A Markovian Approach for Stochastic Scheduling in Manufacturing-to-Order Production Systems to Support Due Date Quoting

In the production of complex Manufacturing-to-Order products, uncertainty may stem from a number of possible sources, both internal and external, affecting the execution of the scheduled production activities. A disrupted schedule could incur high costs due to missed due dates, resource idleness, or higher work-in-process inventory. Academic research has investigated robust scheduling approaches trying to assure adequate average performance but, at the same time, robust scheduling must also be able to provide a balanced compromise between expected profit and the protection against extremely unfavorable events having a low occurrence probability. Tackling this problem entails being able of estimating the probability distribution associated with a scheduling objective function. In this paper we propose a markovian approach to estimate the distribution of the completion time of a network of activities with generic stochastic durations. This estimation can serve as a support to the decisions related to the negotiation of due dates with the customers and to the allocation of the inventory budget. The proposed approach is applied to a real industrial case in the machining tool sector