We examine a stochastic resource allocation problem where simultaneously servers are partitioned into parallel work centers and job types are assigned to the work centers. Each job type has a distinct Poisson arrival rate and a distinct work-in-process (WIP) weight. The goal is to minimize the expected total WIP cost. Both identical server and non-identical server problems are considered.

When servers are identical, each work center is a queueing system with an exponential service time distribution. The problem is solvable in polynomial time if a job type can be divided between the work centers, and NP-hard if dividing job types is not allowed. When there are two servers and job types cannot be divided, a heuristic is constructed where the relative error is bounded above by 4/3. Analysis demonstrates that the heuristic finds an optimal solution for a large class of problem instances. When there are multiple work centers and job types cannot be divided, a heuristic is constructed where the relative error is bounded above by 1+e.

When servers are non-identical, the server assignment discipline has a significant impact on the WIP cost. Tight lower and upper bounds of the expected system time function are explored. Heuristics are constructed for the random available server assignment discipline and the fastest available server assignment discipline. Theoretical bounds are developed for the relative errors of the heuristics. The relative error for the random available discipline is bounded above by a function of the service rate. The relative error for the fastest available discipline is bounded above by the number of servers. Also, heuristic performance is empirically evaluated.

Dr. Hui-Chih Hung is a Post-Doctoral Researcher in Department of Industrial and Systems Engineering at the Ohio State University, where he received his Ph.D. in Operations Research. He received his Master’s degree in Mathematics from National Tsing Hua University and his Bachelor’s degree in Mathematics from National Taiwan University in Taiwan. Dr. Hung’s doctoral research is in the area of layout design and stochastic resource allocation. A portion of this work has been submitted to Queueing Systems and Operations Research for publication. Some of his current research interests include ecology networks and resilient optimization. This work is supported by OSU\'s Center for Resilience and the Environmental Protection Agency.