network including manufacturers, distribution centers, retailers and final customers is proposed. The proposed model minimizes the total supply chain costs and transforming time of products for customers in the chain. The proposed model is in the class of linear integer programming problems. The complexity of the problem is large and in the literatur, this problem has been shown to be NP-hard. Therefore, for solving this problem, two multi objective meta-heuristic approaches based on Pareto method including non-dominated Sorting Genetic Algorithm-II (NSGA-II) and non-dominated Ranking Genetic Algorithm (NRGA) have been suggested. Since the output of meta- heuristic algorithms are highly dependent on the input parameters of the algorithm, Taguchi method (Taguchi) is used to tune the parameters. Finally, in order to evaluate the performance of the proposed solution methods, different test problems with different dimensions have been produced and the performances of the proposed algorithms on the test problems have been analyzed.