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

Gabi Hanukov, Tal Avinadav, Tatyana Chernonog and Uri Yechiali

International Journal of Production Research, 2021, vol. 59, issue 14, 4384-4402

Abstract: 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.

Date: 2021
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Citations: View citations in EconPapers (6)

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DOI: 10.1080/00207543.2020.1762945

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