Optimizing Supplier Selection and Order Lot-Sizing Decisions in a Two-Stage Supply Chain

This paper analyzes different lot-sizing policies for the supplier selection and order allocation problem in a two-stage supply chain. The supply chain consists of multiple candidate suppliers and a single buyer. In this system, selected suppliers produce a product in batches at finite production rates, ship it to the buyer, and the buyer sells it to the market at a constant demand rate. Our goal is to evaluate two lot-sizing policies and select the one that optimizes the supply chain by minimizing the total cost and maximizing supplier efficiency. A bi-objective mixed-integer nonlinear programming (BOMINLP) model is proposed. The first objective consists of the development of a coordination mechanism for supplier selection and order allocation that minimizes the entire supply chain cost, and the second objective comprises a data envelopment analysis (DEA) approach to evaluate the overall performance of suppliers to optimize supplier efficiency. Then, the lot-for-lot and order frequency policies are applied to the BOMINLP model separately to determine the set of selected suppliers as well as the corresponding order quantities and number of orders allocated to each selected supplier per replenishment cycle. Numerical examples that illustrate the solution approach and compare the two lot-sizing policies are provided.