Optimal control of a dynamic production-inventory system with various cost criteria

Subrata Golui (), Chandan Pal (), R. Manikandan () and Abhay Sobhanan ()
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Subrata Golui: Indian Institute of Technology Guwahati
Chandan Pal: Indian Institute of Technology Guwahati
R. Manikandan: Central University of Kerala
Abhay Sobhanan: University of South Florida

Annals of Operations Research, 2024, vol. 337, issue 1, No 4, 75-103

Abstract: Abstract In this article, we investigate the dynamic control problem of a production-inventory system. Here, demands arrive at the production unit according to a Poisson process and are processed in an FCFS manner. The processing time of the customer’s demand is exponentially distributed. Production manufacturers produce items on a make-to-order basis to meet customer demands. The production is run until the inventory level becomes sufficiently large. We assume that the production time of an item follows an exponential distribution and that the amount of time for the produced item to reach the retail shop is negligible. In addition, we assume that no new customer joins the queue when there is void inventory. Moreover, when a customer is waiting in an infinite FIFO queue for service, he/she does not leave the queue even if the inventory is exhausted. This yields an explicit product-form solution for the steady-state probability vector of the system. The optimal policy that minimizes the discounted/average/pathwise average total cost per production is derived using a Markov decision process approach. We find an optimal policy using value/policy iteration algorithms. Numerical examples are discussed to verify the proposed algorithms.

Keywords: Production-inventory system; Controlled Markov chain; Cost criterion; Value iteration algorithm; Policy iteration algorithm; Primary 93E20; Secondary 49L20; 60J27 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10479-023-05716-5

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