A Game Theoretical Analysis for the Quantity Discount Problem with Weibull Ameliorating Items
This paper presents a model for determining optimal all-unit quantity discount strategies in a channel of one seller (poultry farmer) and one buyer (retailer). The poultry farmer’s stock increases due to the growth of items. In contrast, the retailer purc
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Abstract This paper presents a model for determining optimal all-unit quantity discount strategies in a channel of one seller (poultry farmer) and one buyer (retailer). The poultry farmer’s stock increases due to the growth of items. In contrast, the retailer purchases items as fresh chicken meat from the poultry farmer, the inventory level of the retailer is therefore depleted due to the combined effects of its demand and deterioration. The poultry farmer attempts to increase her profit by controlling the retailer’s ordering schedule through a quantity discount strategy. We formulate the above problem as a Stackelberg game between the poultry farmer and the retailer to analyze the existence of the poultry farmer’s optimal quantity discount pricing policy, which maximizes her total profit per unit of time. Numerical examples are presented to illustrate the theoretical underpinnings of the proposed formulation. Keywords Ameliorating items Stackelberg game Total profit
Deteriorating items Weibull distribution
Quantity discounts
H. Kawakatsu (&) Department of Economics and Information Science, Onomichi City University, 1600-2 Hisayamada-cho, Onomichi 722-8506, Japan e-mail: [email protected] T. Homma Faculty of Business Administration of Policy Studies, Osaka University of Economics, 2-2-8 Osumi, Higashiyodogawa-ku, Osaka, Japan e-mail: [email protected] K. Sawada Department of Policy Studies, University of Marketing and Distribution Sciences, 3-1 Gakuen-Nishimachi, Nishi-ku, Kobe 651-2188, Japan e-mail: [email protected]
G.-C. Yang et al. (eds.), IAENG Transactions on Engineering Technologies, Lecture Notes in Electrical Engineering 186, DOI: 10.1007/978-94-007-5651-9_10, Springer Science+Business Media Dordrecht 2013
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1 Introduction Retailers who deal in fresh food-stuffs are particular about farms that produce high-quality products since their consumers today are concerned about food safety. For this reason, the number of retailers who directly deal with the poultry farmers has been increasing in Japan. The poultry farmers are expected to frequently ship the products in order to provide the fresh items for the retailers. In this study, we consider the case where the poultry farmer uses a quantity discount strategy to control the retailer’s ordering schedule. Many researchers have considered the seller’s quantity discount decision. By offering a discounted price to induce the buyer to order in larger quantities, the seller can increase her/his profit through reductions in her/his total transaction cost associated with ordering, shipment, and inventorying. Monahan [1] was one of the early authors who formulated the transaction between the seller and the buyer, and proposed a method for determining an optimal all-unit quantity discount policy with a fixed demand (see also Rosenblatt and Lee [2] and Data and Srikanth [3]). Lee and Rosenblatt [4] generalized Monahan’s model to obtain the ‘‘exact’’ discount rate offered by the seller, and to relax the implic
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