Inventory Optimization Model with Quadratic Demand Pattern and Non-instantaneous Deterioration Rate with Mixed Cash and Advance Payment Scheme

Anshu Sharma  lowast; Sumeet Gill; Anil Kumar Taneja

doi:10.17485/IJST/v17i26.688

Article

Inventory Optimization Model with Quadratic Demand Pattern and Non-instantaneous Deterioration Rate with Mixed Cash and Advance Payment Scheme

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v17i26.688

Year: 2024, Volume: 17, Issue: 26, Pages: 2763-2777

Original Article

Inventory Optimization Model with Quadratic Demand Pattern and Non-instantaneous Deterioration Rate with Mixed Cash and Advance Payment Scheme

Anshu Sharma^1∗, Sumeet Gill², Anil Kumar Taneja³

¹Research Scholar, Department of Mathematics, Maharshi Dayanand University, Rohtak, Haryana, India
²Professor, Department of Mathematics, Maharshi Dayanand University, Rohtak, Haryana, India
³Department of Mathematics, Sh. L. N. Hindu College, Rohtak, Haryana, India

*Corresponding Author
Email: [email protected]

Received Date:08 March 2024, Accepted Date:17 June 2024, Published Date:06 July 2024

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objectives: To develop a mathematical model for cost minimization by examining a scenario involving a seasonal product retail market, evaluating the outcome, and providing solutions to unanswered queries of existing models are the highlights of this present work. Methods: 1. Using dynamic differential equations with initial and boundary conditions, we mathematically model a retail market scenario for perishable commodities and determine the retailer's total cost. 2. We consider a quadratic function of time to precisely describe the maintenance cost and demand function. Also, a combination of cash and advance payment schemes is implemented in our model. 3. Our model was numerically formulated using a dataset deduced from earlier research. We have included a sensitivity analysis and a numerical example with a graphical depiction of the total cost function that highlights the most and least influential factors. 4. Based on the Hessian matrix condition and the calculus derivative approach, we developed an algorithm to calculate the optimal cost. Findings: This model provides retailers with insights for effective stock management while optimizing the cost of retailing perishable commodities with non-linear demand patterns. Sensitivity analysis showed that the two factors that have the biggest impact on retailers' overall costs are non-linear demand and holding cost parameters. The smaller optimal inventory cycle time and the large value of time at which a shortage happens raise the overall cost. Additionally, because of higher demand, the time-dependent deterioration rate has the least impact on overall cost. Additionally, a three-dimensional graph of cost minimization is offered to illustrate the convexity of total cost. Novelty: Implementation of Quadratic time-dependent demand and non-linear holding costs under a mixed cash advance payment structure, along with time-dependent deterioration and partial backlog shortages.

Keywords: Quadratic Demand pattern, Noninstantaneous decay rate, Cash and Advance Payment scheme, Partial Backlog Shortages

