Cooperative advertising in a capacitated manufacturer–retailer supply chain: a game‐theoretic approach

• Published date: 01 September 2018
• Date: 01 September 2018
• Author: Pooya Hoseinpour,Amir Ahmadi‐Javid
• DOI: http://doi.org/10.1111/itor.12213

Intl. Trans. in Op. Res. 25 (2018) 1677–1694

DOI: 10.1111/itor.12213

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RESEARCH

Cooperative advertising in a capacitated manufacturer–retailer

supply chain: a game-theoretic approach

Amir Ahmadi-Javid and Pooya Hoseinpour

Department of Industrial Engineering, Amirkabir University of Technology, Tehran, Iran

E-mail: ahmadi_javid@aut.ac.ir [Ahmadi-Javid]

Received 23 February2015; received in revised form 4 September 2015; accepted 9 September 2015

Abstract

To achieve a more realistic understanding of how the supply chain’s components interact, it is helpful to con-

sider the operational limitations of the underlying supplychain while analyzing cooperative advertising. This

paper studies cooperative advertisingin a manufacturer–retailer supply chain under the practical operational

assumption that the manufacturer’s production capacity is limited. The retailer advertises locally, and the

manufacturer advertises in national media and supports part of the retailer’s promotional costs. Equilibria

are determined under two different scenarios. In the first scenario, both retailer and manufacturer move

simultaneously, while in the second scenario, they move sequentially, with the manufacturer being the leader.

The sales function is a bivariate version of the diminishing returns response function. When the production

capacity is unlimited, several important properties can be proven, which cannot be shown analytically for

the existing sales functions. Considering the production-capacity constraint leads to new managerial insights

into cooperative advertising.For example, only if the production capacityis large enough, both manufacturer

and retailer are better off under the second scenario than the first scenario. In other words, the sequential

move is not necessarily Pareto-improving when the production capacity is limited. It is also observed that,

under the first scenario, there are multiple equilibria whenever the production capacity is not too high. Under

the second scenario, the manufacturer supports the retailer only when the retailer’s margin is relatively small

compared to the manufacturer’s margin and production capacity.

Keywords:application of game theory; cooperative advertising; supply chain management; production capacity

1. Introduction

Cooperative advertising is a vertical coordination mechanism in a supply chain. To encourage

sales of a supply-chain product, manufacturers and retailers advertise nationally and locally. In

cooperative advertising, the manufacturers prefer to contribute to the retailers’ advertising costs

for practical purposes, such as strengthening brand image and motivating immediate sales (see

Hutchins, 1953; Bergen and John, 1997).

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1678 A. Ahmadi-Javid and P. Hoseinpour / Intl. Trans.in Op. Res. 25 (2018) 1677–1694

Several papers have studied cooperative advertising models featuring static relationships. These

models can be classified as either price-insensitive or price-sensitive. In price-insensitive models,

prices are known and the sales volume depends only on advertising efforts; see, for example, Berger

and Magliozzi (1992), Karray and Zaccour (2007), Huang and Li (2001), and Ahmadi-Javid and

Hoseinpour (2011, 2012). However, in price-sensitive models, the sales volume depends on both

advertising efforts and retail price; see, for example, Karray and Zaccour (2006), Xie and Neyret

(2009), Xie and Wei (2009), Szmerekovsky and Zhang (2009), Zaccour (2008), and Yan (2009).

Unlike static cooperative advertising models, the environment in dynamic game-theoretic models

changes dynamically, and players should adapt their decisions by learning from the game history.

Moreover, the sales volume is typically modeled as a function of the advertising goodwill stock

(brand image), which evolves according to an ordinary differential equation. For more on this

topic, one may refer to, for example, Karray and Zaccour (2005), Jørgensen et al. (2006), He et al.

(2009), and Zhang et al. (2013).

In this paper,our focus is on a price-insensitive static cooperative advertising model. For a review

of the various game-theoretic models developed for cooperative advertising, the reader may refer to

recent surveys by Aust and Buscher (2014) and Jørgensen and Zaccour (2014).

In all the papers dealing with (static or dynamic) cooperative advertising, it is commonlyassumed

that the manufacturer has an unlimited production capacity, which may be quite unrealistic. In

practice, a manufacturernormally cannot produce beyond a known finite capacity, and development

of this capacity is either impossible or incurs a considerable establishment cost. This led us to study

the case of price-insensitive vertical cooperative advertising in a capacitated supply chain with one

retailer and one manufacturer, wherethe manufacturer advertises globally and shares in the retailer’s

local advertising. The manufacturer has a limited production capacity, which implies that local and

global advertising efforts should not result in sales volume that surpasses this production capacity.

The problem under different scenarios is studied using game theory.

The paper is organized as follows. Section 2 presents the notation and mathematical model.

Section 3 presents the analyses of the model under two scenarios: simultaneous and sequential

moves. Section 4 discusses the managerial implications of this research. Section 5 considers the

coordination problemfor the case where the Nash game has multiple equilibria. Section 6 concludes

the paper, and Section 7 provides the proofs.

2. Model description

Consider a supply chain with one retailer and one manufacturer. The gross profits of the retailer

and manufacturer, denoted by πr(a,q,t)and πm(a,q,t), respectively, are determined as follows:

πr(a,q,t)=ρrS(a,q)−(1−t)a

πm(a,q,t)=ρmS(a,q)−ta −q,

where S(a,q)is the sales function. The decision variables and parameters are defined as follows:ais

the retailer’slocal advertising expenditures; qis the manufacturer’sinvestment in the national brand,

including national advertising costs; tis the fraction of the total local advertising expenditure that

the manufacturer agrees to share with the retailer (0≤t≤1);ρmis the manufacturer’s marginal

profit for each product unit; and ρris the retailer’s marginal profit for each product unit.

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2015 The Authors.

International Transactionsin Operational Research C

2015 International Federation of OperationalResearch Societies