数据、模型与决策(运筹学)课后习题和案例答案019.doc

数据、模型与决策(运筹学)课后习题和案例答案019 作者： 日期：2 个人收集整理 勿做商业用途CHAPTER 19INVENTORY MANAGEMENT WITH UNCERTAIN DEMANDReview Questions19.1-1Freddie should consider the trade-off between too much inventory and too little inventory。19.1-2Based on Freddies data, 9, 10, and 11 are the only numbers of copies that he has sold in the past.19。13The state of nature for each day is the number of requests to purchase a copy that will occur。 The number of requests is the state of nature because it is the random variable.19。21Only a single time period is needed because perishable products cannot be sold later。19.22The only decision to be made is how many units to order so they can be placed into inventory at the beginning of the period。19.2-3It is assumed that the demand during the period is uncertain but that the probability distribution of demand is known.19。24The unit cost of underordering is the decrease in profit that results from failing to order a unit that could have been sold during the period. The unit cost of overordering is the decrease in profit that results from ordering a unit that could not be sold during the period。19。25Bayes decision rule will make the same decision since both approaches are applying Bayes decision rule, but with different payoffs， where one is to be maximized and the other minimized.19.26The service level is the probability that no shortage will occur.19.27Optimal service level = Cunder / （Cunder + Cover）.19。2-8The point at which the optimal service level hits the cumulative distribution function gives the optimal order quantity。19。2-9Yes.19。3-1There have been four stockouts of panoramic disposable cameras during the year with durations ranging from a few days to a couple weeks。19.3-2Recent complaints from distributors about delays in shipping the disposable panoramic camera have concerned the Vice President for Marketing and she is suggesting having more frequent production runs to keep the inventory better stocked.19.3-3The Division Vice President for Production is concerned about the frequent interruptions in the production of other models caused by setting up for a production run for the disposable panoramic cameras。 He is recommending having much longer production runs much less frequently。19.3-4The Division President is skeptical about his Vice Presidents recommendation because it would increase inventory levels. He has been promoting the justin-time philosophy of minimizing inventory.19.4-1The management science team began by trying to diagnose why the frequent stockouts were occurring under the current inventory policy。19.4-2Under the old inventory policy， the probability of a stockout is 50% and the maximum size of a stockout is 8，000。19.43Reorder point = average sales during lead time + amount of safety stock.19.44Even when the amount of safety stock provided still permits occasional short stockouts， this safety stock can dramatically improve the service to customers by greatly reducing both the number and length of the delays in filling customer orders。19。45Management made the decision on how much safety stock to provide。19。46The relevant cost factors for choosing the order quantity are acquisition costs， setup costs, holding costs， and shortage costs。19.4-7The main component of shortage costs is lost future profit from lost future sales caused by customer dissatisfaction with delays in filling current orders。19。48Increasing the order quantity decreases the average monthly setup costs because this decreases the average number of setups required per month。 Increasing the order quantity increases the average monthly holding costs, since this increases the average inventory level。 Increasing the order quantity decreases the average monthly shortage costs, because this decreases the average number of opportunities for stockout per month.19。49The management science team used the EOQ model with planned shortages to find the approximately optimal order quantity.19。4-10The President is unhappy about the large increase in inventory levels。 The Vice President for Marketing is concerned that shortages of various magnitudes still can be expected to occur about once per year。 The Vice President for Production is unhappy because the policy would only slightly decrease the frequency of production runs。19.4-11The high setup cost, the long lead time， and the high variability in monthly sales were the three factors the caused the cost of this inventory policy to be unusually high.19.4-12The setup cost and lead time will be greatly reduced by acquiring some additional production facilities that would be used solely for production of the disposable panoramic cameras.19.5-1The camera is considered a stable product because each camera in inventory will remain sellable indefinitely。