运筹学学报
運籌學學報
운주학학보
OR TRANSACTIONS
2008年
3期
23-34
,共12页
运筹学%库存模型%最优订货量%替代%重新进货
運籌學%庫存模型%最優訂貨量%替代%重新進貨
운주학%고존모형%최우정화량%체대%중신진화
Operations research%inventory model%optimal order quantity%substitution%reorder
市场上,很多产品之间可相互替代,商家为了获得的更多的利润,经常会用一种产品替代另一种产品.不仅如此.某种产品缺货时,也可以重新进货以满足顾客的需求.我们从销售商的角度,讨论这两个因素对库存策略的影响,建立了这类问题有两个产品的单周期的利润最大化模型,证明了目标函数是凹的和子模的,从而问题的解是存在的,给出了最优订货量(原始库存)的必要条件,讨论了各参数对库存的影响.通过比较,证明了商家采取替代策略和允许再订货可以提高利润并且可减少库存总量.
市場上,很多產品之間可相互替代,商傢為瞭穫得的更多的利潤,經常會用一種產品替代另一種產品.不僅如此.某種產品缺貨時,也可以重新進貨以滿足顧客的需求.我們從銷售商的角度,討論這兩箇因素對庫存策略的影響,建立瞭這類問題有兩箇產品的單週期的利潤最大化模型,證明瞭目標函數是凹的和子模的,從而問題的解是存在的,給齣瞭最優訂貨量(原始庫存)的必要條件,討論瞭各參數對庫存的影響.通過比較,證明瞭商傢採取替代策略和允許再訂貨可以提高利潤併且可減少庫存總量.
시장상,흔다산품지간가상호체대,상가위료획득적경다적리윤,경상회용일충산품체대령일충산품.불부여차.모충산품결화시,야가이중신진화이만족고객적수구.아문종소수상적각도,토론저량개인소대고존책략적영향,건립료저류문제유량개산품적단주기적리윤최대화모형,증명료목표함수시요적화자모적,종이문제적해시존재적,급출료최우정화량(원시고존)적필요조건,토론료각삼수대고존적영향.통과비교,증명료상가채취체대책략화윤허재정화가이제고리윤병차가감소고존총량.
In market, many same or similar-characteristic products can substitute for each other, retailers usually adopt substitution strategy for more benefits, and excess demand for product can also be met by reorder. For single-period two-product inventory problem of this kind, we develop the profits maximization model with stochastic demands and proportional costs and revenues. We show that the objective function is concave and submodular, and therefore the optimal stock policy exists. We present the optimal conditions for stock quantities, and provide some properties of the optimal stock quantities. We explore the impacts of parameters on the profits and the optimal stock quantities. By comparison we prove that reorder, and adoption of the substitution strategy for special cases, can raise the profits and reduce the general stock level.
