A revised sales rebate contract with effort‐dependent demand: a channel coordination approach

• Author: Javad Asl‐Najafi,Jafar Heydari
• DOI: http://doi.org/10.1111/itor.12556
• Published date: 01 January 2021
• Date: 01 January 2021

Intl. Trans. in Op. Res. 28 (2021) 438–469

DOI: 10.1111/itor.12556

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A revised sales rebate contract with effort-dependent demand:

a channel coordination approach

Jafar Heydaria,∗and Javad Asl-Najafia,b

aSchool of Industrial Engineering, College of Engineering, University of Tehran, Tehran,Iran

bSchool of Industrial Engineering, Iran University of Science and Technology, Tehran,Iran

E-mail: J.Heydari@ut.ac.ir [Heydari]; j_aslnajafi@ind.iust.ac.ir[Asl-Najafi]

Received 12 January 2017; received in revised form 13 January 2018; accepted 10 April 2018

Abstract

In this paper,simultaneous coordination of order quantity and sales effort(SE) decisions in a supplier/retailer

system with stochastic effort-dependent demand is investigated. The main aim of the proposed model is to

attain an optimal balance that results in a Pareto-efficient solution for both channel members. A revised

sales rebate (RSR) contract is developed to achieve channel coordination. In addition to the usual incentive

approach of sales rebateschemes, a punitive approach is designed for the newproposed contract as a stockout

penalty.Furthermore, some numerical experiments are examined to analyze the performance of the presented

model under three decision-making scenarios (i.e., decentralized, centralized, and RSR). Additionally, some

in-depth sensitivity analyses are conducted to examine the behavior of the supply chain performance under

alteration of different parameters. The results show that the proposed RSR contract leads to channel coordi-

nation, while both channel members experience a Pareto improving situation. Moreover, it is proved that the

RSR contract has significant potential on neutralizing adverse impacts of demand fluctuations on channel

performance indicators.

Keywords:supply chain coordination; contracts; sales effort; revised sales rebate; penalty

1. Introduction

In order to implement the holistic view in supply chain (SC) systems, coordination models try to

encourage SC members to make decisions as well as centralized systems. In other words, we can

claim that a channel is coordinated if all of the decision variables gain the values that maximize

the sum of members’ profits (Ingene and Parry, 1995, 2004). The main purposes of coordination

mechanisms are (1) increasing the profitability of total SC in the decentralized mode up to the

∗Corresponding author.

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J. Heydariand J. Asl-Najafi / Intl. Trans. in Op. Res.28 (2021) 438–469 439

amount in the centralized one and (2) realization of a Pareto optimal solution for all SC members

without making any other individual worse off (Heydari et al., 2017). Among the coordination

mechanisms, designing incentive contracts is an efficient method to achieve channel coordination.

Some popular contracts that have been explored in the literature are quantity discount, revenue

sharing, return policies or buyback, credit option or delay in payments, quantity flexibility, option

contract, and sales rebate (SR). Additionally, based on De Giovanni et al. (2016), some other

coordinating solutions exist in the literature that are known as incentive strategies in which the

channel parties deal with the best reply strategies.

Among the mentioned contracts, the SR contract has been investigated less often. Generally, two

kinds of channel rebates have been defined in the coordination literature: (1) linear sales rebate

(LSR) in which the supplier pays a certain rebate for each unit sold by the retailer and (2) target

sales rebate (TSR) in which the supplier pays the retailer for each unit sold beyond the sales target

level. The TSR contract provides a high motivation for the retailer to promote the level of efforts

with the aim of increasing the sales amount. TSR would be a suitable coordinating mechanism for

the SC to overcome problems such as double marginalization (Heydari and Asl-Najafi, 2016). Due

to the direct motivation for the retailer to increase the sales volume, the channel rebates would be

more efficient than other incentive plans, which concentrate on order quantity (Wong et al., 2009).

SR with various forms can be addressed in hardware, software, fashion, and auto industries (Chiu

et al., 2011a). Between 1996 and 1997, companies such as IBM, Compaq, and Hewlett-Packard

decided to shift their channel incentive formulas to rebates that are dependent on the amount of

sales to end customers. Moreover,the channel rebate was implemented by Microsoft, Novell, Lotus,

and Symantec as software developers. Another important aspect of the channel rebate appeared

in the auto industry known as “dealer incentives.” Existing evidence indicates that 13 automakers

including Ford, Mazda, Toyota, Chrysler, General Motors, and so on have used “dealer incentives”

