The Bi-Level Particle Swarm Optimization for Joint Pricing in a Supply Chain

Abstract

This study examines the integration of pricing and lot-sizing strategies within a system comprising only one producer and retailer. The adoption of a bi-level programming technique is justified in establishing a bi-level joint pricing model guided by the producer owing to the hierarchical nature of the supply chain. This problem maximizes manufacturer and retailer profitability by setting the wholesale quantity, lot size, and retail price simultaneously. We created a bi-level particle swarm optimization to solve bi-level programming challenges. This algorithm effectively addresses BLPPS by eliminating the need for any priori assumptions about the conditions of the problem. The bi-level particle swarm optimization algorithm demonstrated a commendable level of efficacy when applied to a set of eight benchmark bi-level issues. The proposed bi-level model was solved using the BPSO and analyzed using experimental data.