References

Ghare PM, Schrader GH. A model for exponentially decaying inventory system”. International Journal of Production Research. 1963;21:449–460. Available from: https://cir.nii.ac.jp/crid/1573105974082745472
Sharma A, Kaushik J. Inventory model for deteriorating items with ramp type demand under permissible delay in payment. International Journal of Procurement Management. 2021;14(5):578–595. Available from: https://doi.org/10.1504/IJPM.2021.117292
Poswal P, Chauhan A, Rajoria YK, Boadh R, Goel A. Fuzzy optimization model of two parameter weibull deteriorating rate with quadratic demand and variable holding cost under allowable shortages. Yugoslav Journal of Operations Research. 2022;32(4):453–470. Available from: http://dx.doi.org/10.2298/YJOR220115021P
Swain P, Mallick C, Singh T, Mishra PJ, Pattanayak H. Formulation of an optimal ordering policy with generalised time-dependent demand, quadratic holding cost and partial backlogging. Journal of Information and Optimization Sciences. 2021;42(5):1163–1179. Available from: https://doi.org/10.1080/02522667.2021.1938988
Mashud AHM, Wee HM, Huang CV. Preservation technology investment, trade credit and partial backordering model for a non-instantaneous deteriorating inventory. . RAIRO-Operations Research. 2021;55:51–77. Available from: https://doi.org/10.1051/ro/2019095
Momena AF, Haque R, Rahaman M, Mondal SP. A Two-Storage Inventory Model with Trade Credit Policy and Time-Varying Holding Cost under Quantity Discounts. . Logistics. 2023;7(4):77. Available from: https://doi.org/10.3390/logistics7040077
Shah NH, Keswani M, Khedlekar UK, Prajapati NM. Non-instantaneous controlled deteriorating inventory model for stock-price-advertisement dependent probabilistic demand under trade credit financing. Opsearch. 2024;61(1):421–459. Available from: https://doi.org/10.1007/s12597-023-00701-9
Khan MAA, Halim MA, Alarjani A, Shaikh AA, Uddin MS. Inventory management with hybrid cash-advance payment for time-dependent demand, time-varying holding cost and non-instantaneous deterioration under backordering and non-terminating situations. Alexandria Engineering Journal. 2022;61(11):8469–8486. Available from: https://doi.org/10.1016/j.aej.2022.02.006
Khan MAA, Cárdenas-Barrón LE, Treviño-Garza G, Céspedes-Mota A. Optimizing retailer prepayment installment in inventory systems with link-to-order discounts and power demand patterns of price and time: An effective decision support framework. Expert Systems with Applications. 2024;242:122708. Available from: https://doi.org/10.1016/j.eswa.2023.122708
Khan MAA, Cárdenas-Barrón LE, Treviño-Garza G, Céspedes-Mota A, Loera-Hernández IDJ, Smith NR. Inventory model for livestock farm under quantity discount, power demand, prepayment and carbon rules. Journal of Cleaner Production. 2024;441:140642. Available from: https://doi.org/10.1016/j.jclepro.2024.140642
Khan MAA, Cárdenas-Barrón LE, Treviño-Garza G, Céspedes-Mota A, De J, Loera-Hernández I. Integrating prepayment installment, pricing and replenishment decisions for growing items with power demand pattern and non-linear holding cost under carbon regulations. Computers & Operations Research. 2023;156:106225. Available from: https://doi.org/10.1016/j.cor.2023.106225
Khan MAA, Cárdenas-Barrón LE, Treviño-Garza G, Céspedes-Mota A. Installment for advance payment and pricing decisions for an inventory system under power demand pattern and all-units discount. International Journal of Production Economics. 2023;265:108951. Available from: https://doi.org/10.1016/j.ijpe.2023.108951
Das SC, Ali H, Khan MAA, Shaikh AA, Alrasheedi AF. Inventory model for green products with payment strategy, selling price and green level dependent demand using teaching learning based optimization algorithm. Scientific Reports. 2024;14(1):3033. Available from: https://doi.org/10.1038/s41598-024-53109-w
Khan MAA, Cárdenas-Barrón LE, Smith NR, et-Díaz REB, Loera-Hernández IDJ, Peimbert-García RE, et al. Effects of all-units discount on pricing and replenishment policies of an inventory model under power demand pattern. International Journal of Systems Science: Operations & Logistics. 2023;10(1):2161712. Available from: https://doi.org/10.1080/23302674.2022.2161712
Khan MAA, Cárdenas-Barrón LE, Treviño-Garza G, Céspedes-Mota A, Loera-Hernández IDJ, Smith NR. Effects of variable prepayment installments on pricing and inventory decisions with power demand pattern and non-linear holding cost under carbon cap-and-price regulation. Operations Research Perspectives. 2024;12:100289. Available from: https://doi.org/10.1016/j.orp.2023.100289
Khan MAA, Shaikh AA, Panda GC, Bhunia AK, Konstantaras I. Non-instantaneous deterioration effect in ordering decisions for a two-warehouse inventory system under advance payment and backlogging. Annals of Operations Research. 2020;289:243–275. Available from: https://link.springer.com/article/10.1007/s10479-020-03568-x
Liao JJ, Srivastava HM, Lin SD. Inventory models for non-instantaneous deteriorating items with expiration dates under the joined effect of preservation technology and linearly time-dependent holding cost when order size linked to advance payment. Annals of Operations Research. 2024;p. 1–37. Available from: https://doi.org/10.3390/sym13091695
Saha S, Sen N. An inventory model for deteriorating items with time and price dependent demand and shortages under the effect of inflation. International Journal of Mathematics in Operational Research. 2019;14(3):377–388. Available from: https://doi.org/10.1504/IJMOR.2019.099385
Shaikh AA, Mondal R, Bhattacharyya AN, Kumar N, Mandal G. Analysis of a Two-Storage System for Advance Payment Policies with the Partial Backlogged Shortage. Advances in Industrial Engineering. 2020;54(3):221–242. Available from: https://doi.org/10.22059/jieng.2021.323934.1766
Duary A, Das S, Arif MG, Abualnaja KM, Khan MAA, Zakarya M, et al. Advance and delay in payments with the price-discount inventory model for deteriorating items under capacity constraints and partially backlogged shortages. Alexandria Engineering Journal. 2022;61(2):1735–1745. Available from: https://doi.org/10.1016/j.aej.2021.06.070
Duary A, Khan MAA, Pani S, Shaikh AA, Hezam IM, Alrasheedi AF, et al. Inventory model with nonlinear price-dependent demand for non-instantaneous decaying items via advance payment and installment facility. AIMS Mathematics. 2022;7(11):19794–19821. Available from: https://dx.doi.org/10.3934/math.20221085
Panda GC, Khan MAA, Shaikh AA. A credit policy approach in a two-warehouse inventory model for deteriorating items with price-and stock-dependent demand under partial backlogging. Journal of Industrial Engineering International. 2019;15(1):147–170. Available from: https://link.springer.com/article/10.1007/s40092-018-0269-3
Rahman MS, Khan MAA, Halim MA, Nofal TA, Shaikh AA, Mahmoud EE. Hybrid price and stock dependent inventory model for perishable goods with advance payment related discount facilities under preservation technology. Alexandria Engineering Journal. 2021;60(3):3455–3465. Available from: https://dx.doi.org/10.1016/j.aej.2021.01.045
Mashud AHM. An EOQ deteriorating inventory model with different types of demand and fully backlogged shortages. International Journal of Logistics Systems and Management. 2020;36(1):16–45. Available from: https://doi.org/10.1504/IJLSM.2020.107220

Copyright

© 2024 Sharma et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)