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1、Slide 1 ，The Newsvendor Model报童模型Slide 2 ，“Too much” and “too little” costsCo = overage cost-The cost of ordering one more unit than what you would have ordered had you known demand. -In other words, suppose you had left over inventory (i.e., you over ordered). Co is the increase in profit you would
2、 have enjoyed had you ordered one fewer unit. Cu = underage cost-The cost of ordering one fewer unit than what you would have ordered had you known demand.-In other words, suppose you had lost sales (i.e., you under ordered). Cu is the increase in profit you would have enjoyed had you ordered one mo
3、re unit. Slide 3 ，Balancing the risk and benefit of ordering a unitOrdering one more unit increases the chance of overage -Expected loss on the Qth unit = Co x F(Q)-F(Q) = Distribution function of demand = ProbDemand The ratio Cu / (Co + Cu) is called the critical ratio. （临界比或关键比例） Hence, to maximiz
4、e profit, choose Q such that we dont have lost sales (i.e., demand is Q or lower) with a probability that equals the critical ratioSlide 5 ，The Newsvendor Model: Performance measures绩效指标Slide 6 ，Newsvendor model performance measuresFor any order quantity we would like to evaluate the following perfo
5、rmance measures:-Expected lost sales （期望销售损失）uThe average number of units demand exceeds the order quantity-Expected sales （期望销售）(compared to expected demand)uThe average number of units sold.-Expected left over inventory（期望售后剩余库存）uThe average number of units left over at the end of the season.-Expe
6、cted profit-Expected fill rate （期望订单完成率）uThe fraction of demand that is satisfied immediately-In-stock probability（存货满足概率）uProbability all demand is satisfied -Stockout probability（缺货概率）uProbability some demand is lostSlide 7 ，formulaExpected sales = m - Expected lost salesm : Expected demandL(z): l
7、oss function (标准正态)损失函数, 随机变量超过一个固定值的期望值之和。Expected Left Over Inventory = Q - Expected SalesSlide 8 ，formulaIn-stock probability = F(Q) = (z)Stockout probability = 1 F(Q) =1 In-stock probabilitySlide 9 ，The Newsvendor Model: The target in-stock probability and the target fill- rate objectives for ch
8、oosing Qin-stock probability：缺货情况，对杂货店较重要 fill-rate：多少顾客满足的情况，对目录零售商较重要Slide 10 ，Choose Q subject to a minimum in-stock probability Suppose we wish to find the order quantity for the Hammer 3/2 that minimizes left over inventory while generating at least a 99% in-stock probability.Step 1:-Find the z
9、-statistic that yields the target in-stock probability.-In the Standard Normal Distribution Function Table we find F(2.32) = 0.9898 and F(2.33) = 0.9901. -Choose z = 2.33 to satisfy our in-stock probability constraint.Step 2: -Convert the z-statistic into an order quantity for the actual demand dist
10、ribution.-Q = m + z x s = 3192 + 2.33 x 1181 = 5944Slide 11 ，Choose Q subject to a minimum fill rate constraintSuppose we wish to find the order quantity for the Hammer 3/2 that minimizes left over inventory while generating at least a 99% fill rate.Step 1:-Find the lost sales with a standard normal
11、 distribution that yields the target fill rate.Step 2:-Find the z-statistic that yields the lost sales found in step 1.-From the Standard Normal Loss Function Table, L(1.53)=0.0274 and L(1.54) = 0.0267-Choose the higher z-statistic, z = 1.54Step 3: -Convert the z-statistic into an order quantity for
12、 the actual demand distribution.-Q = m + z x s = 3192 + 1.54 x 1181 = 5011Slide 12 ，讨论不足成本大时（毛利高），订购量大于期望需求（关键比例大于0.5）；反之 相反。剩余成本可能是可见成本，而销售损失是机会成本，在报表中看不到。剩余成本可能是积压的库存，如未及时清理，造成虚假利润除了利润最大化目标外，很多情况下会选服务水平目标，因为要考虑长期效 应。Slide 13 ，Assemble-to-order, make-to-order and Quick Response with reactive capaci
13、ty按订单装配、按订单生产和以反应性能力快速响应Slide 14 ，The demand-supply mismatch costDefinition the demand supply mismatch cost includes the cost of left over inventory (the “too much” cost) plus the opportunity cost of lost sales (the “too little” cost):The maximum profit is the profit without any mismatch costs, i.e.
14、, every unit is sold and there are no lost sales:The mismatch cost can also be evaluated with Mismatch cost = Maximum profit Expected profit Slide 15 ，When is the mismatch cost high?Mismatch cost as a percent of the maximum profitwhere f(z) = density function of the Normal distribution (In Excel f(z
15、)=normdist(z,0,1,0) The mismatch cost is high when (f(z) / F(z) and (s / m) are high.Slide 16 ，Low critical ratios high mismatch costsThe mismatch cost is high when (f(z) / F(z) is high (f(z) / F(z) is high when the critical ratio is low:Slide 17 ，变差系数反映预测质量，提高预测精确性，可有更高利润。关键比例小的产品，剩余成本高，容易过时的和容易腐败的
16、产品采购少。若残值为零，关键比例即为毛利率，故食堂原材料备料库存少（毛利低，积 压成本大），餐厅备料较充分，过期库存多。Slide 18 ，不同的不匹配成本与运营管理模式MTS报童模型不匹配成本为过量或不足，MTS适合于关键比例高、需求变动小MTO排队系统不匹配成本为生产闲置、顾客排队MTO适合于短途运输、短提前期、机器 或劳动力便宜 中间状态为使用反应性能力进行快速响应 两种反应性能力： 第二次订购能力无限但较第一次订购昂贵 的反应性能力 第二次订购能力有限的反应性能力Slide 19 ，Some U.S. airline industry observationsSince deregulation (1978) 137 carriers have filed for bankruptcy.From 95-99 (the industrys best 5 years ever) airl
