Minimizing transportation cost of a joint inventory location model using modified adaptive differential evolution algorithm

Transportation is a key issue in supply chain management and is a major concern for a company. This paper considers a joint-location inventory problem involving a set of suppliers producing different products and a set of retailers where some retailers are treated as distribution centers (DCs). The problem is to determine which retailers to be assigned as DCs, which retailers to receive direct shipments, how much of the retailer's demand to allocate to the DCs, and how much of the DC's demand is to be met by different suppliers. The problem is formulated as a mixed integer model and it has been solved through an adaptive differential evolution algorithm known as modified J. Adaptive Differential Evolution. The solutions obtained are compared with that of simple genetic algorithm. This paper also shows that the proposed model is robust in nature and offers near-optimal results for different distributions. The sum of the cost of establishing some retailers as DCs and the total transportation cost incurred in shipping products from the suppliers to the retailers via DCs(for some retailers) or directly (for the other retailers) is also compared with the total transportation cost incurred when all the products are shipped directly from the suppliers to the retailers.