Cooperative Scheduling and Subcontracting Strategies for Products with Yield Decay: A Mixed-Integer Programming Approach

Abstract

This study introduces a mixed-integer programming framework to analyze cooperative scheduling and outsourcing decisions for perishable products affected by yield decay. We study two manufacturers that share a subcontractor, operate under sequence-dependent setup times, and aim to schedule their operations to maximize profit. Three subcontracting strategies are assessed: no subcontracting, non-cooperative subcontracting, and cooperative scheduling. Our illustrative example and extensive numerical experiments across 18 scenarios demonstrate notable efficiency gains. Cooperation improves total supply chain profit by 4.55 % under low setup times and up to 147.37 % under high setup times. Changes in subcontractor costs cause asymmetric profit redistributions, with decreases of 19.6 % for the lead firm and increases of 47.4 % for the follower in the Principal-Agent framework. When tardiness penalties are high, cooperation improves profit by 30.2 % compared to non-cooperation. A probabilistic analysis of subcontractor access indicates that total supply chain profit peaks when the follower has priority, despite this conflicting with individual firm incentives. Conditional Value-at-Risk analysis emphasizes the asymmetric downside risks of decentralization, with one firm being more vulnerable in worst-case scenarios. Overall, these findings highlight the benefits of cooperative subcontracting and underscore the importance of incentive-compatible contracts and risk-sharing mechanisms in shared-capacity environments with time-sensitive yield decay.