In-house production and outsourcing under different discount schemes on the total outsourcing cost

In this paper we consider a coordinated in-house production scheduling and outsourcing model, where a manufacturer might outsource part of the production to a subcontractor so as to achieve a tight production due date. The manufacturer pays a specific outsourcing cost for each job that is outsourced. To encourage the manufacturer to outsource more jobs, the subcontractor provides a specific discount scheme on the total outsourcing cost. Previous studies focus on the balance between in-house production performance and the total outsourcing cost. Our model is the first to investigate the impact on the manufacturer’s decision-making under different discount schemes on the total outsourcing cost. Four distinct discount schemes on the total outsourcing cost are studied. We either show the intractability of those problems, or provide efficient exact or approximation algorithms.