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Optimal Prices of an M/G/1 Jobshop

Author

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  • Søren Glud Johansen

    (University of Aarhus, Aarhus, Denmark)

Abstract

This paper concerns the optimal control of input to a FIFO jobshop with a single workstation. The input is jobs for which the processing and delivery times are observable upon arrival. The control is exercised by charging a price for each completed job. The objective is either profit maximization or welfare maximization. The semi-Markov decision processes that maximize the two objectives are studied simultaneously. Optimal prices are specified in terms of opportunity costs. The opportunity cost of a job is the expected future loss of earnings caused by having the job submitted to the shop. Results for the cases with and without discounting are established simultaneously by a new approach. It is based on the idea of studying the infinite-horizon model directly and it allows the state space and the decision set to be denumerable. Mild assumptions ensure that the opportunity cost is increasing as a function of the work backlog, and increasing and convex as a function of the processing time.

Suggested Citation

  • Søren Glud Johansen, 1994. "Optimal Prices of an M/G/1 Jobshop," Operations Research, INFORMS, vol. 42(4), pages 765-774, August.
    • Handle: RePEc:inm:oropre:v:42:y:1994:i:4:p:765-774
    DOI: 10.1287/opre.42.4.765
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    Cited by:

    1. Jae‐Dong Son & Yaghoub Khojasteh Ghamari, 2008. "Optimal admission and pricing control problems in service industries with multiple servers and sideline profit," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 24(4), pages 325-342, July.

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