19.52A continuousreview inventory system is one where the inventory level of a stable product is monitored on a continuous basis so that a new order can be placed as soon as the inventory level drops to the reorder point.19.5-3The traditional method of implementing a continuous-review inventory system was to use a two-bin system。19。54The common modern method of implementing a continuousreview inventory system is a computerized inventory system.19。55An （R， Q） inventory policy controls a continuous-review inventory system by using a fixed reorder point R and a fixed order quantity Q。19。5-6Except for the setup cost， the cost of the order is proportional to the order quantity Q。 A certain holding cost is incurred for each unit in inventory per unit time。 When a stockout occurs, a certain shortage cost is incurred for each unit backordered per unit time until the backorder is filled。19.5-7The EOQ model with planned shortages is used to approximate the optimal order quantity.19.58The key difference between the models is that rather than having known demand with a fixed rate， the model in this chapter assumes uncertain demand. The main difference in the results from the two models is that because of the uncertain demand for the current model, some safety stock needs to be added when setting the reorder point to provide some cushion for having well-above-average demand during the lead time。19.5-9The most convenient measure of the service level is the probability that a stockout will not occur between the time an order is placed and the order quantity is received.19。510R = m + KLs.19。61The products in the A group are the particularly important ones that are to be carefully monitored according to a formal inventory model。 Products in the C group are the least important, so they are only monitored informally on a very occasional basis. Group B products receive an intermediate treatment。19。62Occasionally it is not appropriate to apply a singleproduct inventory model because of interactions between the products.19.63A multiechelon inventory system is a system with multiple echelons of inventory where each echelon (except the bottom one) is used to replenish the inventories at the various sites of the next lower echelon.19。6-4The echelons of IBMs system start with the manufacture of the parts, then national or regional warehouses， then field distribution centers, then parts stations， and finally many thousands of outside locations。19.6-5The three factors that proved to be especially important were the inclusion of a user team as advisors to the project team， a very extensive user acceptance test whereby users could identify problem areas that needed rectifying prior to full implementation, and that the new system was phased in gradually, with careful testing at each phase。19。66The cost savings were about 20 million per year through improved operational efficiency and even larger annual savings in holding costs。19.67A supply chain spans procurement， manufacturing， and distribution。19。6-8HP faced inventories mounting into the billions of dollars and alarming customer dissatisfaction with its order fulfillment process。19.6-9WINO deals with inventories of finished products as well as inventories of incoming goods and departing goods at each site along the supply chain。19.6-10A key intangible benefit was to enhance HPs reputation as a progressive company that can be counted on by its customers to fill their orders promptly.Problems19.1a)When maximizing profit, Freddie should order 16 copies (expected profit = $15.20)。b）When minimizing the cost of underordering or overordering， Freddie should order 16 copies (expected cost = $0.90）.Freddies most profitable alternative is to order 16 copies.c)Service level if order 15 copies = 0。4Service level if order 16 copies = 0。6Service level if order 17 copies = 0。9Service level if order 18 copies = 1Cunder = $1Cover = 1Optimal service level = Cunder / （Cunder + Cover） = $1 / （$1 + 1） = 0.5Freddie should order 16 copies。d）19.2a）Cunder =3 $1 = 2Cover = $1 0。50 = 0.50b）Prepare 4 doughnuts each day to minimize costs。c）Service level if 0 made = 0.1Service level if 1 made = 0.25Service level if 2 made = 0。45Service level if 3 made = 0.75Service level if 4 made = 0。9Service level if 5 made = 1Optimal service level = Cunder / （Cunder + Cover） = $2 / (2 + 0。50） = 0。8Prepare 4 doughnuts each day。d)The probability of running short will be 1 0。9 = 0。1 = 10%。e)Before 5 doughnuts are prepared， the optimal service level needs to exceed 0.9。Let g be the cost of lost customer goodwill。 Then Cunder = 2 + g.Cunder / (Cunder + Cover） 0.9($2 + g) / （$2.5 + g) 0.9g 2。