Separable models for interconnected production-inventory systems
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In: Stochastic Models, Vol. 36, No. 1, 02.01.2020, p. 48-93.
Research output: Journal contributions › Journal articles › Research › peer-review
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TY - JOUR
T1 - Separable models for interconnected production-inventory systems
AU - Otten, Sonja
AU - Krenzler, Ruslan
AU - Daduna, Hans
PY - 2020/1/2
Y1 - 2020/1/2
N2 - We investigate a new class of separable systems which exhibit a product-form stationary distribution. These systems consist of parallel production systems (servers) at several locations, each with a local inventory under base stock policy, connected with a common supplier network. Demand of customers arrives at each production system according to a Poisson process and is lost if the local inventory is depleted (“lost sales”). To satisfy a customer’s demand a production server needs raw material from the associated local inventory. The supplier network is a classical queueing network. We investigate two different lost sales regimes, either based on total inventory or on available inventory. We perform cost analysis to find the optimal base stock levels, which is due to the product-form stationary distribution a separable optimization problem. Finally, we demonstrate that the explicit product forms for both stationary distributions enable us to compare main performance metrics of the systems under the different lost sales admission regimes.
AB - We investigate a new class of separable systems which exhibit a product-form stationary distribution. These systems consist of parallel production systems (servers) at several locations, each with a local inventory under base stock policy, connected with a common supplier network. Demand of customers arrives at each production system according to a Poisson process and is lost if the local inventory is depleted (“lost sales”). To satisfy a customer’s demand a production server needs raw material from the associated local inventory. The supplier network is a classical queueing network. We investigate two different lost sales regimes, either based on total inventory or on available inventory. We perform cost analysis to find the optimal base stock levels, which is due to the product-form stationary distribution a separable optimization problem. Finally, we demonstrate that the explicit product forms for both stationary distributions enable us to compare main performance metrics of the systems under the different lost sales admission regimes.
KW - Admission control
KW - base stock policy
KW - inventory control
KW - lost sales
KW - Markovian analysis
KW - product-form steady state
KW - queueing networks
KW - separability
KW - supply chain dynamics
KW - Informatics
KW - Business informatics
UR - http://www.scopus.com/inward/record.url?scp=85076908113&partnerID=8YFLogxK
UR - https://doi.org/10.1080/15326349.2019.1692667
U2 - 10.1080/15326349.2019.1692667
DO - 10.1080/15326349.2019.1692667
M3 - Journal articles
AN - SCOPUS:85076908113
VL - 36
SP - 48
EP - 93
JO - Stochastic Models
JF - Stochastic Models
SN - 1532-6349
IS - 1
ER -