TY - JOUR

T1 - Models for integrated production-inventory systems

T2 - steady state and cost analysis

AU - Otten, Sonja

AU - Krenzler, Ruslan

AU - Daduna, Hans

N1 - Keywords: inventory control, queueing networks, supply chain dynamics, Markovian analysis, separability, product form stationary distribution

PY - 2016/10/17

Y1 - 2016/10/17

N2 - We consider a two-echelon production-inventory system with a central supplier connected to production systems (servers) at several locations, each with a local inventory. Demand of customers arrives at each production system according to a Poisson process and is lost if the local inventory is depleted. To satisfy a customer’s demand, a server at the production system takes exactly one unit of raw material from the associated local inventory. The central supplier manufactures raw material to replenish the local inventories, which are controlled by a continuous review base stock policy. We derive stationary distributions of joint queue length and inventory processes in explicit product form. After performing a cost analysis, we find out that the global search for the vector of optimal base stock levels can be reduced to a set of independent optimisation problems. The explicit form of the stationary distribution enables us to get additional structural insights, e.g. about monotonicity properties and stability conditions. Obtaining the product form relies on some simplifying assumptions. The results are therefore compared with simulations of a more realistic system, which supports to use it as approximation.

AB - We consider a two-echelon production-inventory system with a central supplier connected to production systems (servers) at several locations, each with a local inventory. Demand of customers arrives at each production system according to a Poisson process and is lost if the local inventory is depleted. To satisfy a customer’s demand, a server at the production system takes exactly one unit of raw material from the associated local inventory. The central supplier manufactures raw material to replenish the local inventories, which are controlled by a continuous review base stock policy. We derive stationary distributions of joint queue length and inventory processes in explicit product form. After performing a cost analysis, we find out that the global search for the vector of optimal base stock levels can be reduced to a set of independent optimisation problems. The explicit form of the stationary distribution enables us to get additional structural insights, e.g. about monotonicity properties and stability conditions. Obtaining the product form relies on some simplifying assumptions. The results are therefore compared with simulations of a more realistic system, which supports to use it as approximation.

KW - Business informatics

KW - inventory control

KW - Markovian analysis

KW - product form stationary distribution

KW - queueing networks

KW - separability

KW - supply chain dynamics

UR - http://www.scopus.com/inward/record.url?scp=84941248295&partnerID=8YFLogxK

U2 - 10.1080/00207543.2015.1082669

DO - 10.1080/00207543.2015.1082669

M3 - Journal articles

VL - 54

SP - 6174

EP - 6191

JO - International Journal of Production Research

JF - International Journal of Production Research

SN - 0020-7543

IS - 20

ER -