Joint optimal pricing and inventory management policy and its sensitivity analysis for perishable products: Lost sale case

Xue Qiao; Zheng Wang; Haoxun Chen

doi:10.3934/jimo.2021079

Article Contents

2022, Volume 18, Issue 4: 2533-2552. Doi: 10.3934/jimo.2021079

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Joint optimal pricing and inventory management policy and its sensitivity analysis for perishable products: Lost sale case

1.
School of Automation, Southeast University, Nanjing, Jiangsu 210096, China
2.
Industrial Systems Optimization Laboratory, University of Technology of Troyes, Troyes 10004, France

^* Corresponding author: Zheng Wang
^* Corresponding author: Zheng Wang

Received: July 31, 2020

Revised: January 31, 2021

Published: July 2022

This work is supported by National Natural Science Foundation of China under grant 61673109

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Abstract

In the real world, the demand cannot be depicted exactly because of customer behavior cannot be forecasted without error. In this paper, we study the effect of the error of the estimated price-demand parameters by analyzing the sensitivity of the optimal joint pricing and ordering policy on the price-demand parameters based on a periodic-review, multi-period and lost sale inventory model for perishable products with constant quantity decay rate and price-sensitive demand. Firstly, we formulate the joint pricing and inventory control problem and find the optimal ordering quantity and the optimal price for deterministic price-demand function. The optimal solutions show that the retailer tends to set a lower price in early periods of each ordering cycle in order to reduce the inventory holding costs. Furthermore, the sensitivity of the optimal joint pricing and inventory control system with respect to the price-demand parameters is examined analytically and evaluated numerically. The sensitivity analysis reveals that compared to the optimal ordering quantity, the optimal prices are less sensitive in the demand-price parameters. Finally, according to the findings of the sensitivity analysis, a heuristic method of regulating the estimated demand-price parameters is employed to improve the average profit. 185 words.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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Figure 1. Proof of the zero-inventory property

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Figure 2. Repetitive ordering cycles

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Figure 3. Change of the optimal ordering cycle

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Figure 4. Sensitivity coefficient of the optimal ordering quantity

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Figure 5. Sensitivity coefficient of the optimal price

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Figure 6. Change of the optimal ordering cycle

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Figure 7. Sensitivity coefficient of the optimal ordering quantity

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Figure 8. Sensitivity coefficient of the optimal price

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Figure 9. Performance of the heuristic regulation method on $ s $

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Figure 10. Performance of the heuristic regulating method on $ \alpha $

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Table 1. Sensitivity analysis on perishability problem

Paper	optimization	Backlog or lost sale or no shortage	Sensitivity analysis objective
Qin et al.[21]	Price, order	No shortage	Decision variables on price-demand parameter and on deterioration function
Lu et al.[18]	Price, order, quality keeping	No shortage	Decision variables on all the system parameters
Chen et al.[3]	Price, order	backlog	Decision variables on decay rate, demand change, holding cost

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Table 2. Sensitivity analysis on perishability problem

$ \Delta s $	$ \Delta \alpha $	$ TP_{{\rm{new}}}^* $
$ \Delta s >0 $	$ \Delta \alpha=0 $	$ TP_{{\rm{new}}}^* \le T{P^*} $
$ \Delta s <0 $	$ \Delta \alpha=0 $	$ TP_{{\rm{new}}}^* \ge T{P^*} $
$ \Delta s=0 $	$ \Delta \alpha >0 $	$ TP_{{\rm{new}}}^* \ge T{P^*} $
$ \Delta s=0 $	$ \Delta \alpha <0 $	$ TP_{{\rm{new}}}^* \le T{P^*} $

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