Partial myopia vs. forward-looking behaviors in a dynamic pricing and replenishment model for perishable items

Musen Xue; Guowei Zhu

doi:10.3934/jimo.2019126

Article Contents

2021, Volume 17, Issue 2: 633-648. Doi: 10.3934/jimo.2019126

This issue Previous Article Competition in a dual-channel supply chain considering duopolistic retailers with different behaviours Next Article Supplier's investment in manufacturer's quality improvement with equity holding

Partial myopia vs. forward-looking behaviors in a dynamic pricing and replenishment model for perishable items

Musen Xue^1, and
Guowei Zhu^2, ,

1.
School of Management, Tianjin Normal University, Tianjin 300387, China
2.
Business School, Hunan University, Changsha, Hunan 410082, China

^* Corresponding author: Guowei Zhu
^* Corresponding author: Guowei Zhu

Received: November 2018

Revised: July 2019

Early access: October 28, 2019

Published online: October 28, 2019

The first author is supported by the Tianjin Philosophy and Social Sciences Planning Year Project grant TJGLQN17-010; The second author is supported by National Natural Science Foundation of China grant 71871089.

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Abstract

This paper studies a dynamic pricing and replenishment problem for perishable items considering the behavior of decision-maker (partially myopic or forward-looking) and the dynamic effects of cumulative sales. A dynamic optimization model is presented to maximize the total profit per unit time and solved on the basis of Pontryagin's maximum principle. The optimal pricing and replenishment strategies for partially myopic and forward-looking scenarios are obtained. By comparing the partially myopic and forward-looking strategies through numerical analysis, we find the main results: First, applying a skimming pricing strategy might be a good choice when the saturation effects are considered. Second, the decreasing rate of product sales, deterioration coefficient, and holding cost of perishable items per unit exhibit impact on the behavioral preference of decision-maker. Under certain conditions, partially myopic behavior can bring more profit than forward-looking behavior. These managerial implications provide useful guidelines for the decision-maker.

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Mathematics Subject Classification: Primary: 49J52, 49M30.

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Figure 1. The unit time total profits $ J_m(T) $ and $ J_f(T) $ versus $ T $

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Figure 2. The optimal pricing strategies $ p^*_m $ and $ p^*_f $ versus $ t $

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Figure 3. The effect of $ \delta $ on the unit time total profits $ J_m $ and $ J_f $

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Figure 4. The effect of $ \theta $ on the unit time total profits $ J_m $ and $ J_f $

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