Production scheduling with outsourcing scenarios: a mixed integer programming and efficient solution procedure

When market demand exceeds the company's capacity to manufacture, outsourcing is commonly considered as an effective alternative option. In traditional scheduling problems, processing of received orders is just possible via in-house resources, while in practice, outsourcing is frequently found in various manufacturing industries, especially in electronics, motor and printing companies. This paper deals with the scheduling problem, minimising the cost of outsourcing and a scheduling measure represented by weighted mean flow time, in which outsourcing of manufacturing operations is allowed through subcontracts. Each order can be either scheduled for in-house production or outsourced to an outside supplier in order to meet customer due dates. In this problem, not only should the sequence of orders be determined, but also decision on picking the jobs for outsourcing, selecting the appropriate subcontractor, and scheduling of the outsourced orders are considered as new variables. To formulate the given problem, four different outsourcing scenarios are derived and mixed integer programming models are developed for each one separately. Furthermore, to solve the suggested problem, a computationally effective team process algorithm is devised and then a constraint handling technique is embedded into the main algorithm in order to ensure satisfaction of customer due dates. Numerical results show that the suggested approach possesses high global solution rates as well as fast convergence.