راه حل های شکل بسته برای مدل هایEOQ مارتین و وی با تخفیف قیمت به طور موقت

In this article, we use closed-form solutions to solve Wee and Yu (1997) deteriorating inventory model with a temporary price discount and Martin’s (1994) EOQ model with a temporary sale price. In Wee and Yu (1997) and Martin’s (1994), the benefits during the temporary price discount purchase cycle are represented by their objective functions. Wee and Yu (1997) and Martin (1994) only used search methods to find approximate solutions. Following the theorems we suggested, you can find closed-form solution directly when there are integer operators involve in an objective function. Using the data of Wee and Yu (1997) and Martin (1994), we can find the results are more quick and more accurate.

In the real life, the manufacturer increases the sales volume and profit by temporarily reducing price. Ghare and Schrader (1963) first considered inventory model for items deteriorating at a constant rate. They derived an EOQ model for an exponentially decaying inventory. Tersine (1994) proposed a temporary price discount model, the optimal EOQ policy is obtained by maximizing the difference between regular EOQ cost and special quantity cost during the sale period. But in Tersine’s (1994) article, the average inventory was represented as 0.5Q⁎ deserved something to discuss. Martin (1994) did average inventory appropriate correction. But Tersine (1994) and Martin (1994) did not consider the fact that some commodities may deteriorate with time. Wee and Yu (1997) considered the items deteriorated exponentially with time when temporary price discount purchase occurs at the regular and non-regular replenishment time. Martin (1994) and Wee and Yu (1997) sacrificed the closed-form solutions in solving their objective functions, instead of using search methods to find special order quantity and maximum gain. Wee et al. (2003) showed that Tersine’s (1994) EOQ optimal solution could be derived algebraically without using differential calculus. Saker and Kindi (2006) proposed five different cases of the discount sale scenarios in order to maximize the annual gain of the special ordering quantity. Cárdenas-Barrón (2009a) extended Saker and Kindi (2006) to determine the optimal ordering policies when a supplier establishes a minimum order size. Cárdenas-Barrón (2009b) pointed out that there are some technical and mathematical expression errors in Saker and Kindi (2006) and presented the closed form solutions for the optimal total gain cost. Li (2009) presented a new method for determining the optimal number of orders for the finite-horizon discrete-time EOQ model. García-Laguna et al. (2010) presented methods to obtain solutions of the EOQ and EPQ models when the lot sizes are integer variables to be determined. The related analysis on global optimization has been performed by Abad (2003), Chung and Wee (2008), Chung et al. (2008), Wee et al. (2009), Yang et al. (2010), Cárdenas-Barrón et al. (2010),etc. The remainder of this paper is organized as follows. In Section 2, we describe the notation which is used throughout this paper. In Section 3, we describe the mathematical models and suggest theorems to determine the optimal ordering policy. Numerical examples are provided in Section 4. Finally, we make a conclusion in the last section.

In Wee and Yu (1997) and Martin’s (1994) EOQ models with a temporary price discount, they help purchasers to make decisions how much to order when there is a temporary price discount. In Wee and Yu (1997) deteriorating inventory model, Fibonacci’s search technique is used to derive the optimal solutions of two models. In Martin’s (1994) non-deteriorating inventory model, Martin used Tersine’s (1994) value to initialize and find some adjacent gains. Then they compared those obtained gains to find the maximum gain. In this paper, we propose three theorems to find the closed-form solutions of Wee and Yu (1997) and Martin’s (1994) EOQ models. It not only solves the tediously numerical calculations, but also finds accurate results.