Stochastic customer order scheduling to minimize long-run expected order cycle time

This study considers a dynamic customer order scheduling problem in stochastic setting. Customer orders arrive at the machine station dynamically according to a Poisson process. Each order consists of multiple product types with random workloads. Each order’s workloads will be assigned to and processed by a set of unrelated parallel machines. The objective is to determine the optimal workload assignment which minimizes the long-run expected order cycle time. Through the Fork–Join queue model, a lower bound on the objective function is established by stochastically comparing the original system to other queueing systems with less complex service structures. This proposed lower bound is proved to be equal to the optimal objective value in two important sub-classes of the problem. Inspired by the design of the lower bound, three polynomial-time heuristic algorithms are proposed. The effectiveness of the lower bound and the scheduling heuristics is demonstrated through computational experiment. This study brings new perspective to the stochastic modeling of the order scheduling problem and suggests ways to enhance the effectiveness of various managerial options for improving production efficiency.