Channel coordination with price discount mechanism under price‐sensitive market demand

• Date: 01 September 2020
• Published date: 01 September 2020
• DOI: http://doi.org/10.1111/itor.12678

Intl. Trans. in Op. Res. 27 (2020) 2509–2533

DOI: 10.1111/itor.12678

INTERNATIONAL

TRANSACTIONS

IN OPERATIONAL

RESEARCH

Channel coordination with price discount mechanism under

price-sensitive market demand

Sumon Sarkara, Sunil Tiwarib,∗, Hui-Ming Weecand B.C. Giria

aDepartment of Mathematics, Jadavpur University,Kolkata 700032, West Bengal, India

bThe Logistics Institute – Asia Pacific, National Universityof Singapore, 21 Heng Mui Keng Terrace, Singapore119613,

Singapore

cDepartment of Industrial and Systems Engineering, Chung Yuan Christian University,200 Chung-Pei Rd., 32023,

Chung-li, Taiwan

E-mail: ss.sumonsarkar@gmail.com [Sarkar]; sunil.tiwari04@gmail.com [Tiwari];weehm@cycu.edu.tw [Wee];

bibhas_pnu@yahoo.com [Giri]

Received 8 May2018; received in revised form 23 February 2019; accepted 26 April 2019

Abstract

This paper considers a two-echelon supply chain with single vendor single buyerfor trading a single product.

The buyer’s demand has been assumed to be price-sensitive. We have assumed three-level inspection at the

vendor’s end in orderto maintain good quality of the items delivered to the buyer. Wehave developed models

for both decentralized and centralized scenarios and have determined the optimal solution using the basic

concepts of analytic geometry and algebra. In addition, we have proposed a price discount mechanism, where

the vendor has provided discounts on the purchase cost to the buyer against the buyer’s (increased) order

quantity. Finally, in order to illustrate and validate the proposed model, a numerical example and sensitivity

analysis is carried out, which has providedsome important managerial implications. It has been observedfrom

the numerical study that the proposed price discount policy coordinates the supply chain and has improved

the profitability of the supply chain and its members.

Keywords:supply chain; coordination; price discount; price-sensitive demand; variable back-order

1. Introduction

A supply chain (SC) is a combination of collection of raw materials, converting it into the final

product by manufacturers, movements of the product through distributors, sold by retailers to end-

customers. It can be categorized into centralized and decentralized. In a centralized supply chain,

all the decisions on behalf of the supply chain members are taken by one decision maker, whereas

in a decentralized supply chain, the objective of every member is to optimize its profit without

∗Corresponding author.

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2019 International Federation ofOperational Research Societies

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2510 S. Sarkar et al. / Intl. Trans.in Op. Res. 27 (2020) 2509–2533

considering the entire supply chain’s profit. However,it seems hypothetical that only a single decision

maker has been handling and managing the entire supply chain efficiently. Therefore, to improve

the efficiency of a supply chain, significant coordination is required. Hence, achieving effective

coordination between the vendor and the buyer has become an important managerial concern as

well as an important research issue. To increase sales volume, the vendor often gives efforts that

may influence the buyer’s behavior. For example, the vendor may offer various discounts so that the

buyer ordersmore than his economic order quantity, which directlymaximizes channel profit. Proper

demand analysis is another important aspect of improvingsupply chain profit. Factors such as price

of the commodity, after-sales service, advertisement, and quality of the product have been directly

influencing market demand of the product. For example, in the telecommunication sector, Apple is

well known for its product quality and high price, whereas Samsung and Lenovo are renowned for

their new features at relatively lower prices. Customers who prefer quality over cost will naturally

go for Apple’s products. Similarly, customers who prefer features and lower prices would prefer

Samsung or Lenovo products. Product quality depends on the manufacturer’s production processes

and also on the raw material quality. Therefore, if the manufacturer wants to produce high-quality

products, both manufacturing process and raw material quality play an important role. However,

higher quality components may involve higher prices. It is, therefore, necessary to make a balance

between price and quality in order to optimize the profit. In this study, we have incorporated price

dependency of demand into our supply chain model. The production-delivery supply chain models

have often assumed that the quality of product is constantly perfect. However, in practice, this

assumption for any production model is rarely satisfied as a productionsystem often produces some

defective products due to incomplete processcontrol, long run of the machine without maintenance,

or sometimes due to human mistakes. The appearance of those defective products in a production

lot may deviate from the planned strategies to infeasible due to unexpected early shortage and high

quality related cost. Sometimes, due to the appearance of poor quality of items in the received lot,

the buyer might disagree to coordinate with the vendor. Therefore, inspection at different stages of

manufacturing before delivery is an essential factor to achieve the required quality of the product.

Keeping in mind the importance of inspection and product quality, we have considered three-level

inspection in our model. Here, the vendor does inspection in three stages: (a) initial check, (b)

inspection during production, and (c) final inspection check before delivery to ensure that the buyer

will receive a good-quality item.

The paper is organized as follows. Section 2 provides a brief description of the literature review.

Section 3 provides the mathematical model. In Section 4, we provide a numerical example and

sensitivity analysis in order to validate the proposed model. Finally, in Section 5, we conclude the

paper by summarizing the work.

2. Literat ure review

During the last few decades, the concept of integrated vendor–buyer inventory management has

attracted considerableattention of many supply chain researchers. The cooperation among vendors

and buyers for improving the performance of the supply chain has been the key point of their

research. The objective of developing an integrated vendor–buyer model is to avoid the act of max-

imizing profits independently by supply chain members. Consequently, determining joint ordering

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2019 The Authors.

International Transactionsin Operational Research C

2019 International Federation ofOperational Research Societies