Subcontracting price schemes for order acceptance and scheduling

In this paper we study subcontracting price schemes between a subcontractor and a firm that are engaged in subcontracting of heterogeneous orders with distinct due dates, revenues, and processing times. We assume that the subcontractor proposes the subcontracting pricing and the firm follows by determining the subcontracted orders by solving its order acceptance and scheduling problem. When the subcontractor adopts a linear pricing scheme, we find the firm's optimal decisions and develop an algorithm to derive the subcontractor's own optimal pricing. We then design a fixed pricing with transfer payment scheme and a quantity discount pricing scheme to coordinate the firm's and subcontractor's decisions. We examine if the subcontractor can make a higher profit using either of these schemes than the linear pricing scheme, and if they will induce the firm to make decisions that lead to system-wide optimal outcomes.