TY - JOUR
T1 - A multi-server system with inventory of preliminary services and stock-dependent demand
AU - Hanukov, Gabi
AU - Avinadav, Tal
AU - Chernonog, Tatyana
AU - Yechiali, Uri
N1 - Publisher Copyright:
© 2020 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
KW - Markov process
KW - economic analysis
KW - matrix geometric analysis
KW - queueing-inventory system
KW - stock-dependent demand
UR - http://www.scopus.com/inward/record.url?scp=85085040733&partnerID=8YFLogxK
U2 - 10.1080/00207543.2020.1762945
DO - 10.1080/00207543.2020.1762945
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:85085040733
SN - 0020-7543
VL - 59
SP - 4384
EP - 4402
JO - International Journal of Production Research
JF - International Journal of Production Research
IS - 14
ER -