Throughputs Maximization of Stochastic Customer Orders Under Two Production Schemes

摘要

This paper considers a stochastic customer order scheduling problem to maximize throughputs. Customer orders dynamically arrive at a server station that consists of a set of heterogeneous servers. Each incoming order contains multiple product types with random workloads. These workloads will be processed by the servers under two commonly applied production schemes named workload assignment scheme and server assignment scheme. The objective is to determine the optimal assignments that maximize the long-term stable throughputs. The optimization problems under both production schemes are formulated as corresponding mathematical programs whose adequacy is validated through fluid model analysis. It is further proved that the two programs share the same optimal objective value and their corresponding optimal assignments can be transformed into each other. Based on these results, the equivalency of the two production schemes is established with regard to processing time allocation. Optimal assignments of several important special cases are also explored. The numerical experiment shows that the maximum throughputs can be achieved through the proposed mathematical programs, and demonstrates the equivalency relationship between the two assignment schemes.