数据模型与决策(运筹学)课后习题和案例答案(8).docx

CHAPTER 19 INVENTORY MANAGEMENT WITH UNCERTAIN DEMANDReview Questions19.1-1 Freddie should consider the trade-off between too much inventory and too little inventory.19.1- 2 Based on Freddie's data, 9, 10, and 11 are the only numbers of copies that he has sold in the past.19.1-3 The state of nature fbr 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.19.2-1 Only a single time period is needed because perishable products cannot be sold later.19.2- 2 The 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- 3 It is assumed that the demand during the period is uncertain but that the probability distribution of demand is known.19.2- 4 The 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.19.2- 5 Bayes' 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.19.2- 6 The service level is the probability that no shortage will occur.19.2- 7 Optimal Service level = Cunder / (Cunder + Cover).19.2- 8 The point at which the optimal service level hits the cumulative distribution function gives the optimal order quantity.19.2- 9 Yes.19.3- 1 There have been four stockouts of panoramic disposable cameras during the year with durations ranging from a few days to a couple weeks.19.4- 2 Recent complaints from distributors about delays in shipping the disposable panoramic camera have concerned the Vice President fbr Marketing and she is suggesting having more frequent production runs to keep the inventory better stocked.b)Purchase 4 additional $100 checks, for a total of $1,600.c) Service level fbr buying 0 = 0.3Service level fbr buying 1 = 0.55Service level fbr buying 2 = 0.75Service level for buying 3 = 0.85Service level fbr buying 4 = 0.95Service level fbr buying 5 = 1Optimal service level = Cunder / (Cunder + Cover) = $49 / ($49 + $3) = 0.94.Buy 4 additional checks.19.7 a) Optimal service level = Cunder / (Cunder + Cover) = $3,000 / ($3,000 + $1,000) = 0.75.b) When the demand is less-than-or-equal-to Q. no shortage will occur. Therefore the probability that the demand is less-than-or-equal-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 (demand <Q) = L.c) 0=|i + Klg = 50+ (0.675)(15) = 60.19.8 a) 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 fbr accepting 2 = 0.3Service level fbr accepting 3 = 0.45Service level fbr accepting 4 = 0.6Service level fbr accepting 5 = 0.75Service level for accepting 6 = 0.85Service level for accepting 7 = 0.95Service level fbr accepting 8 = 1Optimal service level = Cunder / (Cunder + Cover) = $250 / ($250 + $150) = 0.625.Accept 5 overbooked reservation.19.9 a)。* is cut in half. R is unchanged. This will reduce the average monthly holding cost. However, it will increase the average monthly shortage cost (since the number of order cycles per month increases). The smaller setup cost reduces the average monthly setup cost.b)IIIIII2is unchanged. R is reduced from 12,000 to 10,000. This will reduce the average monthly holding cost (less safety stock to hold). The average monthly shortage costs and setup costs will be unchanged.c)0* is unchanged. R is reduced from 12,000 to 2,300. This will reduce the average monthly holding cost. The average monthly shortage costs and setup costs will be unchanged.IIIIII20* is cut in half. R is reduced from 12,000 to 2,300. This will reduce the average monthly holding cost. However, it will increase the average monthly shortage cost (since the number of order cycles per month increases). The smaller setup cost reduces the average monthly setup cost.19.10 a)h±UP2KD$3,000+ $L000$1,0002($L500)(900)$3,000d) Average inventory just before an order is received = 2,300 - 1,600 = 700. Average inventory just after an order is received = 700 + 12,837 = 13,537. Average inventory = (700 + 13,537) / 2 = 7,119.Average monthly holding cost = 7,119 ($0.30) = $2,136.Average number of orders per year = (8,000)/(12,837) = 0.62.Probability of stockout before order received = 0.25.Expected number of stockouts per month = (0.25)(0.62) = 0.155.Average stockout size = 700 / 2 = 350.Estimate of average delay per camera delayed = 1/15 week = 0.015 months. Average monthly shortage