Optimization of stochastic production-inventory model for deteriorating items in a definite cycle using Hamilton-Jacobi-Bellman equation

• Autorzy: Hau Bui Minh , Kim Hwan-Seong , Long Le Ngoc Bao , You Sam-Sang

Identyfikatory

DOI

10.17270/J.LOG.2022.770

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

production inventory model; deteriorating items; stochastic optimal control; HJB equation

PL

model zapasów produkcyjnych; elementy niszczące; optymalna kontrola stochastyczna; równanie HJB

• Wydawca: Wyższa Szkoła Logistyki
• Czasopismo: LogForum
• Rocznik: 2022
• Tom: Vol. 18, no. 4
• Strony: 397--411
• Opis fizyczny: Bibliogr. 12 poz., rys., tab., wykr.

Twórcy

autor

Hau Bui Minh

• Department of Logistics, Korea Maritime and Ocean University, Busan, Republic of Korea

autor

Kim Hwan-Seong

• Department of Logistics, Korea Maritime and Ocean University, Busan, Republic of Korea

• https://orcid.org/0000-0001-7035-7994

autor

Long Le Ngoc Bao

• Department of Logistics, Korea Maritime and Ocean University, Busan, Republic of Korea

• https://orcid.org/0000-0002-4588-2786

autor

You Sam-Sang

• Division of Mechanical Engineering, Korea Maritime and Ocean University, Busan, Republic of Korea

• https://orcid.org/0000-0003-2660-4630

Bibliografia

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• 2. Alshamrani A.M. (2013). Optimal control of a stochastic production-inventory model with deteriorating items. Journal of King Saud University-Science, 25(1), 7-13. https://doi.org/10.1016/j.jksus.2012.01.004
• 3. Chen J.M. & Lin C.S. (2002), An optimal replenishment model for inventory items with normal distributed. Production Planning & Control, 13(5), 471-480. https://doi.org/10.1080/09537280210144446
• 4. Chung K.J. & Tsai S.F. (2001), Inventory systems for deteriorating items with shortages and a linear trend in demand-taking account of time value. Computer & Operations Research, 28(9), 915-934. https://doi.org/10.1016/S0305-0548(00)00016-2
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• 6. Jamal A.M.M., Sarker B.R., & Wang S. (1997), An ordering policy for deteriorating items with allowable shortage and permissible delay in payment. Journal of the Operational Research Society, 48(8), 826-833. https://doi.org/10.1057/palgrave.jors.2600428
• 7. Krzyżaniak S. (2022), Optimisation of the stock structure of a single stock item taking into account stock quantity constraints, using a LaGrange multiplier, Scientific Journal of Logistics, 18(2). http://doi.org/10.17270/J.LOG.2022.730
• 8. Kumari M. & De P.K. (2022). An EOQ model for deteriorating items analyzing retailer’s optimal strategy under trade credit and returns. An International Journal of Optimization and Control: Theories & Applications, 12(1), 47-55. https://doi.org/10.11121/ijocta.2022.1025
• 9. Li S., Zhang J., & Tang W. (2015), Joint dynamic pricing and inventory control policy for a stochastic inventory system with perishable products. International Journal of Production Research, 53(10), 2937-2950. https://doi.org/10.1080/00207543.2014.961206
• 10. Soni H.N. & Suthar D.N. (2019), Pricing and inventory decisions for noninstantaneous deteriorating items with price and promotional effort stochastic demand. Journal of Control and Decision, 6(3), 191-215. https://doi.org/10.1080/23307706.2018.1478327
• 11. Sethi S.P. & Thompson G.L. (2000). Optimal control theory: Applications to management science and economics, Second ed. Springer New York. https://doi.org/10.1007/0-387-29903-3
• 12. Wee H.M., Chung S.L., & Yang P.C. (2003). Technical note a modified EOQ model with temporary sale price derived without derivatives. The Engineering Economist, 48(2), 190-195. https://doi.org/10.1080/00137910308965060

Uwagi

PL

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).