A game theoretic approach for two echelon supply chains with continuous depletion

Supply chain members coordinate with each other in order to obtain more profit. The major mechanisms for coordination among supply chain echelons are pricing, inventory management, and ordering decisions. Regarding to these mechanisms, supply chain participants have conflicts of interest. This paper concerns coordination of enterprise decisions including pricing, advertising, ordering, and inventory decisions in a multi-echelon supply chain consisting of multiple suppliers, one manufacturer, and multiple retailers. In the current study, a novel inventory model is presented for both the manufacturer, and the retailers who are able to determine the number of orders for each product. Moreover, each supply chain member has equal power and make their decisions simultaneously. The proposed model considers the relationships among three echelon supply chain members based on a non-cooperative Nash game with pricing and inventory decisions. An iterative solution algorithm is proposed to find Nash equilibrium point of the game. Several numerical examples are presented to study the application of the model as well as the effectiveness of the algorithm. Finally, a comprehensive sensitivity analysis is performed and some important managerial insights are highlighted.2010 Mathematics Subject Classification. Primary: 91A10, 90B60, 90B05.

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“…(i) [24] show his objective function of buyer is strictly pseudo concave. Simply we replace Equation (19) of their paper (A = ψ…”

Section: Appendix Amentioning

confidence: 99%

A game theoretic approach to coordination of pricing, advertising, and inventory decisions in a competitive supply chain

Sadigh¹,

Chaharsooghi²,

Sheikhmohammady³

2015

JIMO

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“…Proof. See Naimi Sadigh et al [37]. According to proposition 1, since the objective function is pseudo concave, the optimal values of the decision variables are obtained when the partial derivatives of the objective function vanish.…”

Section: The Optimality Conditions For the Retailersmentioning

confidence: 99%

Optimal pricing and advertising decisions with suppliers' oligopoly competition: Stakelberg-Nash game structures

Naimi-Sadigh¹,

Chaharsooghi²,

Mozafari³

2021

Journal of Industrial &Amp; Management Optimization

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This paper addresses the coordination of pricing, advertising, and production-inventory decisions in a multi-product three-echelon supply chain composed of multiple suppliers, single manufacturer, and multiple retailers. The demand of each product is considered to be non-linearly influenced by the retail price and advertising expenditure. Taking into account the dominant power of the manufacturer and the suppliers' oligopoly competition, this paper aims at obtaining the equilibrium prices at each level of the supply chain and comparing two different scenarios of competitions and cooperation: The former focuses on the situation where the single manufacturer has the dominant power in the supply chain and acts as the leader followed by the retailers and the suppliers simultaneously. The latter implies the situation in which the dominant manufacturer enters cooperation with each independent retailer to boost sales while the suppliers play the role of the followers simultaneously. We develop the Stackelberg-Nash game (SNG), and the Stackelberg-Nash game with cooperation (SNGC) formulations to model the two market structures. The equilibrium decisions are achieved through the optimization methods and the existence and uniqueness properties are explored. Finally, analytical and computational analyses are carried out through a numerical example, and a comprehensive sensitivity analysis is conducted to discuss some managerial insights such as increasing competition among suppliers leads to reducing retail prices.2010 Mathematics Subject Classification. Primary: 91B25, 91A12, 91A40; Secondary: 90B60, 90B30, 90B05.

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“…Proof. In order to prove the pseudo-concavity of the retailers' objective functions, we use the approach presented by Naimi Sadigh et al [43] due to the similarity of the retailers' objectives with the buyer's objective in their model. Since the bene t function of each retailer is separable, we can replace Eq.…”

Section: Appendix B Propositionmentioning

confidence: 99%

Game-theoretic analysis of coordinating pricing and marketing decisions in a multi-product multi-echelon supply chain

2016

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Supply chain coordination aims at improving supply chain performance by aligning the decisions and the objectives of individual rms. Supply chain participants can cooperate for di erent decisions such as pricing, inventory management, and marketing to gain more pro t. The current research considers coordination of these decisions in a multiproduct multi-echelon supply chain composed of multiple suppliers, single manufacturer, and multiple retailers. It is assumed that the demand of each product is non-linearly in uenced by retailing price and marketing expenditure. Since all the supply chain members possess equal power in the market and make their decisions simultaneously, the threeechelon supply chain problem is a non-cooperative Nash game. In order to nd the Nash equilibrium, we formulate a Non-linear Complementarity Problem (NCP) based on the optimality conditions, and also an iterative algorithm is proposed to solve largesize instances. Finally, a numerical example is presented and a comprehensive sensitivity analysis is conducted to discuss important managerial insights.

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A game theoretic approach for two echelon supply chains with continuous depletion

Cited by 8 publications

References 10 publications

A game theoretic approach to coordination of pricing, advertising, and inventory decisions in a competitive supply chain

A game theoretic approach to coordination of pricing, advertising, and inventory decisions in a competitive supply chain

Optimal pricing and advertising decisions with suppliers' oligopoly competition: Stakelberg-Nash game structures

Game-theoretic analysis of coordinating pricing and marketing decisions in a multi-product multi-echelon supply chain

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