Journal
ANNALS OF OPERATIONS RESEARCH
Volume -, Issue -, Pages -Publisher
SPRINGER
DOI: 10.1007/s10479-022-05061-z
Keywords
Production-inventory theory; Lost sales; Second order properties; Queueing network theory; Norton's theorem
Categories
Funding
- Projekt DEAL
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This paper investigates a base stock policy for inventory control in a single-item production-inventory system and models the system as a closed Gordon-Newell network. By analyzing the queue length behavior of a two node system, the convexity of the mean queue length in relation to the number of customers is established, leading to the convexity of a standard cost function.
We consider a single-item production-inventory system under a base stock policy for inventory control. We model the system as a closed Gordon-Newell network. The population size of the network is equal to the base stock level, which is the sum of the finished goods and work-in-process inventory. Each exogenous demand, which follows a Poisson process, releases a production order for a new unit and increases the amount of the work-in-process inventory. When there are no items in the finished goods inventory available, arriving demand is lost. The replenishment network operates with state dependent service rates, which we assume to be increasing and concave. First, we analyze the queue length behavior of a two node system and provide conditions under which the mean queue length at the production server is convex in the number of customers in the system. We prove that this leads to convexity of a standard cost function. Using Norton's theorem, we are able to generalize our results for arbitrarily large production-inventory systems.
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