Article ID: | iaor201524696 |
Volume: | 23 |
Issue: | 3 |
Start Page Number: | 489 |
End Page Number: | 503 |
Publication Date: | Mar 2014 |
Journal: | Production and Operations Management |
Authors: | Kolisch Rainer, Barz Christiane |
Keywords: | management, allocation: resources, programming: markov decision, simulation, queues: applications, programming: linear |
We formulate a discrete time Markov decision process for a resource assignment problem for multi‐skilled resources with a hierarchical skill structure to minimize the average penalty and waiting costs for jobs with different waiting costs and uncertain service times. In contrast to most queueing models, our application leads to service times that are known before the job is actually served but only after it is accepted and assigned to a server. We formulate the corresponding Markov decision process, which is intractable for problems of realistic size due to the curse of dimensionality. Using an affine approximation of the bias function, we develop a simple linear program that yields a lower bound for the minimum average costs. We suggest how the solution of the linear program can be used in a simple heuristic and illustrate its performance in numerical examples and a case study.