A bi-level programming approach for production-distribution supply chain problem

- A Stackelberg game framework for production-distribution supply chain is proposed.
- Two bi-level programming models for production-distribution supply chain are proposed.
- To tackle the bi-level programming models four hierarchical algorithms are proposed.
- Computational experiments are carried out to analyze the proposed solution procedures.

This paper investigates a decentralized production-distribution supply chain consisting of one manufacturer and one distributor where the demand is jointly influenced by pricing and advertising policies. The control of decision variables is partitioned amongst the members. The manufacturer decides about wholesale price, production interval, expenditure of global advertising, and participation rate in the distributor's local advertising expenditure while the decisions on selling price, local advertising expenditure, and allocation of demands to depots are made by the distributor. We propose a Stackelberg game framework and develop two nonlinear bi-level programming models by switching the leader and follower roles between the manufacturer and the distributor. Four hierarchical solution algorithms are proposed by combining genetic algorithm and particle swarm optimization to tackle the bi-level programming models. Finally, computational experiments are carried out to analyze and compare the efficiency and effectiveness of the proposed solution procedures.