Optimization of single outsourcer–single subcontractor outsourcing relationship under reliability and maintenance constraints

In this paper, we focus on outsourcing activities optimization problem in single period setting. In some situations, capacity planning or outsourcing is a one-time event and can be modeled as a single period problem. The aim of this research is to balance the trade-off between two echelons of a supply chain consisting of a single outsourcer and a single subcontractor. Each part is composed of a failure-prone single machine that produces one product type to satisfy market requirements. The outsourcer’s manufacturing system is not able to satisfy the demand; in this case, outsourcing is allowed to recover the lack of capacity. We consider that the subcontractor can satisfy the demands of strategic clients and rent his machine for the outsourcer under a win–win partnership contract. We assume that the hazard failure rate depends on time and the adopted manufacture rate. When unforeseen failures occur, minimal repairs are implemented. Overhaul can be performed to reduce the degradation effects. Hence, we develop a mathematical model to define a profitability interval so that both parties of supply chain can be considered as winners. We seek to determine the contract parameters that suit both parties (duration, start and end dates, the production and outsourcing rates). Then, we develop an exact algorithm to solve the problem of single period optimization, which offers a better execution time through a series of test problems. Finally, we consider a sensitivity analysis based on outsourcing parameters (cost, periodicities, etc) to analyze their effects on partial costs and individual profit of each part, as well as the total profit generated by the system.