Integrating the logistics network design with order quantity determination under uncertain customer demands

This paper aims to design an optimal logistics network including suppliers and retailers by taking into account the order quantity of products under uncertain consumer demand pattern. This research proposes a mixed-integer bi-level programming model and employs the iterative-optimization method. In the bi-level programming, the upper model is the logistics network design (LND) problem, which is designed for suppliers and consists of the hub locations, wholesale price of the products as well as the transportation flow of the commodity. The lower model is the order quantity determination (OQD) problem for retailers. It processes a special case of inventory problem in which the customer demand is stochastic and follows a series of assumed probability distributions. By applying the proposed methodology in a computational experiment, this research shows that if there were a large number of suppliers in the logistics system, retailers could order the product with relatively low price and the largest profit belongs to the retailer who could sell the commodity at the highest price.