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Game-Theoretic Analysis of Coordinating Pricing and Marketing Decisions in a Multi-Product Multi-Echelon Supply Chain

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Game-Theoretic Analysis of Coordinating Pricing and Marketing Decisions in a Multi-Product Multi-Echelon Supply Chain Scientia Iranica E (2016) 23(3), 1459{1473 Sharif University of Technology Scientia Iranica Transactions E: Industrial Engineering www.scientiairanica.com Game-theoretic analysis of coordinating pricing and marketing decisions in a multi-product multi-echelon supply chain A. Naimi Sadigh, S. Kamal Chaharsooghi and M. Sheikhmohammady Department of Industrial Engineering, Faculty of Engineering, Tarbiat Modares University, Tehran, Iran. Received 18 October 2014; received in revised form 10 January 2015; accepted 20 April 2015 KEYWORDS Abstract. Supply chain coordination aims at improving supply chain performance by aligning the decisions and the objectives of individual rms. Supply chain participants can Pricing; cooperate for di erent decisions such as pricing, inventory management, and marketing to Marketing; gain more pro t. The current research considers coordination of these decisions in a multi- Inventory product multi-echelon supply chain composed of multiple suppliers, single manufacturer, management; and multiple retailers. It is assumed that the demand of each product is non-linearly Game theory; in uenced by retailing price and marketing expenditure. Since all the supply chain members Multi-product; possess equal power in the market and make their decisions simultaneously, the three- Multi-echelon supply echelon supply chain problem is a non-cooperative Nash game. In order to nd the chain. Nash equilibrium, we formulate a Non-linear Complementarity Problem (NCP) based on the optimality conditions, and also an iterative algorithm is proposed to solve large- size instances. Finally, a numerical example is presented and a comprehensive sensitivity analysis is conducted to discuss important managerial insights. © 2016 Sharif University of Technology. All rights reserved. 1. Introduction which are investigated in the current research. In real world, supply chains mostly provide multiple A supply chain is a system of di erent rms involved types of products in order to ful ll di erent customer in moving materials and products from suppliers to demands. customers. In three-echelon supply chains, there In this paper, we address a competitive three- are multiple suppliers that provide raw materials to echelon supply chain, in which there are multiple re- manufacturers, the manufacturers produce products tailers who sell di erent products to the end consumers for retailers, and the retailers sell nal products to and spend money for marketing purposes. On the customers. Coordination is an appropriate mechanism second echelon, there is a manufacturer who produces in a decentralized supply chain in order to align the all types of products in a common production interval objectives of di erent supply chain members with the and presents them to the retailers at a wholesale price. goal of improving supply chain performance. Some The manufacturer requires several raw materials which of the most important coordination mechanisms are are purchased from several competing suppliers. In the pricing, marketing, and production decisions [1,2] upstream, there are multiple suppliers who compete to obtain more market share of raw materials needed by the manufacturer. Therefore, we investigate a three- *. Corresponding author. Tel.: +98 21 82883345 E-mail addresses: [email protected] (A. Naimi Sadigh); echelon decentralized model with pricing decisions in [email protected] (S.K. Chaharsooghi); each echelon. The main purpose of this paper is to [email protected] (M. Sheikhmohammady) investigate the coordination of three major decisions 1460 A. Naimi Sadigh et al./Scientia Iranica, Transactions E: Industrial Engineering 23 (2016) 1459{1473 of supply chain members: pricing, marketing, and Zhao [12] developed an EOQ model for deteriorating inventory management in a three-echelon supply chain products with linearly increasing time-varying demand consisting of multiple suppliers, one manufacturer, and under trade credit and presented an ecient solu- multiple retailers. Since all the supply chain members tion algorithm to solve the optimal replenishment possess equal power and determine their strategies cycle. simultaneously, we formulate the model as a Nash Multi-product supply chains are more compli- game in which each player aims to maximize its own cated due to limited production capacity and customer pro t with regard to the actions selected by the other needs [13]. The impact of product variation on supply members. We propose an iterative solution approach chain performance has been studied by Thonemann to nd the equilibrium point of the multi-echelon and Bradley [14]. Song and Xue [15] investigated Nash game with high precision in large-size problem pricing problem of multiple products in dynamic inven- instances. Furthermore, we formulate the Karush- tory environment with backlogging. They developed Kuhn-Tuker (KKT) optimality conditions of the Nash an algorithm to compute the optimal solutions. Zhu game as Non-linear Complementarity Problem (NCP) and Thonemann [16] and Dong et al. [17] studied a as an alternative approach. two-product joint pricing and inventory management The reminder of this paper is structured as fol- problem in which substitution e ect of products was lows. The relevant research is reviewed in Section 2. included to improve the pro t relative to the two Section 3 is devoted to problem description and math- independent products. Maihami and Karimi [18] con- ematical formulation. In Section 4, we propose an sidered the problem of replenishment policy and pricing iterative solution approach and NCP formulation. A decisions for non-instantaneous deteriorating products numerical example with a comprehensive sensitivity subject to promotional e ort. Hsieh et al. [19] con- analysis is discussed in Section 5. The nal section sidered multiple manufacturers and a common retailer includes the concluding remarks and presents several with substitutable product sold through the common extensions for consideration in future research. retailer and the direct channels under decentralized and centralized conditions. The abovementioned research considered only 2. Literature review coordination of pricing and inventory management in Lack of coordination can lead to poor performance of a two-echelon supply chain channel where manufac- supply chain, such as high inventory cost, improper turer(s) and retailer(s) made their decisions. However, utilization of production capacity, and low customer they have not investigated suppliers' echelon. satisfactory [3]. Thereby, some research has studied channel coordination from di erent perspectives of 2.2. Advertising models business decisions, including pricing, marketing expen- Advertisement in supply chain is used to encourage, diture, production, and inventory decisions. However, persuade, or manipulate a customer in order to in- there are a few studies which have considered more crease the demand. Cooperative advertising is a than one aspect of coordination. For a comprehensive nancial agreement where a manufacturer o ers to review on channel coordination, refer to [4]. share a speci c percentage of his retailer's marketing expenditures. Many researchers including Karray [20], 2.1. Coordination of inventory and pricing Kunter [21], and Zhang et al. [22] have studied the models static models that consist of one retailer. Aust and Many researchers have investigated pricing and in- Buscher [23] proposed a vertical cooperative adver- ventory coordination in supply chains. Goyal [5] tising model for duopolistic channel, consisting of presented integrated models for an inventory system multiple retailers and a single manufacturer. Moreover, in which the manufacturer made all replenishment Sayadi and Makui [24] proposed advertising decisions decisions for its retailers to minimize the joint in- for both retail and online channels with one retailer ventory cost. Tersine and Price [6], Martin [7], and and one manufacturer and analyzed the model through Abad [8] proved that the retailer(s) could achieve a di erential game theory approach. more pro ts when coordinating the price and order Another main criterion of mathematical formula- quantity decisions in various environments. Yu et tions in this eld is the demand function. Concerning al. [9], SeyedEsfahani et al. [10], and Esmaeili and the mathematical modeling of advertising costs, it is Zeephongeskul [11] studied joint pricing and order obvious that a linear integration is generally used in inventory problem for pro t optimization with price- terms of advertising expenditures [25,26], while non- dependent demand in a two-echelon supply chain. linear advertising expenditures are rare [27,28]. How- They showed that the supply chain members could ever, as in previous subsection, all the articles reviewed obtain more pro t in comparison with the situation above have studied advertising decisions considering in which they made decisions individually. Wu and duopolistic market. A. Naimi Sadigh et al./Scientia Iranica, Transactions E: Industrial Engineering 23 (2016) 1459{1473 1461 2.3. Nash equilibrium for supply chain games 3. Problem description In order to study the independence of supply chain members, each member tries to improve its own pro t. The problem of this study is a three-echelon supply Non-cooperative game mechanism, especially Nash chain including multiple suppliers, single manufacturer, equilibrium concept, is mostly used to devise di erent and multiple retailers. The suppliers sell multiple raw decisions of supply chain members
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