An Optimized Single Warehouse Inventory Model for Decaying Goods with Time and Price Dependent Demand and Time Dependent Holding Cost Using the ABC Algorithm
About this article
Keywords:
Inventory Model; Deteriorating Items; Time and Price Dependent Demand; Time-Dependent Holding Cost; Complete Backlogging; Artificial Bee Colony Algorithm; Optimization; Sensitivity AnalysisAbstract
This paper presents a single-warehouse inventory model for items subject to deterioration, where shortages are fully backlogged. The model considers a demand rate that is dependent on both time and selling price, while the holding cost is assumed to be a linear function of time. To enhance the practical applicability of the model, deterioration and shortage costs are also included in the total cost function. The main objective is to minimize the total inventory cost by determining the optimal cycle length and selling price. The Artificial Bee Colony (ABC) algorithm, a nature-inspired metaheuristic, is applied to efficiently solve the nonlinear optimization problem associated with the model. A numerical example illustrates the effectiveness of the proposed approach, and a sensitivity analysis is conducted to examine the impact of key parameters on the total cost. The results demonstrate that the ABC algorithm performs robustly under varying conditions and provides a reliable tool for optimizing inventory decisions involving deteriorating items.
References
Nath, B. K., & Sen, N. (2021). A completely backlogged two-warehouse inventory model for non-instantaneous deteriorating items with time and selling price dependent demand. International Journal of Applied and Computational Mathematics, 7(4), 1–22. https://doi.org/10.1007/s40819-021-01070-x.
Nath, B. K., & Sen, N. (2021). A partially backlogged two-warehouse EOQ model with non-instantaneous deteriorating items, price and time de-pendent demand and preservation technology using interval number. International Journal of Mathematics in Operational Research, 20(2), 149–181. https://doi.org/10.1504/IJMOR.2021.118744.
Verma, V. S., Kumar, V., & Khan, N. A. (2017). An inventory model for Gompertz distribution deterioration rate with ramp type demand rate and shortages. International Journal of Statistics and Systems, 12(2), 363–373.
Ghare, P. M., & Schrader, G. F. (1963). A model for an exponentially decaying inventory. Journal of Industrial Engineering, 14(5), 238–243.
Covert, R. P., & Philip, G. C. (1973). An EOQ model for items with Weibull distribution deterioration. AIIE Transactions, 5(4), 323–326. https://doi.org/10.1080/05695557308974918.
View more references (13)
Misra, R. B. (1975). Optimum production lot size model for a system with deterioration. International Journal of Production Research, 13(5), 495–505. https://doi.org/10.1080/00207547508943019.
Goyal, S. K., & Giri, B. C. (2001). Recent trends in modeling of deteriorating inventory. European Journal of Operational Research, 134(1), 1–16. https://doi.org/10.1016/S0377-2217(00)00248-4.
Hwang, H., Lee, S. H., & Park, Y. S. (1995). Optimal ordering policy under inflation when a delay in payment is permitted. Journal of the Opera-tional Research Society, 46(3), 296–302.
Chang, H. J. (2004). An inventory model under inflation for deteriorating items with stock-dependent consumption rate. Production Planning & Control, 15(2), 178–186.
Buzacott, J. A. (1975). Economic order quantities with inflation. Operational Research Quarterly, 26(3), 553–558. https://doi.org/10.1057/jors.1975.113.
Pal, A. K., & Choudhury, P. K. (2016). A two-warehouse inventory model for deteriorating items with stock-dependent demand under partial backlogging. Mathematics and Computers in Simulation, 121, 37–52.
Khouja, M. (2003). The economic lot and quantity discount scheduling problem for items with deterioration. Computers & Operations Research, 30(2), 283–295.
Raafat, F. (1991). Survey of literature on continuously deteriorating inventory models. Journal of the Operational Research Society, 42(1), 27–37. https://doi.org/10.1057/jors.1991.4.
Hariga, M. A., & Ben-Daya, I. (1999). Optimal inventory replenishment in the presence of time-varying demand and shortages. International Jour-nal of Production Economics, 59(1–3), 45–53.
Singh, S. R., & Saxena, S. P. (2009). An inventory model with price dependent demand and time dependent holding cost. International Journal of Management Science and Engineering Management, 4(3), 219–226.
He, Z., & Liu, H. (2015). An ABC algorithm for solving the inventory optimization problem with constraints. Applied Soft Computing, 34, 351–358.
Karaboga, D. (2005). An idea based on honey bee swarm for numerical optimization (Technical Report-TR06). Erciyes University, Engineering Faculty, Computer Engineering Department.
Karaboga, D., & Basturk, B. (2007). A powerful and efficient algorithm for numerical function optimization: Artificial Bee Colony (ABC) algo-rithm. Journal of Global Optimization, 39(3), 459–471. https://doi.org/10.1007/s10898-007-9149-x.