Equilibrium Joining Strategies and Optimal Control of a Make-to-Stock Queue

Qingying Li, Pengfei Guo, Chung Lun Li, Jing Sheng Song

Research output: Journal article publicationJournal articleAcademic researchpeer-review

19 Citations (Scopus)


To balance the setup and inventory related costs, the production manager adopts a two-critical-number control policy, where the production starts when the number of waiting customers reaches a certain level and shuts down when a certain quantity of inventory has accumulated. Once the production is set up, the unit production time follows an exponential distribution. Potential customers arrive according to a Poisson process. Customers are strategic, i.e., they make decisions on whether to stay for the product or to leave without purchase based on their utility values, which depend on the production manager's control decisions. We formulate the problem as a Stackelberg game between the production manager and the customers, where the former is the game leader. We first derive the equilibrium customer purchasing strategy and system performance. We then formulate the expected cost rate function for the production system and present a search algorithm for obtaining the optimal values of the two control variables. We further analyze the characteristics of the optimal solution numerically and compare them with the situation where the customers are non-strategic.
Original languageEnglish
Pages (from-to)1513-1527
Number of pages15
JournalProduction and Operations Management
Issue number9
Publication statusPublished - 1 Sept 2016


  • equilibrium analysis
  • make-to-Stock queue
  • strategic customers
  • vacation queue

ASJC Scopus subject areas

  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering
  • Management of Technology and Innovation


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