50。The goodwill cost would need to be at least $2.50 before 5 doughnuts should be prepared。19。3a)Optimal service level = Cunder / (Cunder + Cover) = 1 / ($1 + $0。50) = 0。667.b）c)Q* = 300 + 0。667（600 300） = 500.d）The probability of running short is 1 0.667 = 0。333 = 33.3%e)Optimal service level = Cunder / (Cunder + Cover) = (1 + 1。50) / （1 + 1。50 + 0。50) = 0.833.Q = 300 + 0.833（600 300） = 550.The probability of running short is 1 0.833 = 0.167 = 16.7.19。4a）Revenue (with shortages) = 500（3) = $1，500b)Average number of loaves sold （without shortages) = 300 + （500300）/2 = 400。Average daily revenue （without shortages） = 400(3) = $1,200。c）$1，500 x 0。333 = 500 (with shortages）1，200 x 0.667 = 800 （without shortages）Average daily revenue over all days = $500 + 800 = $1,300d）Average number of loaves not sold = (2000）/2 = 100. Average number of dayold loaves obtained over all days = 100 x 0。667 = 66。7。Average daily revenue from dayold bread = (66.7）(1.50） = $100.e）Average total daily revenue = 1，300 + 100 = 1,400.Average daily profit = $1,400 （$2)（500） = $400。f）Average daily profit （600 loaves）= 3(450) 2（600） + $1.50（150） = $375.g）Average daily profit （550 loaves) = $375 + （$400 375）/2 = $387。50.h）Average size of shortage (550 loaves) = (600 550)/2 = 25 loaves. Average daily shortage over all days = (25）（0。167） = 4。167.Average daily cost of loss of goodwill = (4。167)（1。50) = 6.25。Average daily profit (550 loaves loss of goodwill） = $387。50 6。25 = 381。25。i)Average size of shortage （500 loaves） = （100 0）/2 = 50 loaves. Average daily shortage over all days = (50)(0。333） = 16.67.Average daily cost of loss of goodwill = (16.67）(1。50) = $25。Average daily profit (500 loaves loss of goodwill） = $400 $25 = 375.19。5a）Q = a + (service level） (b a） = a + （0。667）(75） = a + 50。b）Probability of incurring shortage = 1 0.667 = 33。3% which is the same as in problem 19.3.c)Maximum shortage = 25.Maximum number of loaves that wont be sold = 50.The corresponding numbers for problem 19。3 are 100 and 200 respectively which are four times the amounts here.d）The average daily costs of underordering and overordering for the new plan are 25% of the original costs. Thus, it is quite valuable to obtain as much information as possible about demand before placing the final order for a perishable product。e）Q* = a + （service level） （b a） = a + (0.833)(75） = a + 62.5.Probability of incurring shortage = 1 0。833 = 16.67。Maximum shortage = 12。5.Maximum number of loaves that wont be sold = 62。5。19.6a）This problem can be interpreted as an inventory problem with uncertain demand for a perishable product with travelers checks as the product。 Once Stan gets back from his trip the checks are not good anymore so they are a perishable product。 He can redeposit the amount into his savings account but will incur a fee of lost interest。 Stan must decide how many checks to buy without knowing how many he will need。Cunder = value of 1 day cost of 1 day cost of 1 check = 150 $100 $1 = $49。Cover = cost of check + lost interest = 1 + 2 = $3.文档为个人收集整理，来源于网络文档为个人收集整理，来源于网络b)Purchase 4 additional $100 checks, for a total of $1,600。c)Service level for buying 0 = 0。3Service level for buying 1 = 0。55Service level for buying 2 = 0.75Service level for buying 3 = 0。85Service level for buying 4 = 0。95Service level for buying 5 = 1Optimal service level = Cunder / （Cunder + Cover） = $49 / （$49 + 3) = 0。94。Buy 4 additional checks。d)19.7a）Optimal service level = Cunder / （Cunder + Cover) = $3,000 / （3,000 + $1,000） = 0.75。b）When the demand is lessthan-orequalto Q, no shortage will occur。 Therefore the probability that the demand is lessthanorequal-to Q gives us the service level that corresponds to choosing the order quantity Q. Increasing Q increases this probability。 Therefore the smallest order quantity that provides the service level L is the value of Q such that P(demand Q） = L。c）Q = m + KLs = 50 + (0。675)（15) = 60。 19。8a）When interpreting this problem as an inventory problem, overbooked reservations are the perishable products that are being placed into inventory。b)Cunder = lost fare = 250。Cover = cost of certificate = 150.c)Service level for accepting 0 = 0。05Service level for accepting 1 = 0.15Service level for accepting 2 = 0。3Service level for accepting 3 = 0.45Service level for accepting 4 = 0。6Service level for accepting 5 = 0.75Service level for accepting 6 = 0.85Service level for accepting 7 = 0。95Service level for accepting 8 = 1Optimal service level = Cunder / （Cunder + Cover） = 250 / ($250 + $150) = 0。625.Accept 5 overbooked reservation。d）19.9a） Q* is cut in half。 R is unchanged. This will reduce the average monthly holding cost. However, it will i