Stochastic Scheduling of Machining Centers Production, Estimating the Makespan Distribution

In the scheduling of manufacturing systems, uncertain events are rather the rule than the exception and are the main responsible of cost increase due to missed due dates, resource idleness, higher work-in-process inventory. Robust scheduling approaches aim at devising schedules insensitive, at least to some degree, to the occurrence of uncertain events. However, robust scheduling must always deal with finding a balanced compromise between expected profit and the protection against extremely unfavorable events having a low occurrence probability. Tackling this problem implies being able of estimating the distribution probability associated with a scheduling objective function, or at least some of its quantiles. In this paper we propose a Markovian approach to estimate the distribution of the completion time of a general network of activities. Grounding on this estimation, an estimation of the objective function distribution can be easily calculated. To demonstrate its viability, the proposed approach is applied to a real industrial case in the machining tool sector.