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Creative Commons licence CC BY-NC (Attribution-NonCommercial) Logforum. 2022. 18(4), article 2, 397-411; DOI: https://doi.org/10.17270/J.LOG.2022.770

OPTIMIZATION OF STOCHASTIC PRODUCTION-INVENTORY MODEL FOR DETERIORATING ITEMS IN A DEFINITE CYCLE USING HAMILTON-JACOBI-BELLMAN EQUATION

Bui Minh Hau1, Hwan-Seong Kim1, Le Ngoc Bao Long1, Sam-Sang You2

1Department of Logistics, Korea Maritime and Ocean University, Busan, Republic of Korea
2
Division of Mechanical Engineering, Korea Maritime and Ocean University, Busan, Republic of Korea

Abstract:

Background: Inventory control is essential for a manufacturer to achieve the desired profit in successful supply chain management. This paper deals with the production-inventory system under the decrease in production rate. The model includes three stages: before the decrease in production, after the decrease in production, and after a period of inventory shortage. Throughout the stages, the stochastic inventory model is always affected by random factors and the deterioration of inventory quality.

Method: The article uses the economic order quantity (EOQ) framework to evaluate costs in the production-inventory model. To optimize the manufacturer’s profit with the stochastic factor, Hamilton–Jacobi–Bellman (HJB) equation is presented to find the production rate to make the inventory model to guarantee its intended goals in a determined cycle.

Result: Analytical solutions are provided for optimization of the stochastic production-inventory model. Numerical experiments show that inventory level, production rate, and profit over time are based on the optimal initial value of the production rate.

Conclusion: The manufacturer’s profit comes from the stages of importing raw materials, processing and producing, storing and supplying items. Finding the initial value of the production rate can make the inventory level and production rate to ensure their desired value and get the target profit within a specified time.

 

Keywords: Production inventory model, deteriorating items, stochastic optimal control, HJB equation
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For citation:

MLA Hau, Bui Minh, et al. "Optimization of stochastic production-inventory model for deteriorating items in a definite cycle using Hamilton-Jacobi-Bellman equation." Logforum 18.4 (2022): 2. DOI: https://doi.org/10.17270/J.LOG.2022.770
APA Bui Minh Hau, Hwan-Seong Kim, Le Ngoc Bao Long, Sam-Sang You (2022). Optimization of stochastic production-inventory model for deteriorating items in a definite cycle using Hamilton-Jacobi-Bellman equation. Logforum 18 (4), 2. DOI: https://doi.org/10.17270/J.LOG.2022.770
ISO 690 HAU, Bui Minh, et al. Optimization of stochastic production-inventory model for deteriorating items in a definite cycle using Hamilton-Jacobi-Bellman equation. Logforum, 2022, 18.4: 2. DOI: https://doi.org/10.17270/J.LOG.2022.770