Separable models for interconnected production-inventory systems

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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.

Original languageEnglish
JournalStochastic Models
Issue number1
Pages (from-to)48-93
Number of pages46
Publication statusPublished - 02.01.2020

    Research areas

  • Admission control, base stock policy, inventory control, lost sales, Markovian analysis, product-form steady state, queueing networks, separability, supply chain dynamics
  • Informatics
  • Business informatics