Optimal inventory policies under decreasing cost functions via geometric programming

Jung, Hyunwoo; Klein, Cerry M.

doi:10.1016/s0377-2217(00)00168-5

Cited by 73 publications

(23 citation statements)

References 10 publications

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“…Also, D=KP -α M β , see Lee and Kim (1993). In these models demand function is not assumed to be constant such as some other researchers done, see (Abad, 1994;Kim & Lee, 1993;Lee et al, 1996;Kim and Lee, 1998;Jung & Klein, 2001;Jung & Klein 2005;Esmaeili et al, 2009). …”

Section: Assumptionmentioning

confidence: 99%

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New Approach of Game Theory for Seller’s Price Selecting Strategies in Bi-Level Programming

Shahanaghi¹,

Rad²

2016

MAS

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The relationships between the members of supply chain were modeled in many researches, such as cooperative and non-cooperative situation. In our paper, the main question is how much and for which price should each seller offer her product to maximize the profit. In the proposed methodology, Bi-level programming is used for modeling and then GAMS (general algebraic modeling system) language for solving the problem. In the presented model, the first level, called upper sub-problem and supposed as leader is trying to maximize each seller profits by obtaining the optimal offered quantity of individual seller. The objective of follower (buyer) is at second level. The lower sub-problem uses the results of the seller's model and then maximizes its profit. These optimizations are obtained with regard to the some other constraints. Similar the other game theories problems, the Nash equilibrium point(s) is (are) the optimum decision of this seller-buyer supply chain. A numerical example is employed to illustrate the application of the proposed method. Keywords: Bi-level programming, Nash equilibrium, seller-buyer, supply chain management 1. Introduction In recent decades, big changes happen in different industries, so more competition is observed in selling markets. Each members of supply chain such as seller and buyer will try to maximize its own profit or on the other hand minimize its costs. In seller-buyer models, the seller produces a product, and after that in a wholesale price sells that to the buyer. Buyer in her turn retails the mention product to the consumer (Yang & Zhou, 2006; Chen et al, 2006;Dai et al, 2005) A wide literature exists on the suppliers' competition and their strategic choices. In categorizing the strategic behavior of seller-buyer supply chain, it could be falls into game theory decision making. Nash equilibrium is one of the solutions which are accepted by all players. Also, using this solution concept is very common. Hence, at first the profit of each seller will be calculated in different possible strategy. Then, after considering the buyer conditions Nash equilibrium points and its optimum selected strategy of each seller would be found. On the other hand the proposed method is a seller selecting with regard to the parameters, decision variables and objects functions of not only sellers but the buyer. Generally, each seller are intended in selling its products as high as it is possible, but exist competition forced seller to offer acceptable prices. The strategy of offering prices of seller depends on other seller (the opponents) behavior, total demand and many other factors. For a seller, it is so significant and critical to select a good price choosing strategy according to its opponents' behavior and other conditions. Hence, it's better for sellers to solve their problem by game theory. The game based methods, which will be used in this article, are more useful in solving these problems. The game based problem solutions can be classified as follows in (Soleymani et al, 2007;Ferr...

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Section: Assumptionmentioning

confidence: 99%

“…In those models demand rate is fixed and seller and buyer both select cooperative condition. Also, Abad (1994), Kim & Lee (1993), Kim & Lee (1998a), Lee & Kim (1998b) and Jung & Klein (2001), Jung & Klein (2005) calculate the optimal price and order quantity by joint lot sizing and pricing approaches. They assumed that price is related to demand.…”

mentioning

confidence: 99%

New Approach of Game Theory for Seller’s Price Selecting Strategies in Bi-Level Programming

Shahanaghi¹,

Rad²

2016

MAS

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“…Applied structures for the power functions in current article were used by many researchers with a little difference (Sadjadi et al 2005(Sadjadi et al , 2010(Sadjadi et al , 2012Lee and Kim 1993;Jung and Klein 2001;Leung 2007;Panda and Maiti 2009).…”

Section: ð1þmentioning

confidence: 99%

“…Chen (2000) used GP technique to determine the quality level, the selling quantity and the purchasing price of a product for the intermediate firms. Jung and Klein (2001) investigated two economic order quantity base in inventory model via GP technique. The very notable thing in this study is deep sensitivity analysis which has been conducted on the models.…”

Section: Introductionmentioning

confidence: 99%

Joint pricing and production management: a geometric programming approach with consideration of cubic production cost function

et al. 2014

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Coordination and harmony between different departments of a company can be an important factor in achieving competitive advantage if the company corrects alignment between strategies of different departments. This paper presents an integrated decision model based on recent advances of geometric programming technique. The demand of a product considers as a power function of factors such as product's price, marketing expenditures, and consumer service expenditures. Furthermore, production cost considers as a cubic power function of outputs. The model will be solved by recent advances in convex optimization tools. Finally, the solution procedure is illustrated by numerical example.

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“…Alpha considers negative price behaviour in the model devised by the article authors (Abad 1994;Lee 1993;Lee et al 1996;Kim, Lee 1998;Jung, Cerry 2001;Jung, Cerry 2005;Esmaeili 2008;Jaafarnejad et al 2012). 3.…”

Section: Assumptionsmentioning

confidence: 99%

Leadership Selection in an Unlimited Three-Echelon Supply Chain

Jia

Mahdiraji

Govindan

et al. 2013

Journal of Business Economics and Management

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Abstract. Supply chain (SC) management aims to increase the overall profit through improvement of various activities and components. Many contradictions between parts and different levels of a SC have been identified in order to achieve overall objectives. Such shortfalls may result in decreased strength and competitiveness of the SC. This paper considers the main conflicts related to inventory, pricing and marketing costs in an unlimited three-echelon supply chain. Aimed at avoiding a profit decrease, the research focuses on finding an equilibrium between inventory, pricing and marketing cost of an unlimited three-echelon SC. On each level, the best leadership option with the greatest payoff is sought for between K retailer, M manufacturer and S supplier. According to Stackelberg non-cooperative game theory, each SC level can become a decision-making leader depending on the available negotiating power. Consequently, three leadership types are modelled on each level and the total SC profit is calculated and compared to ascertain the best option. The authors of the article found that transfer of leadership from a retailer to supplier results in reduction of the total profit. In addition, the research focused on the main effects of parameters used in leadership models. Finally, validation of the proposed model was examined by simulation and Arena software, which indicated that models based on a game theory were performed accurately.

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Optimal inventory policies under decreasing cost functions via geometric programming

Cited by 73 publications

References 10 publications

New Approach of Game Theory for Seller’s Price Selecting Strategies in Bi-Level Programming

New Approach of Game Theory for Seller’s Price Selecting Strategies in Bi-Level Programming

Joint pricing and production management: a geometric programming approach with consideration of cubic production cost function

Leadership Selection in an Unlimited Three-Echelon Supply Chain

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