Optimal pricing of perishable products with replenishment policy in the presence of strategic consumers

Guodong Yi; Xiaohong Chen; Chunqiao Tan

doi:10.3934/jimo.2018112

Article Contents

2019, Volume 15, Issue 4: 1579-1597. Doi: 10.3934/jimo.2018112

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Optimal pricing of perishable products with replenishment policy in the presence of strategic consumers

1.
School of Business, Central South University, Changsha 410083, China
2.
Institute of Big Data and Internet Innovation, Hunan University of Commerce, Changsha 410205, China
3.
School of Business, Central South University, Changsha 410083, China

* Corresponding author: Xiaohong Chen
* Corresponding author: Xiaohong Chen

Received: August 31, 2016

Revised: April 30, 2018

Early access: August 2018

Published: July 2019

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Abstract

Recognizing that strategic consumers have become increasingly common in the perishable products market, we develop a two-stage pricing model for a monopolistic firm with two classes of inventory strategies: non-replenishment and replenishment. First, the retailer mapping out his pricing policy, and then consumers determining their buying behavior given the retailers policy. Our results indicate that the game equilibrium exists between retailers and consumers in both cases. For a given realized price and inventory policy, the consumer's space is split into several areas by the optimal threshold functions. Inventory replenishment decisions are affected by market demand and a decline factor of consumers reservation value. The retailers profit loss is not necessarily related to the consumers waiting behavior but results from the ignorance of this behavior when pricing.

Keywords:

Mathematics Subject Classification: Primary: 90B60; Secondary: 91B06.

Citation:

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Figure 1. Customer types for the case without inventory replenishment¹

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Figure 2. Customer types for the case with inventory replenishment2

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Figure 3. Impact of Pricing Strategies on Consumer Waiting Behavior

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Figure 4. Variation of the Profits of a Seller with an Initial Stock

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Figure 5. Impact of Q and $\lambda$ on the Profits of Sellers

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Figure 6. Profits of a Seller with $\alpha$ Change

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Table 1. Pricing Strategy and Retailer Expected Profits Under Both Scenarios³

Q	$[p_1, p_2]$	Expected profits	Distribution of expected profits
0	[0.419, 0.392]	0.909	(45.4%, 9.8%, 44.8%)
1	[0.548, 0.362]	0.790	(1.1%, 42.8%, 37.5%, 13.4%, 5.1%)

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Table 2. Optimal Pricing and Expected Profit When Customers Are Non-strategic⁴

Q	$[p_1, p_2]$	Expected profits	Distribution of expected profits
0	[0.454 0.357]	0.933	(56.2%, 43.8%)
1	[0.487 0.312]	0.862	(49.8%, 38.7%, 11.5%)

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Table 3. Influence of Consumer Waiting Behavior on Seller Profit⁶

	Case Ⅰ (%)			Case Ⅱ(%)
Q	$\alpha=0.5$	$\alpha=1$	$\alpha=1.5$	$\alpha=0.5$	$\alpha=1$	$\alpha=1.5$
0	-2.61	-10.04	-38.74	-4.95	-11.7	-33.31
1	-9.21	-16.73	-40.92	-4.64	-20.52	-71.89
5	7.08	22.32	52.68	-12.30	-17.79	-43.36

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