Prioritized customer order scheduling to maximize throughput

• The two production schemes share the same maximum throughput.
• The optimal assignments can be transformed into each other in polynomial time.
• The two schemes are equivalent in terms of server-time allocation.
• The optimal solutions remain unchanged even when constraints are relaxed.
• Problems under both schemes can be solved through linear programmes.

This study is concerned with a throughput maximization problem of prioritized customer orders. Customer orders with different priorities arrive at a server station dynamically. Each order consists of multiple product types with random workloads. These workloads will be assigned to and processed by a set of unrelated servers. Two commonly applied assignment schemes, named Workload Assignment Scheme (WAS) and Server Assignment Scheme (SAS) are considered. The objective is to determine the optimal assignments under the two assignment schemes to maximize the long-run throughput. Mathematical programming models with relaxed stability constraints are developed for the two assignment schemes, and the adequacy of the programes is guaranteed through fluid limit model analysis. It is shown that these two mathematical programes share the same optimal value, and that there exists a one-to-one correspondence between the optimal assignments. Numerical experiment verifies that the two proposed mathematical programes yield the same optimal throughput, and demonstrates that the corresponding optimal assignments under the two assignment schemes can be transformed into each other.