On the Problem of Production Deadline and Maintenance Outsourcing

Sharafali Moosa, Singapore Management University
Hakan Tarakci, Melbourne Business School

Abstract

In this paper we consider a production-maintenance problem in which a buyer and a supplier have already entered into a contractual relationship for a firm delivery date. Our focus is on the production-related decisions of the supplier rather than the nature of the contract itself. We assume that production rate is actually constant as long as the system is up and running but randomness arises in production due to downtimes as a result of unpredictable failures (breakdowns) and scheduled preventive maintenance activities. Production maintenance is outsourced. As production output is random due to unreliable production facilities, the supplier needs to make two important decisions: (i) how much time to allow for production taking into account the trade off between the penalty fee if actual production time turns out to be longer than the allowed time and the inventory holding cost if the production time is shorter than the allowed time and (ii) how to design the maintenance outsourcing contract to maximize its own profit while satisfying the contractor’s reservation (minimum) profit requirements. This is a finite horizon optimization problem. A regenerative stochastic process is identified and analyzed to develop the cost function over the finite horizon. The optimization problem is illustrated through numerical examples. Some managerial insights with regard to coordination are also provided.