Inventory model with nonlinear price-dependent demand for non-instantaneous decaying items via advance payment and installment facility

Avijit Duary; Md. Al-Amin Khan; Sayan Pani; Ali Akbar Shaikh; Ibrahim M. Hezam; Adel Fahad Alrasheedi; Jeonghwan Gwak; Avijit Duary; Md. Al-Amin Khan; Sayan Pani; Ali Akbar Shaikh; Ibrahim M. Hezam; Adel Fahad Alrasheedi; Jeonghwan Gwak

doi:10.3934/math.20221085

AIMS Mathematics

2022, Volume 7, Issue 11: 19794-19821. doi: 10.3934/math.20221085

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Research article

Inventory model with nonlinear price-dependent demand for non-instantaneous decaying items via advance payment and installment facility

1.
Department of Mathematics, Maulana Abul Kalam Azad University of Technology, Haringhata 741249, West Bengal, India
2.
Department of Mathematics, Jahangirnagar University, Savar, Dhaka 1342, Bangladesh
3.
Department of Mathematics, The University of Burdwan, West Bengal, India
4.
Department of Statistics & Operations Research, College of Sciences, King Saud University, Riyadh, Saudi Arabia
5.
Department of Software, Korea National University of Transportation, Chungju 27469, South Korea
6.
Department of Biomedical Engineering, Korea National University of Transportation, Chungju 27469, South Korea
7.
Department of AI Robotics Engineering, Korea National University of Transportation, Chungju 27469, South Korea
8.
Department of IT & Energy Convergence (BK21 FOUR), Korea National University of Transportation, Chungju 27469, South Korea

Received: 27 April 2022 Revised: 04 August 2022 Accepted: 10 August 2022 Published: 07 September 2022
MSC : 90B05

Determining the joint pricing and ordering policy is a challenging task for policy-makers dealing with perishable items. This research deals with the inventory coordination for a decaying commodity under a non-linear price-sensitive demand structure where the policy-maker completes the payment partially in advance, exploiting the multiple installments facility to control supply disruptions. Moreover, an inventory-out situation is incorporated to make the model more representative; shortages are backlogged partially through a variable rate in exponential form, depending on the customer waiting times. Though the formulated inventory coordination creates a highly complex optimization problem, the existence of the joint optimal pricing and ordering policy is explored by developing several theoretical outcomes. Three numerical illustrations are adopted to ensure the effectiveness of the model in providing the joint optimal pricing and ordering policy for the decision manager. Furthermore, to visualize the concavity of the average profit of the policy manager, as well as to demonstrate the adequacy of the optimum condition, MATLAB software was utilized. Finally, sensitivity studies for known key parameters are done using graphic presentation and a few supportive guidelines for the manager are also shown. The inventory manager should motivate the supplier to allow a higher installment frequency to implement the prepayment regulation, thus reducing the capital cost against the prepayment amount.
- EOQ,
- non-linear price-dependent demand,
- non-instantaneous decay items,
- advance payment,
- partial backlogged shortages
Citation: Avijit Duary, Md. Al-Amin Khan, Sayan Pani, Ali Akbar Shaikh, Ibrahim M. Hezam, Adel Fahad Alrasheedi, Jeonghwan Gwak. Inventory model with nonlinear price-dependent demand for non-instantaneous decaying items via advance payment and installment facility[J]. AIMS Mathematics, 2022, 7(11): 19794-19821. doi: 10.3934/math.20221085

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Abstract

Determining the joint pricing and ordering policy is a challenging task for policy-makers dealing with perishable items. This research deals with the inventory coordination for a decaying commodity under a non-linear price-sensitive demand structure where the policy-maker completes the payment partially in advance, exploiting the multiple installments facility to control supply disruptions. Moreover, an inventory-out situation is incorporated to make the model more representative; shortages are backlogged partially through a variable rate in exponential form, depending on the customer waiting times. Though the formulated inventory coordination creates a highly complex optimization problem, the existence of the joint optimal pricing and ordering policy is explored by developing several theoretical outcomes. Three numerical illustrations are adopted to ensure the effectiveness of the model in providing the joint optimal pricing and ordering policy for the decision manager. Furthermore, to visualize the concavity of the average profit of the policy manager, as well as to demonstrate the adequacy of the optimum condition, MATLAB software was utilized. Finally, sensitivity studies for known key parameters are done using graphic presentation and a few supportive guidelines for the manager are also shown. The inventory manager should motivate the supplier to allow a higher installment frequency to implement the prepayment regulation, thus reducing the capital cost against the prepayment amount.

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