A Note on a One-Parameter Weibull Distributed Deteriorating Item EOQ Inventory Model with Varying Quadratic Demand and Delay in Payments — Oak Academic Publishing
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A Note on a One-Parameter Weibull Distributed Deteriorating Item EOQ Inventory Model with Varying Quadratic Demand and Delay in Payments
Department of Mathematics, C. V. Raman Global University, Bhubaneswar, India
,
Department of Mathematics, C. V. Raman Global University, Bhubaneswar, India
,
Department of Mathematics, Indian Institute of Technology, Roorkee, India
1 Department of Mathematics, C. V. Raman Global University, Bhubaneswar, India
2 Department of Mathematics, C. V. Raman Global University, Bhubaneswar, India
3 Department of Mathematics, Indian Institute of Technology, Roorkee, India
In this paper, an EOQ inventory model is developed for deteriorating items with variable rates of deterioration and conditions of grace periods when demand is a quadratic function of time. The deterioration rate considered here is a special type of Weibull distribution deterioration rate, i.e. , a one-parameter Weibull distribution deterioration rate and it increases with respect to time. The quadratic demand precisely depicts of the demand of seasonal items, fashion apparels, cosmetics, and newly launched essential commodities like android mobiles, laptops, automobiles etc., coming to the market. The model is divided into three policies according to the occurrence of the grace periods. Shortages, backlogging and complete backlogging cases are not allowed to occur in the model. The proposed model is well-explained with the help of a simple solution procedure. The three numerical examples are taken to illustrate the effectiveness of the EOQ inventory model along with sensitivity analysis.
KeywordsEconomic Order Quantity (EOQ)One-Parameter Weibull Distribution DeteriorationPermissible Delay in PaymentsTime-Dependent Quadratic Demand
Ghare, P.M. and Schrader, G.F. (1963) A Model for Exponentially Decaying Inventories. The Journal of Industrial Engineering , 15, 238-243.
Donaldson, W.A. (1977) Inventory Replenishment Policy for a Linear Trend in Demand—An Analytical Solution. Journal of the Operational Research Society , 28, 663-670. https://doi.org/10.1057/jors.1977.142
Dave, U. and Patel, L.K. (1981) ( T , S i ) Policy Inventory Model for Deteriorating Items with Time Proportional Demand. Journal of the Operational Research Society , 32, 137-142. https://doi.org/10.1057/jors.1981.27
Bahari-Kashani, H. (1989) Replenishment Schedule for Deteriorating Items with Time-Proportional Demand. Journal of the Operational Research Society , 40, 75-81. https://doi.org/10.1057/jors.1989.7
Goswami, A. and Chaudhuri, K.S. (1991) An EOQ Model for Deteriorating Items with Shortages and a Linear Trend in Demand. Journal of the Operational Research Society , 42, 1105-1110. https://doi.org/10.1057/jors.1991.204
Covert, R.P. and Philip, G.C. (1973) An EOQ Model for Items with Weibull Distribution Deterioration. AIIE Transactions , 5, 323-326. https://doi.org/10.1080/05695557308974918
Misra, R.B. (1975) Optimum Production Lot Size Model for a System with Deteriorating Inventory. International Journal of Production Research , 13, 495-505. https://doi.org/10.1080/00207547508943019
Nahmias, S. (1982) Perishable Inventory Theory: A Review. Operations Research , 30, 680-708. https://doi.org/10.1287/opre.30.4.680
Raafat, F. (1991) Survey of Literature on Continuously Deteriorating Inventory Models. Journal of the Operational Research Society , 42, 27-37. https://doi.org/10.1057/jors.1991.4
Goyal, S.K. and Giri, B.C. (2001) Recent Trends in Modeling of Deteriorating Inventory. European Journal of Operational Research , 134, 1-16. https://doi.org/10.1016/s0377-2217(00)00248-4
Li, R., Lan, H. and Mawhinney, J.R. (2010) A Review on Deteriorating Inventory Study. Journal of Service Science and Management , 3, 117-129. https://doi.org/10.4236/jssm.2010.31015
Singh, T., Sahoo, N.C. and Sahoo, C.K. (2016) An EOQ Model for Deteriorating Items with Inventory Dependent Demand and Initial Order Quantity Dependent Deterioration. International Journal of Management Concepts and Philosophy , 9, 306-329. https://doi.org/10.1504/ijmcp.2016.079840
Singh, T., Pattanayak, H., Nayak, A.K. and Sethy, N.N. (2018) An Optimal Policy with Three-Parameter Weibull Distribution Deterioration, Quadratic Demand, and Salvage Value under Partial Backlogging. International Journal of Rough Sets and Data Analysis , 5, 79-98. https://doi.org/10.4018/ijrsda.2018010106
