A modeling framework and local search solution methodology for a production-distribution problem with supplier selection and time-aggregated quantity discounts.

Highlights • We model a new quantity discounts supply chain planning problem. • The model is very hard to solve using leading commercial solvers. • We develop MIP-based local search algorithms for our problem. • We apply our model to a realistic food supply chain. • We show the efficiency of our algorithms in getting high quality solutions quickly. Abstract Supplier selection with quantity discounts has been an active research problem in the literature. In this paper, we focus on a new real-world quantity discounts scheme, where suppliers are selected in the beginning of a strategic planning period (e.g., 5 years). Monthly orders are placed from the selected suppliers, but the quantity discounts are based on the aggregated annual order quantities. We incorporate this type of cost structure in a multi-period, multi-product, multi-echelon supply chain planning problem, and develop a mixed integer linear programming (MIP) model for it. Our model is highly intractable; leading commercial solvers cannot construct high quality feasible solutions for realistic instances even after multiple hours of solution time. We develop an algorithm that constructs an initial feasible solution and a large neighborhood search method that combines two customized iterative algorithms based on MIP-based local search and improves such solution. We report numerical results for a food supply chain application and show the efficiency of using our methodology in getting very high quality primal solutions quickly. [ABSTRACT FROM AUTHOR]