Journal of Korean Society of Industrial and Systems Engineering (산업경영시스템학회지)

Society of Korea Industrial and System Engineering (한국산업경영시스템학회)
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A Study on a Multi-period Inventory Model with Quantity Discounts Based on the Previous Order

주문량 증가에 따른 할인 정책이 있는 다기간 재고 모형의 해법 연구

  • Lim, Sung-Mook (College of Business and Economics, Korea University)
  • 임성묵 (고려대학교 경상대학 경영학부)
  • Published : 2009.12.31
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Abstract

Lee[15] examined quantity discount contracts between a manufacturer and a retailer in a stochastic, two-period inventory model where quantity discounts are provided based on the previous order size. During the two periods, the retailer faces stochastic (truncated Poisson distributed) demands and he/she places orders to meet the demands. The manufacturer provides for the retailer a price discount for the second period order if its quantity exceeds the first period order quantity. In this paper we extend the above two-period model to a k-period one (where k < 2) and propose a stochastic nonlinear mixed binary integer program for it. In order to make the program tractable, the nonlinear term involving the sum of truncated Poisson cumulative probability function values over a certain range of demand is approximated by an i-interval piecewise linear function. With the value of i selected and fixed, the piecewise linear function is determined using an evolutionary algorithm where its fitness to the original nonlinear term is maximized. The resulting piecewise linear mixed binary integer program is then transformed to a mixed binary integer linear program. With the k-period model developed, we suggest a solution procedure of receding horizon control style to solve n-period (n < k) order decision problems. We implement Lee's two-period model and the proposed k-period model for the use in receding horizon control style to solve n-period order decision problems, and compare between the two models in terms of the pattern of order quantities and the total profits. Our computational study shows that the proposed model is superior to the two-period model with respect to the total profits, and that order quantities from the proposed model have higher fluctuations over periods.

Keywords

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