Supplier Selection and Order Allocation with Intermodal Transportation Cost

In this paper, a mixed integer non-linear program (MINLP) is proposed for the single item supplier selection, economic lot-sizing, and order allocation problem considering inventory holding, ordering, transportation, and item cost under quantity discount. The proposed MINLP determines the optimal economic lot-size, the allocation of order quantities among suppliers, and the number of trucks. In the proposed MINLP model lead time, the capacity of the supplier and truck, and demand of the product are incorporated as constraints. In order to understand the effect of transportation cost in the selection of suppliers and allocation of order quantities, the model is solved twice with and without the transportation cost function. Finally, the MINLP is solved in AIMMS (Advanced Interactive Multidimensional Modeling System) using its outer approximation algorithm to select the best supplier, to determine the economic lot-size, the corresponding order quantities and number of trucks needed to meet the demand.