cost = (0.155)(350)(0.015)($ 10) = $8.Average number of setups per month = 8000 / 12,837 = 0.62.Average monthly setup cost = (0.62)($35000) = $1,860.Average monthly cost = $2/36 + $8 + $1,860 = $4,004.This is less than half the cost before the changes ($8,896).19.11 a)h±UP2KD $8 + $l /2($40)(40)$8=60./? = a + L(b-a) = 5 + (0.8)(15 - 5)=13.b) R = pi+ Klq = 50+ (0.675)(15) = 60.d) Safety Stock = R- mean = 60 - 50 = 10.e) If demand during the delivery time exceeds 60 (the order quantity), then the reorder point will be hit again before the order arrives, triggering another order.b)c) Average number of orders per year = (40)(12) / 60 = 8. Probability of a stockout before order received = 0.2.Average number of stockouts per year = (8)(0.2) = 1.6.19.12 a)LC = KloCase 1 =$1, 0=1Case 2 /z=$1009 o=lCase 3 =$1, <5=100Case 4 =$100, o=l 000.5$0$0$0$00.750.67567.567.56,7500.91.282128.2128.212,8200.951.645164.5164.516,4500.992.327232.7232.723,2700.9993.098309.8309.830,980b)ALACCase 1 h=$l,Case 2 h=$100,Case 3 h=$l,o=100Case 4 h=$100, o=l 000.25$0,675$67.5$67.5$6,7500.150.60760.760.76,0700.050.36336.336.33,6300.040.68268.268.26,8200.0090.77177.177.17,710c) As the service level gets higher, increasing the service level further costs more for smaller increases. Thus, there will be diminishing returns when raising the service level further and further. You should balance the cost of the safety stock with the cost of stockouts to determine the best service level.19.13 a) C = hKLo = ($ 100)( 1.282)( 100) = $ 12,820.b) o =(<团6 => 100 = (4)cti =><5i = 50.If the lead time were 1 day, then C = hKhS = ($100)(1.282)(50) = $6,410.This is a 50% reduction in the cost of the safety stock.c) o = (8)(50) = 141.4.C = hKLs = ($ 100)(1.282)(141.4) = $18,127. This isa41% increase.d) The lead time would need to quadruple to 16 days.19.14 a) The safety stock would drop to zero.b) The safety stock would decrease.c) The safety stock is unchanged for a given service level. However, with higher shortage costs, there will be an incentive to increase the service level (with a correspondingly higher level of safety stock).d) The safety stock increases.e) The safety stock doubles.f) The safety stock doubles.19.15 a) Ground Chuck:IIIIII2Chuck Wagon:b) Ground Chuck: R = a + L(b - a) = 50 + (0.95)(150 -50)= 145.Chuck Wagon: R = + Kl(j = 500 + (1.645)(200) = 829.c) Ground Chuck: Safety Stock = R- mean = 145 - 100 = 45.Chuck Wagon: Safety Stock = R- mean = 829 - 500 = 329.d) Ground Chuck:Average annual holding cost = ($0.30)(2/83/2 + 45) = $341.Chuck Wagon:Average annual holding cost = ($0.30)(6,175/2 + 329) = $3,417.e) Ground Chuck:Annual shipping cost = K(D/Q) = ($25)(26,000 / 2,183) = $298.Annual purchase cost = Dp = (26,000)($ 1.49) = $38,740.Average annual acquisition cost = $298 + $38,740 = $39,038.Chuck Wagon:Annual shipping cost = K(D/Q) + ($0.10)Z)=($200)(26,000 / 6J 75) + ($0.10)(26,000)=$3,442.Annual purchase cost = Dp = (26,000)($ 1.35) = $35,100.Average annual acquisition cost = $3,442 + $35,100 = $38,542.f) Ground Chuck: $341 + $39,038 = $39,379.Chuck Wagon: $3417 + $38,542 = $41,959.Jed should choose Ground Chuck as their supplier.g) If Jed would like to use the beef within a month of receiving it, then Ground Chuck is the better choice. The order quantity with Ground Chuck is roughly one month's supply, whereas with Chuck Wagon the optimal order quantity is roughly three month's supply.19.16. a) Option 1:Option 2:b) Option 1: A = o + Klo = 250 + (2.327)(50) = 366.Option 2:R = a + L(b-a) = 500 + (0.99)(1,000 - 500) = 995.c) Option 1: Safety Stock = R- mean = 366 - 250 = 116.Option 2: Safety Stock = R- mean = 995 - 750 = 245.d) Option 1: Average annual holding cost = ($6)(1,093/2 + 116) = $3,975.Option 2: Average annual holding cost = ($6)(678/2 + 245) = $3,504.e) Option 1:Annual shipping cost = K(D/Q) + ($3)Z)=($130)(26,000 / 1,093) + ($3)(26,000)= $81,092.Annual purchase cost = Dp = (26,000)($30) = $780,000.Average annual acquisition cost = $81,092 + $780,000 = $861,092.Option 2:Annual shipping cost = K(D/Q) + ($3)Z)=($50)(26,000 / 678) + ($2)(26,000)= $53,917.Annual purchase