# Economic Order Quantity (EOQ) for Perishable Goods with Weibull Distribution and Exponential Demand Rate Proportional to Price

## Authors

• Motunrayo Bankole Department of Statistics, Federal University of Technology, Akure, Nigeria
• Adegoke S Ajiboye Department of Statistics, Federal University of Technology, Akure, Nigeria
• Osafu Augustine Egbon Department of Statistics, Federal University of Technology, Akure, Nigeria
• Jumoke Popoola Department of Statistics, University of Ilorin, Ilorin Nigeria

## Keywords:

economic order quantity, exponential demand rate, perishable goods, weibull distribution

## Abstract

Business organizations that deal with consumable and perishable items have consistently incurred enormous loss as a result of the nature of their goods. The losses have direct negative impact on revenues. Unplanned and lack of precise production prediction models are responsible for this. An appropriate prediction model, developed to guide production plan and processes will help manufacturers in deciding which product to make and in what quantity. In this study, the Economic Order Quantity (EOQ) for perishable goods with Weibull lifetime distribution and exponential demand rate proportional to price was developed for perishable goods. The differential equations governing the instantaneous state of inventory in the interval [0, t2] were obtained and solved for the equation of the quantity of inventory at time t. Using fixed parameters for the weibull and exponential distributions, simulation study was conducted on the derived EOQ model using R programming language. The simulation shows that the EOQ increases with increase in Weibull parameter. Real data on six loafs of bread obtained from Afe Babalola University bakery was used to illustrate how the model works. Result shows a good fit to the data and the average EOQ ranges from 60 to 400 loafs with ordering times of either 1 or two days interval. The pattern of EOQ varies between type of loafs of bread. The EOQ model developed is shown by this result to be appropriate for perishable goods with weibull lifetime distribution and exponential demand rate proportional to price.

## References

Bhunia, A. K., & Maiti, M. (1998). A two warehouse inventory model for deteriorating items with a linear trend in demand and shortages. Journal of the Operational Research Society, 49(3): 287–292.

Chakrabarti, T., & Chaudhuri, K. (1997). An EOQ model for deteriorating items with a linear trend in demand and shortages in all cycles. International Journal of Production Economics, 49(3): 205–213.

CHUNG, K.-J., & TING, P.-S. (1994). On replenishment schedule for deteriorating items with time-proportional demand. Production Planning & Control, 5(4): 392–396.

Covert, R. P., & Philip, G. C. (1973). An EOQ model for items with Weibull distribution deterioration. AIIE Transactions, 5(4): 323–326.

Datta, T., & Pal, A. (1990). A note on an inventory model with inventory-level-dependent demand rate. Journal of the Operational Research Society, 41(10): 971–975.

Dave, U., & Patel, L. (1981). (T, S i) policy inventory model for deteriorating items with time proportional demand. Journal of the Operational Research Society, 32(2): 137–142.

Díaz, R. D. S., Paternina-Arboleda, C. D., Martínez-Flores, J. L., & Jimenez-Barros, M. A. (2020). Economic order quantity for perishables with decreasing willingness to purchase during their life cycle. Operations Research Perspectives, 7: 100146.

Ghare, I. and PM and Schrader, G. F.(1963) A Model for Exponentially Decaying Inventory. Journal of Industrial Engineering. 14. 238, 243.

Giri, B. C., Jalan, A., & Chaudhuri, K. (2003). Economic order quantity model with Weibull deterioration distribution, shortage and ramp-type demand. International Journal of Systems Science, 34(4): 237–243.

Hariga, M. (1995). An EOQ model for deteriorating items with shortages and time-varying demand. Journal of the Operational Research Society, 46(3): 398–404.

Hariga, M. A., & Benkherouf, L. (1994). Optimal and heuristic inventory replenishment models for deteriorating items with exponential time-varying demand. European Journal of Operational Research, 79(1): 123–137.

Harris, F. W. (1915). Operations and costs (Factory Management Series). Aw Shaw Co., Chicago.

Heng, K. J., Labban, J., & Linn, R. J. (1991). An order-level lot-size inventory model for deteriorating items with finite replenishment rate. Computers & Industrial Engineering, 20(2): 187–197.

Hollier, R., & Mak, K. (1983). Inventory replenishment policies for deteriorating items in a declining market. International Journal of Production Research, 21(6): 813–836.

Hung, K.-C. (2011). An inventory model with generalized type demand, deterioration and backorder rates. European Journal of Operational Research, 208(3): 239–242.

Jalan, A., & Chaudhuri, K. (1999). Structural properties of an inventory system with deterioration and trended demand. International Journal of Systems Science, 30(6): 627–633.

Manna, S. K., & Chaudhuri, K. (2006). An EOQ model with ramp type demand rate, time dependent deterioration rate, unit production cost and shortages. European Journal of Operational Research, 171(2): 557–566.

Muriana, C. (2016). An EOQ model for perishable products with fixed shelf life under stochastic demand conditions. European Journal of Operational Research, 255(2): 388–396.

Patriarca, R., Di Gravio, G., Costantino, F., & Tronci, M. (2020). EOQ inventory model for perishable products under uncertainty. Production Engineering, 14(5): 601–612.

Philip, G. C. (1974). A generalized EOQ model for items with Weibull distribution deterioration. AIIE Transactions, 6(2): 159–162.

Sachan, R. (1984). On (T, S i) policy inventory model for deteriorating items with time proportional demand. Journal of the Operational Research Society, 35(11): 1013–1019.

Singh, S., & Banerjee, S. (n.d.). Economic Order Quantity Model for Perishable Items Having Exponentially Increasing Demand.

Skouri, K., Konstantaras, I., Papachristos, S., & Ganas, I. (2009). Inventory models with ramp type demand rate, partial backlogging and Weibull deterioration rate. European Journal of Operational Research, 192(1): 79–92.

Wagner, H. M., & Whitin, T. M. (1958). Dynamic version of the economic lot size model. Management Science, 5(1): 89–96.

Wilson, R. (1934). A scientific routine for stock control. Harvard Univ.

Wu, K.-S. (2001). An EOQ inventory model for items with Weibull distribution deterioration, ramp type demand rate and partial backlogging. Production Planning & Control, 12(8): 787–793.

2022-08-31

## How to Cite

Bankole, M., Ajiboye, A. S., Egbon, O. A., & Popoola, J. (2022). Economic Order Quantity (EOQ) for Perishable Goods with Weibull Distribution and Exponential Demand Rate Proportional to Price. Indonesian Journal of Statistics and Its Applications, 6(2), 261–269. https://doi.org/10.29244/ijsa.v6i2p261-269

Articles