(Taylor, 2002). In fashion industry, “push money” is the term known as a kind of SR that the

suppliers of some national brands like Levi implement on those items they prefer to push to the

market (Chiu et al., 2011a). The mentioned benefits and applications of SR approach persuade the

retailer to apply some direct mechanisms, that is, sales effort (SE), promotions, and even discounted

retail price to increase the sales amount. The consumer’s purchase can be stimulated by applying

some SE methods, such as attractive shelf space provision, free gift, sales team, packaging, and

advertising (Sana, 2013). Readers may refer to Jørgensen and Zaccour (2014) for an analysis of

the advertising methods. An instance for SE is found in famous tablet computer companies, such

as Google, Asus, and Samsung that a power bank or a protective cover is given as a gift to the

clients when they purchase a Nexus 7 or Galaxy Note Pro 12.2 (Tsao, 2015). Other instances are

FedEx and UPS that apply transportation cost discounts to stimulate the consumer demand. A&F

Clothiers and American Eagle provide available shelf space for some particular items to attract the

buyers. Moreover, free trials are offered by Wal-Mart and Target with the aim of sales increment

(Tsao and Sheen, 2012).

In this paper, coordination of a decentralized two-echelon SC with stochastic SE-dependent

demand through a revised sales rebate (RSR) contract is studied. In the proposed RSR contract,

simultaneous punishment and rebate approaches for the retailer have been taken into account.

Because of adverse effectsof inventory shortage on SC performance that can disturb system’sregular

workflow, in the proposed RSR model, a penalty for each unmet demand is attributed. Under both

defined punitive and incentive schemes, which are respectively related to the unmet demands and

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2018 The Authors.

International Transactionsin Operational Research C

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440 J. Heydariand J. Asl-Najafi / Intl. Trans. in Op. Res.28 (2021) 438–469

larger sales amount, the retailer is encouraged to employ more SE and at the same time is forced

to avoid shortage occasions. The adopted solution method ensures achieving an optimal balance in

which at least one member will be better off without making the other one worse off.

Although there are some studies with the combinationof TSR and other complementary contracts

(i.e., return policies) in the related literature, to the best knowledge of the authors, there is no

attempt in the modification of TSR to achieve an efficient contract that is able to overcome more

complicated and realistic situations. In our opinion, adding the punishment approach to the TSR

contract would be a more practical coordination scheme compared to the joint return and rebate

policies. In return policies, transferring items to the supplier is often costly and it can be justified

just when the returned items have enough recycling value. Otherwise, returning the products to the

upstream partner imposes significant costs to the SC, which leads to the reduced profit of total SC.

Of course, some events during the transportation, that is, failure, depreciation, and so on should

not be ignored in return policies. In the meantime, the punishment approach used in our study is

free from all mentioned issues. On the other hand, return policies encourage the retailer to order

more than enough. Obviously, the excess inventory is not suitable for none of the chain members.

Although the punishment approach does not follow the large inventorypolicy, it pursues the enough

inventory policy. It means that the punishment approach motivates the retailer to order as needed

for meeting the market demand. Withthis in mind that the punishment approach does not share the

risk of retailer’s excess inventory with other partners, the retailer would order more cautiously. The

classic TSR contract, which can be defined as a usual SR contract that the upstream pays a certain

rebate to the retailer foreach unit sold over the sales target level, only focuses on increasing the sales

volume and has not a specific plan to control or handle the shortages in the retailer site. However,

when shortages cost for the retailer is negligible, then there is a risk that the retailer makes SE more

than enough (which may cause shortages) to assure the maximum selling amount to exploit rebate.

Regarding the above discussions in this paper, an RSR contract is developed in whichboth incentive

(for selling more than the target level)and punishment (for each unit of unmet demand) approaches

are taken into account simultaneously.

Based on aforementioned descriptions, the contributions in this work that differentiate it from

the other relevant studies are:

rPresenting a revised version of TSR contract that considers punishment approach along with the

rebate one to entice the retailer to make more SE and avoid shortage occasions.

rApplying a practical SE-dependent demand function with individual features.

rProposing a Pareto improving solution procedure that ensures a better (or at least not worse)

situation for all channel members.

The rest of this paper is organized as follows. In Section 2, some practical motivations of pun-

ishment approach are provided. Section 3 addresses a comprehensive literature review. Section 4

contains the notations,model assumptions, and the mathematical modeling under the decentralized,

centralized, and RSR scenarios. In Section 5, we solve the proposed model under the traditional

TSR contract to compare it with RSR. An additional investigation on administrative costs of ap-

plying a novel contract in SCs is briefly discussed in Section 6. An extensive sensitivity analysis has

been performed in Section 7. Finally, concluding remarks, managerial insights, and future research

directions are discussed in Section 8.

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2018 The Authors.

International Transactionsin Operational Research C

2018 International Federation ofOperational Research Societies