Production scheduling with subcontracting: the subcontractor’s pricing game

This paper studies a two-stage game with a manufacturer and a subcontractor who are faced by a production scheduling problem. The manufacturer has a set of jobs to process, a subset of which can be subcontracted to the subcontractor to reduce the tardiness cost. In the game, the subcontractor makes the first decision to ask for a unit price of his machine time to be used by the manufacturer, and then the manufacturer follows to decide which jobs to be subcontracted to process and how the production scheduling is made. We analyze the game and derive how the subcontractor can optimize the unit price to maximize his profit. We then investigate the performance of such a simple contract from the viewpoint of coordination, and propose two other contracts that can achieve coordination between the two players.