Modeling and Heuristic Solution for Inventory Management Problem Considering Various Transportation Modes

The vendor managed inventory is one of the common policies in supply chain partnership that allows a vendor to place orders on behalf of the customers according to the constraint that are agreed upon a contractual agreement. In this paper, we propose a two-echelon supply chain model consisting of a single vendor and multiple retailers under the VMI strategy which specifies the space limits of the retailer's warehouses and penalty costs for excess of stocks by considering different transportation modes under different capacities. Then, the resulted non-linear programming model by proposing a heuristic method. In this model, retailers’ order cycles are considered independent of each other and also independent of the vendor’s distribution cycle. Furthermore, the costs associated with the variety of the items and their shipping is considered based on the orders quantities and transportation mode. The aim of the proposed model is to determine the quantity of the orders along with the number of shipments received by retailers and transportation mode such that the total inventory and transportation costs of the chain are minimized jointly, especially for large dimension problems in a short time. The exact optimal solution of this model is obtained by coding in common mathematical optimization software, Lingo, and the result is compared with the result derived from our proposed heuristic method. It is found that the running time of the exact solution is highly affected by the increase in the number of the retailers, and the suggested heuristic method is capable of solving the model in a much less time.