Effects of extension of subcontracting on a production system in a joint maintenance and production context

This paper considers the problem of subcontracting constraints under a joint maintenance management and production control approach. Our objective is to study the effect of an unforeseen extension of subcontracting duration on a production system provider of subcontracting services.We will study a system with a production unit M subject to corrective maintenance actions, a result of random breakdowns. We perform a preventive maintenance action (PM) for each time T. Corrective and preventive maintenance have random durations. A buffer stock S with a capacity h, is built up with a production rate U in order to satisfy the constant demand d   of the principal costumer, such as Umax>dUmax>d. We note α=Umax-dα=Umax-d, the maximum stock accumulation rate. In addition, the machine M is allocated to perform subcontracting tasks (ST) to a contractor production system, at each moment A1, for a useful duration A2A2, during which it is unavailable for our system. Thus, the machine must satisfy at the same time the constant demand (under a costumer–supplier relationship) and subcontracting tasks (under a contractor–subcontractor relationship).In this context, a mathematical model is developed to determine the impact of an unforeseen extension of subcontracting duration on the generated costs. We will determine the optimal values of T and h   and we will discuss the impact of the extension of a ST with θθ time units.