Separable models for interconnected production-inventory systems

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.

Subjects

Admission control

base stock policy

inventory control

lost sales

Markovian analysis

product-form steady state

queueing networks

separability

supply chain dynamics

DDC Class

000: Allgemeines, Wissenschaft

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Separable models for interconnected production-inventory systems