A multi-server system with inventory of preliminary services and stock-dependent demand

Gabi Hanukov, Tal Avinadav, Tatyana Chernonog, Uri Yechiali

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


This study is motivated by industries in which products can be partially prepared and stored before demand occurs, while demand is stock-dependent. We study a multi-server system in which the servers utilise their idle time to produce and store ‘preliminary services’ (PSs) in order to reduce customers’ sojourn time and, as a result, stimulating demand by creating the anticipation of a shorter sojourn time. In order to facilitate closed-form solutions, we analyse a Markovian queueing-inventory model and apply matrix geometric (MG) methods. In contrast to most applications in which the rate matrix R of the MG analysis is calculated numerically, our analysis enables derivation of explicit solutions for the entries of R and discovers their relation to Catalan numbers, allowing a rapid solution for large systems. Consequently, the system’s stability condition is readily obtained and shown to be identical to that of a regular M/M/s queue. Two models are developed: one for non-perishable PSs, the other for perishable ones. An economic analysis is provided for two case studies: a bike store and a pizza store. We observe that the reward has low sensitivity to deviation from the optimal PSs capacity and high sensitivity to deviation from the optimal promotional level.

Original languageEnglish
Pages (from-to)4384-4402
Number of pages19
JournalInternational Journal of Production Research
Issue number14
StatePublished - 2021
Externally publishedYes


  • Markov process
  • economic analysis
  • matrix geometric analysis
  • queueing-inventory system
  • stock-dependent demand


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