AN ECONOMIC ORDER QUANTITY MODEL FOR DELAYED DETERIORATING ITEMS WITH LINEAR DEMAND RATE AND TWO STORAGE FACILITIES
Keywords:
Two Storage Facilities, Linear Demand Rate, Delayed Deterioration, Economic Order QuantityAbstract
Many inventory models are developed under the presumption that goods begin to deteriorate as soon as they arrive at the warehouse. However, some products, such as dried fruits, cereal grains, etc., have a shelf-life and begin to deteriorate after a period of time. This phenomenon is known as non-instantaneous or delayed deterioration. In addition, situations like price reductions, inexpensive storage, and high demand occur, and one may choose to acquire a large number of goods, creating a storage problem. One should hire a different warehouse to keep the excess inventory because one's own warehouse has a limited storage capacity. In this research, an economic order quantity model for delayed deteriorating items with linear demand and two storage facilities has been investigated. The demand before deterioration sets in is assumed to be time dependent linear demand rate and that after deterioration sets in is assumed to be constant. Shortages are allowed and are completely backlogged. The values of optimal time at which the inventory level reaches zero in OW and optimal cycle length and optimal ordering policy are determined so as to minimize the total variable cost. The optimal solutions' existence and uniqueness are provided with the necessary and sufficient conditions. For each case, various numerical examples are provided to illustrate how the models are applied. The managerial implications of the sensitivity analysis of specific model parameters on optimal solutions are then examined. In the discussions, recommendations are made for lowering the inventory system's total variable cost.
Downloads
References
Silver, E. A. and Meal, H. C. (1969). A simple modification of the EOQ for the case of a varying demand rate. Production and Inventory Management, 10(4), 52–65.
Harris, F. (1913). How many parts to make at once, factory. The Magazine of Management, 10(2), 135–136.
Silver, E. A. and Meal, H. C. (1973). A heuristic for selecting lot size quantities for the case of a deterministic time-varying demand rate and discrete opportunities for replenishment. Production and Inventory Management, 14(1), 64–74.
Donalson, W. A. (1977). Inventory replenishment policy for a linear trend in demand-an analytical solution. Operational Research Quarterly, 28(3), 663–670.
Silver, E. A. (1979). A simple inventory replenishment decision rule for a linear trend in demand. Journal of the Operational Research Society, 30(1), 71–75.
Goswami, A. and Chaudhuri, K. S. (1991). An EOQ model for deteriorating items with a linear trend in demand. Journal of the Operational Research Society, 42(12), 1105–1110.
Usman, Murtala and Babangida J. of NAMP Chakrabarti, T. and Chaudhuri, K. S. (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.
Chakrabarti, T., Giri, B. C. and Chaudhuri, K. S. (1998). A heuristic for replenishment of deteriorating items with time-varying demand and shortages in all cycles. International Journal of Systems Science, 29(6), 551–555.
Ghare, P. M. and Schrader, G. F. (1963). A model for an exponentially decaying inventory. Journal of Industrial Engineering, 14(5), 238–243.
Covert, R. P. and Philip, G. C. (1973). An EOQ model for items with Weibull distribution deterioration. AIIE Transaction, 5, 323-326.
Philip, G. C. (1974). A generalized EOQ model for items with Weibull distribution. AIIE Transactions, 6(2), 159–162.
He, Y., Wang, S.Y. and Lai, K.K. (2010). An optimal production-inventory model for deteriorating items with multiple- market demand. European Journal of Operational Research, 203(3), 593–600.
Sharma, S., Singh, S. and Singh, S. R. (2018). An inventory model for deteriorating items with expiry date and time varying holding cost. International Journal of Procurement Management, 11(5), 650-666.
Taleizadeh, A. A. (2014). An EOQ model with partial back-ordering and advance payments for an evaporating item. International Journal of Production Economics, 155(c), 185–193.
Baraya, Y. M. and Sani, B. (2016). A deteriorating inventory model for items with constant demand rate under warehouse capacity constraint. ABACUS: Journal of the Mathematical Association of Nigeria, 43(2), 180–192.
