《供应链不匹配成本》PPT课件.ppt

The Newsvendor Model,报童模型,“Too much” and “too little” costs,Co = 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 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 more unit.,Balancing the risk and benefit of ordering a unit,Ordering 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 = Q) but the benefit/gain of ordering one more unit is the reduction in the chance of underage: Expected gain on the Qth unit = Cu x (1-F(Q),As more units are ordered, the expected benefit from ordering one unit decreases while the expected loss of ordering one more unit increases.,Newsvendor expected profit maximizing order quantity,To maximize expected profit order Q units so that the expected loss on the Qth unit equals the expected gain on the Qth unit: Rearrange terms in the above equation - The ratio Cu / (Co + Cu) is called the critical ratio. （临界比或关键比例） Hence, to maximize profit, choose Q such that we dont have lost sales (i.e., demand is Q or lower) with a probability that equals the critical ratio,The Newsvendor Model: Performance measures,绩效指标,Newsvendor model performance measures,For any order quantity we would like to evaluate the following performance measures: Expected lost sales （期望销售损失） The average number of units demand exceeds the order quantity Expected sales （期望销售）(compared to expected demand) The average number of units sold. Expected left over inventory（期望售后剩余库存） The average number of units left over at the end of the season. Expected profit Expected fill rate （期望订单完成率） The fraction of demand that is satisfied immediately In-stock probability（存货满足概率） Probability all demand is satisfied Stockout probability（缺货概率） Probability some demand is lost,formula,Expected sales = m - Expected lost sales m : Expected demand L(z): loss 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 Sales,formula,In-stock probability = F(Q) = (z),Stockout probability = 1 F(Q) =1 In-stock probability,The Newsvendor Model: The target in-stock probability and the target fill-rate objectives for choosing Q,in-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,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-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 distribution. Q = m + z x s = 3192 + 2.33 x 1181 = 5944,Choose Q subject to a minimum fill rate constraint,Suppose 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 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 = 1.54 Step 3: Convert the z-statistic into an order quantity for the actual demand distribution. Q = m + z x s = 3192 + 1.54 x 1181 = 5011,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。,Assemble-to-order, make-to-order and Quick Response with reactive capacity,按订单装配、按订单生产和以反应性能力快速响应,The demand-supply mismatch cost,Definition 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., every unit is sold and there are no lost sales: The mismatch cost can also be evaluated with,Mismatch cost = Maximum profit Expected profit,When is the mismatch cost high?,Mismatch cost as a percent of the maximum profit where f(z) = density function of the Normal distribution (In Excel f(z)=normdist(z,0,1,0) The mismatch cost is high when (f(z) / F(z) and (s / m) are high.,Low critical ratios high mismatch costs,The mismatch cost is high when (f(z) / F(z) is high (f(z) / F(z) is high when the critical ratio is low:,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。,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,Some U.S. airline industry observations,Since deregulation (1978) 137 carriers have filed for bankruptcy. From 95-99 (the industrys best 5 years ever) airlines earned 3.5 cents on each dollar of sales: The US average for all industries is around 6 cents. From 90-99 the industry earned 1 cent per $ of sales. Carriers typically fill 72.4% of seats and have a break-even load of 70.4%.,Matching supply to demand when supply is fixed,Examples of fixed supply: Travel industries (fixed number of seats, rooms, cars, etc). Advertising time (limited number of time slots). Telecommunications bandwidth. Size of the MBA program. Doctors availability for appointments. Revenue management is a solution: If adjusting supply is impossible adjust the demand! Segment customers into high willingness to pay and low willingness to pay. Limit the number of tickets sold at a low price, i.e., control the average price by changing the mix of customers.,Revenue management and margin arithmetic,Small changes in revenue can have a big impact on profit, especially for high gross margin and low net profit % industries:,Environments suitable for revenue management,The same unit of capacity (e.g., airline seat) can be used to deliver services to different customer segments (e.g., business and leisure customers) at different prices. High gross margins (so that the variable cost of additional sales is low). Perishable capacity (it cannot be stored) and limited capacity (all possible customers cannot always be served). Capacity is sold in advance of demand. There is an opportunity to segment customers (so that different prices can be charged) and different segments are willing to pay different prices. It is not illegal or morally irresponsible to discriminate among customers.,Revenue Management: Booking limits and protection levels 预定限额和保留水平,Practical problem,The Park Hyatt Philadelphia at the Bellevue. 118 King/Queen rooms. Hyatt offers a rL= $159 (low fare) discount fare for a mid-week stay targeting leisure travelers. Regular fare is rH= $225 (high fare) targeting business travelers. Demand for low fare rooms is abundant. Let D be uncertain demand for high fare rooms. Suppose D has Poisson distribution with mean 27.3. Assume most of the high fare (business) demand occurs only within a few days of the actual stay. Objective: Maximize expected revenues by controlling the number of low fare rooms you sell.,Yield management decisions,The booking limit is the number of rooms you are willing to sell in a fare class or lower. The protection level is the number of rooms you reserve for a fare class or higher. Let Q be the protection level for the high fare class. Q is in effect while you sell low fare tickets. Since there are only two fare classes, the booking limit on the low fare class is 118 Q: You will sell no more than 118-Q low fare tickets because you are protecting (or reserving) Q seats for high fare passengers.,0,118,Q seats protected for high fare passengers,Sell no more than the low fare booking limit, 118 - Q,The connection to the newsvendor,A single decision is made before uncertain demand is realized. There is an overage cost: If D Q then you protected too few rooms (you under protected) so some rooms could have been sold at the high fare instead of the low fare. Choose Q to balance the overage and underage costs.,Optimal protection level,Overage cost: If D Q we protected too few rooms. D Q rooms could have been sold at the high fare but were sold instead at the low fare, so Cu = rH - rL Optimal high fare protection level: Optimal low fare booking limit = 118 Q* Choosing the optimal high fare protection level is a Newsvendor problem with properly chosen underage and overage costs.,Hyatt example,Critical ratio: Poisson distribution with mean 27.3: Answer: 24 rooms should be protected for high fare travelers. Similarly, a booking limit of 118-24 = 94 rooms should be applied to low fare reservations.,Related calculations,How many high-fare travelers will be refused a reservation? Expected lost sales = 4.10. How many high-fare travelers will be accommodated? Expected sales = Expected demand - Lost sales = 27.3 - 4.1 = 23.2 How many seats will remain empty? Expected left over inventory = Q - Expected sales = 24 - 23.2 = 0.8. What is the expected revenue? $225 x Exp. sales + $159 x Booking limit = $20,166. Note: without yield management worst case scenario is $159 x 118 = $18,762.,Revenue Management: Overbooking,Ugly reality: cancellations and no-shows,Approximately 50% of reservations get cancelled at some point in time. In many cases (car rentals, hotels, full fare airline passengers) there is no penalty for cancellations. Problem: the company may fail to fill the seat (room, car) if the passenger cancels at the very last minute or does not show up. Solution: sell more seats (rooms, cars) than capacity. Danger: some customers may have to be denied a seat even though they have a confirmed reservation.,Hyatts Problem,The forecast for the number of customers that do not show up ( X ) is Poisson with mean 8.5. The cost of denying a room to the customer with a confirmed reservation is $350 in ill-will and penalties. How many rooms ( Y ) should be overbooked (sold in excess of capacity)? Newsvendor setup: Single decision when the number of no-shows in uncertain. Underage cost if X Y (insufficient number of seats overbooked).