Dynamic pricing, quality investment, and replenishment model for perishable items

• Published date: 01 July 2019
• Date: 01 July 2019
• Author: Lin Feng
• DOI: http://doi.org/10.1111/itor.12505

Intl. Trans. in Op. Res. 26 (2019) 1558–1575

DOI: 10.1111/itor.12505

INTERNATIONAL

TRANSACTIONS

IN OPERATIONAL

RESEARCH

Dynamic pricing, quality investment, and replenishment model

for perishable items

Lin Feng

School of Economics and Management, Southwest Jiaotong University,Chengdu 610031, Sichuan, China

E-mail: linfeng@swjtu.edu.cn [Feng]

Received 12 March 2017; receivedin revised form 15 September 2017; accepted 29 November 2017

Abstract

The deterioration of perishable items results not only in direct quantitative losses, but also in qualitative

losses, which would reduce the customer acceptability. To maintain or improve the quality level, sellers

usually invest in functionality, aesthetics, safety or any other attributes. In addition to quality, price also

plays a critical role in influencing the purchase choice of consumers and the profit of a firm. Most inventory

management models for perishables are restricted to physical quantity deterioration and do not address

joint dynamic pricing and quality investment strategies. This paper studies an optimal replenishment model

with dynamic pricing and quality investment forperishable products, where the quality and physicalquantity

deteriorate simultaneously. The demand rate is decreasing in sales price and increasing in quality level. A

dynamic optimization model is proposed to maximize the total profitper unit time and solved on the basis of

Pontryagin’s maximum principle. The optimal joint dynamic pricing, quality investment, and replenishment

policy is obtained. A numerical example and sensitivity analysis on the key system parameters are presented

to illustrate the validity of the theoretical results. Some managerial implications for the pricing and quality

investment for the perishables are provided.

Keywords:quality and physical quantity deterioration; dynamic pricing; quality investment; replenishment; Pontryagin’s

maximum principle

1. Introduction

Deterioration refers to decay, change, spoilage, or obsolescence such that the items are not suitable

for their original purpose (Raafat, 1991). Most physical goods undergo deterioration such as

electronic components, alcohol, fresh produce, fashion goods, etc. It will lead to qualitative and

quantitative changes during their normal storage period. The loss of these perishables mainly

stems from inappropriate inventory control, and is up to 15% at grocery retailers (Ferguson and

Ketzenberg, 2006). This will offer a significant opportunity for improvement, and profitability

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L. Feng / Intl. Trans.in Op. Res. 26 (2019) 1558–1575 1559

can be optimized through various efforts such as sales promotion, performance optimization, and

specialized equipment acquisition.

Both from a financial and an operational standpoint, price is one of the most effective variables

that managers can manipulate to influence demand in the short run. It is also a tool that helps

to regulate inventory and replenishment pressures (Bitran and Caldentey, 2003). Advances in in-

formation technologies and the corresponding evolution of the Internet and e-commerce enable

managers to collect market data, learn about customer behavior, and change pricing decisions dy-

namically much easier so as to better match supply with demand. The price differentiation strategy

increases the demand of perishables and reduces obsolescence (Feng et al., 2015). Not surprisingly,

dynamic pricing strategies have been adopted by airlines, fashion retailers, hotels, electric utilities,

and sporting events (Elmaghraby and Keskinocak, 2003).

In addition to sales price, customers are usually sensitive to quality changes of perishables, and

quality degradation reduces their acceptability. The International Organization forStandardization

(ISO) has defined quality as “the totality of features and characteristics of a product or service that

bears its ability to satisfy requirements.” Sensory, nutrition, safety, wholesomeness, and aesthetics

are important attributes of qualitative measures. Timely availability of the product or service is also

the inherent characteristic for customer satisfaction. These features are core criteria to evaluate

a product’s quality and could dramatically influence the purchase choice of consumer (Hsiao

et al., 2017). Provision of high-quality level attracts more consumers to buy the products, but

incurs more cost for improving the quality level. This scheme appears in many industries having

perishables including automobile and food processing industries. For example, food packaging is

used at almost every stage of the food chain to improve its wholesomeness and aesthetics. The

automobile company improves quality by increasing the product’s smoothness and comfort. These

quality improvement strategies have no influence on the deterioration rate of perishables because

their biological and environmental characteristics are not changed. However, these strategies can

make up the degradation of quality and increase consumer satisfaction.

Besides price and quality, establishing the size of inventory is also a major decision of the

firm that sells physical goods. Ordering a large amount of products increases the holding cost

and the possibilities of degradation and potential obsolescence. However, facing a high fixed cost

of replenishment, a large replenishment quantity enables a retailer to reduce the replenishment

frequency. Excelling at replenishment can balance the costs of ordering with the costs of holding

inventory and deterioration.

As mentioned above, pricing, quality investment, and replenishment policies have significant

impacts on a firm’s profitability, especially in the presence of perishable products. These policies

affect and contact mutually (Wang et al., 2017). In this setting, the following natural questions

concerned with management of perishables arise: what are the appropriate pricing and quality

investment policies that lead to a good financial performance of perishable products? How often,

and in what quantities, should the inventory be replenished? What are the impacts of change in per-

ishable characteristic, quality, and cost-related parameters on decisions and profit? Unfortunately,

little justification is given for the joint policy on perishables with quality and physical quantity

deteriorating simultaneously, both in theory and in practice. Due to the dynamics of actual market

and product characteristics, inherent challenges exist in analyzing the above problems. These issues

motivate our study and we formulate a perishable products management model that can decide

the replenishment policy as well as the pricing and quality investment policies. A continuous time

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2018 The Authors.

International Transactionsin Operational Research C

2018 International Federation of OperationalResearch Societies