Tavakoli, S. and Taleizadeh, A. A. (2017). An EOQ model for decaying item with full advanced payment and conditional discount. Annals of Operations Research, 259(3), 1–22.
Chen, Z. (2018). Optimal inventory replenishment and pricing for a single-manufacturer and multi-retailer system of deteriorating items. International Journal of Operational Research, 31(1), 112–139.
Wu, K. S., Ouyang, L. Y. and Yang, C. T. (2006). An optimal replenishment policy for non-instantaneous deterioration items with stock dependent demand and partial backlogging. International Journal of production Economics, 101(2), 369–384.
Geetha, K. V. and Uthayakumar, R. (2010). Economic design of an inventory policy for non-instantaneous deteriorating items under permissible delay in payments. Journal of Computational and Applied Mathematics, 233(10), 2492–2505.
Chang, C. T., Cheng, M. and Ouyang, L. Y. (2015). Optimal pricing and ordering policies for non-instantaneously deteriorating items under order-size-dependent delay in payments. Applied Mathematical Modelling, 39(2), 747–763.
Kumar, S., Malik, A. K., Abhishek, S., Yadav, S. K. and Yashveer, S. (2016). An inventory model with linear holding cost and stock- dependent demand for non-instantaneous deteriorating items. Advancement in Science and Technology AIP Conf. Proc., 1715, 020058.
Palanivel, M., Priyan, S. and Mala, P. (2018). Two-warehouse system for non-instantaneous deterioration products with promotional effort and inflation over a finite time horizon. Journal of Industrial Engineering International, 14, 603-612.
Udayakumar, R. and Geetha, K. V. (2018). An EOQ model for non-instantaneous deteriorating items with two levels of storage under trade credit policy. International Journal of Industrial Engineering, 14(2), 343–365.
Shah, N. H., Soni, H. N. and Patel, K. A. (2013). Optimizing inventory and marketing policy for non-instantaneous deteriorating items with generalized type deterioration and holding cost rates. Omega, 41(2), 421–430.
Jaggi, C. K., Sharma, A. and Tiwari, S. (2015). Credit financing in economic ordering policies for non-instantaneous deteriorating items with price dependent demand under permissible delay in payments: A new approach. International Journal of Industrial Engineering Computations, 6(4), 481–502.
Tsao, Y. C., Zhang, Q., Fang, H. P. and Lee, P. L. (2017). Two-tiered pricing and ordering for non-instantaneous deteriorating items under trade credit. Operational Research International Journal, 19(3), 833–852.
Hartley, R.V., (1976). Operations research—a managerial emphasis. Good Year Publishing Company, Santa Monica, 12,315–317.
Sarma, K. V. S. (1987). A deterministic order level inventory model for deteriorating items with two storage facilities. European Journal of Operational Research, 29(1), 70–73.
Goswami, A. and Chaudhuri, K. S. (1992). An economic order quantity model for items with two-levels of storage for a linear trend in demand. Journal of the Operational Research Society, 43(2), 157–167.
Liang, Y. and Zhou, F. (2011). A two-warehouse inventory model for deteriorating items under conditionally permissible delay in payment. Applied Mathematical Modelling, 35(5), 2221–2231.
Sett, B. K., Sarkar, B., Goswami, A. (2012). A two-warehouse inventory model with increasing demand and time varying deterioration. Scientia Iranica, 19(6), 1969–1977.
Ranja-n, R. S. and Uthayakumar, R. (2015). A two–warehouse inventory model for deteriorating items with permissible delay under exponentially increasing demand. International Journal of Supply and Operation Management, 2(1), 662 -682.
Karthikeyan, K. and Santhi, G. (2015). An inventory model for constant deteriorating items with cubic demand and salvage value. International Journal of Applied Engineering Research, 10, 3723-3728.
Downloads
Published
Issue
Section
License
Copyright (c) 2023 The Journals of the Nigerian Association of Mathematical Physics
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