Singh, T., Sethy, N.N., Nayak, A.K. and Pattnaik, H. (2021) An Optimal Policy for Deteriorating Items with Generalized Deterioration, Trapezoidal-Type Demand, and Shortages. International Journal of Information Systems and Supply Chain Management , 14, 23-54. https://doi.org/10.4018/ijisscm.2021010102
Kumar, R. and Yadav, R.K. (2024) Advanced Payment Strategy for EOQ Model Regarding Perishable Product with Maximum Lifetime, Customer Return, Preservation Technology and Partial Backlogging. International Journal of Operational Research , 50, 1-34. https://doi.org/10.1504/ijor.2024.138143
Goyal, S.K. (1985) Economic Order Quantity under Conditions of Permissible Delay in Payments. Journal of the Operational Research Society , 36, 335-338. https://doi.org/10.1057/jors.1985.56
Aggarwal, S.P. and Jaggi, C.K. (1995) Ordering Policies of Deteriorating Items under Permissible Delay in Payments. Journal of the Operational Research Society , 46, 658-662. https://doi.org/10.1057/jors.1995.90
Jamal, A.M.M., Sarker, B.R. and Wang, S. (1997) An Ordering Policy for Deteriorating Items with Allowable Shortage and Permissible Delay in Payment. Journal of the Operational Research Society , 48, 826-833. https://doi.org/10.1057/palgrave.jors.2600428
Ouyang, L., Wu, K. and Yang, C. (2006) A Study on an Inventory Model for Non-Instantaneous Deteriorating Items with Permissible Delay in Payments. Computers & Industrial Engineering , 51, 637-651. https://doi.org/10.1016/j.cie.2006.07.012
Musa, A. and Sani, B. (2012) Inventory Ordering Policies of Delayed Deteriorating Items under Permissible Delay in Payments. International Journal of Production Economics , 136, 75-83. https://doi.org/10.1016/j.ijpe.2011.09.013
Khanra, S., Ghosh, S.K. and Chaudhuri, K.S. (2011) An EOQ Model for a Deteriorating Item with Time Dependent Quadratic Demand under Permissible Delay in Payment. Applied Mathematics and Computation , 218, 1-9. https://doi.org/10.1016/j.amc.2011.04.062
Singh, T. and Pattnayak, H. (2012) An EOQ Model for a Deteriorating Item with Var-ying Time-Dependent Constant Demand and Weibull Distribution Deterioration under Permissible Delay in Payment. Journal of the Orissa Mathematical Society , 31, 61-76.
Singh, T. and Pattanayak, H. (2017) An Optimal Policy for a Deteriorating Item with Generalised Deterioration Rate and Time-Dependent Demand under Permissible Delay in Payment. International Journal of Data Science , 2, 88-104. https://doi.org/10.1504/ijds.2017.084764
Singh, T., Muduly, M.M., Asmita, N., Mallick, C. and Pattanayak, H. (2020) A Note on an Economic Order Quantity Model with Time-Dependent Demand, Three-Parameter Weibull Distribution Deterioration and Permissible Delay in Payment. Journal of Statistics and Management Systems , 23, 643-662. https://doi.org/10.1080/09720510.2019.1681676
Pant, M., Sharma, S. and Chauhan, A. (2022) Optimal Replenishment and Preservation Investment Policy for Hybrid Demand with Trade Credit Schemes. International Journal of Mathematics in Operational Research , 23, 232-258. https://doi.org/10.1504/ijmor.2022.127055
Mohanty, S. and Singh, T. (2023) A Model on an EOQ Optimal Ordering Policy Varying with Time-Dependent Cubic Demand and Variable Deterioration under Delay in Payment Conditions. International Journal of Mathematics in Operational Research , 26, 37-58. https://doi.org/10.1504/ijmor.2023.133714
Mohanty, S., Singh, T., Routary, S.S. and Naik, C. (2024) A Note on an Order Level Inventory Model with Varying Two-Phased Demand and Time-Proportional Deterioration. American Journal of Operations Research , 14, 59-73. https://doi.org/10.4236/ajor.2024.141003
Pal, M. and Ghosh, S.K. (2007) An Inventory Model with Stock Dependent Demand and General Rate of Deterioration under Conditions of Permissible Delay in Payments. OPSEARCH , 44, 227-239. https://doi.org/10.1007/bf03399209
Rout, I., Singh, T. and Nayak, A.K. (2024) An EOQ Inventory Policy Varying with Exponential-Constant-Exponential Demand and Shortages. International Journal of Mathematics in Operational Research , 27, 145-166. https://doi.org/10.1504/ijmor.2024.137037
Swain, P. and Singh, T. (2024) A Note on an EOQ Inventory Model with Varying Time-Proportional Deterioration, Time-Dependent Demand and Shortages under the Conditions of Permissible Delay in Payment. International Journal of Applied Management Science , 16, 89-112. https://doi.org/10.1504/ijams.2024.136147