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

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 manufact...

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Bibliographic Details
Published inAnnals of operations research Vol. 337; no. 1; pp. 75 - 103
Main Authors Golui, Subrata, Pal, Chandan, Manikandan, R., Sobhanan, Abhay
Format Journal Article
LanguageEnglish
Published New York Springer US 01.06.2024
Springer Nature B.V
Subjects
Algorithms
Business and Management
Combinatorics
Control systems
Customer services
Customers
Dynamic control
Inventory
Inventory management
Iterative algorithms
Markov processes
Operations Research/Decision Theory
Optimal control
Original Research
Probability distribution functions
Queues
Statistical analysis
Theory of Computation
Controlled Markov chain
Cost criterion
Policy iteration algorithm
Primary 93E20
60J27
Value iteration algorithm
Secondary 49L20
Production-inventory system
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Summary: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.
ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-023-05716-5