Inbound Logistic Planning: Minimizing Transportation and Inventory Cost

In today's competitive environment, supply chain management is a major concern for a company. Two of the key issues in supply chain management are transportation and inventory management. To achieve significant savings, companies should integrate these two issues instead of treating them separately. This paper considers the problem of selecting the appropriate distribution strategy for delivering a family of products from a set of suppliers to a set of plants so that the total transportation, pipeline inventory, and plant inventory costs are minimized. With reasonable assumptions, a simple model is presented to provide a good solution that can serve as a guideline for the design and implementation of the distribution network. Due to the plant inventory cost, the problem is formulated as a nonlinear integer programming problem. The problem is difficult to solve because the objective function is highly nonlinear and neither convex nor concave. A greedy heuristic is proposed to find an initial solution and an upper bound. A heuristic and a branch-and-bound algorithm are developed based on the Lagrangian relaxation of the nonlinear program. Computational experiments are performed, and based on the results we can conclude that the performance of the algorithms are promising.