cost = Dp = (26,000)($30) = $780,000.Average annual acquisition cost = $53,917 + $780,000 = $833,917.f) Option 1: $3,975 + $861,092 = $865,067.Option 2: $3,504 + $833,917 = $837,421.Option 2 should be selected.Cases19.1 For the analysis of this case we use the template for perishable products.a) First we need to determine the optimal service level for Howie. The unit sale price equals $5, the unit purchase cost equal $3, and the unit salvage value equals (0.5)($3)- ($0.50) = $1.Since Talia assumes that demand is normally distributed, we must estimate the parameters fbr the demand distribution. The mean is 250 firecracker sets. The standard deviation can be approximated by examining the lowest and highest selling stands from the previous year (120 and 425, respectively). Last year, sales ranged from 130 below to 175 above the mean. Since 99.73% of sales lie within 3 standard deviations, we can assume the standard deviation is approximately 60. This would make three standard deviations above and below the mean just barely hold all of the previous years results.To attain a service level of 50%, Howie should order the mean sales, or 250 firecracker sets.19.3- 3 The 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.19.3-4 The Division President is skeptical about his Vice President's recommendation because it would increase inventory levels. He has been promoting the just-in-time philosophy of minimizing inventory.19.4-1 The management science team began by trying to diagnose why the frequent stockouts were occurring under the current inventory policy.19.4- 2 Under the old inventory policy, the probability of a stockout is 50% and the maximum size of a stockout is 8,000.19.4- 3 Reorder point = average sales during lead time + amount of safety stock.19.4- 4 Even 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.19.4- 5 Management made the decision on how much safety stock to provide.19.4- 6 The relevant cost factors for choosing the order quantity are acquisition costs, setup costs, holding costs, and shortage costs.19.4- 7 The main component of shortage costs is lost future profit from lost future sales caused by customer dissatisfaction with delays in filling current orders.19.4- 8 Increasing 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.19.4- 9 The management science team used the EOQ model with planned shortages to find the approximately optimal order quantity.19.4- 10 The 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 fbr Production is unhappy because the policy would only slightly decrease the frequency of production runs.19.4- 11 The 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- 12 The setup cost and lead time will be greatly reduced by acquiring some additional production facilities that would be used solely fbr production of the disposable panoramic cameras.19.5- 1 The camera is considered a stable product because each camera in inventory will remain sellable indefinitely.b) If Leisure Limited refunds 75% of the purchase cost, then the unit salvage value fbr a returned set equals (0.75)($3)-($0.50) = $1.75. We determine the new optimal service level:From the normal table, Howie should order O.3cr above the mean to attain a service level of 61.5%, or 250 + (03)(60) = 268 firecracker sets. Note that Howie can now order more sets at one time than he could under the scenario of part a because he is not punished as severely as before when he fails to sell all sets.For the case of a 25% refund the unit salvage value equals $0.25.From the normal table, Howie should order 0.2cy below the mean to attain a service level of 42.1%, or 250 - (0.2)(60) = 238 firecracker sets. Howie must now purchase fewer sets at one time (compared to the previous scenarios) because he is punished more severely if he fails to sell sets.c) For a unit sale price of $6 and a 50% refund on returned firecracker sets, the optimal service level can be determined as follows:However, if Howie raises the price of a firecracker set, one would expect that the demand fbr his sets will decrease. Therefore, Talia should not use the same demand distribution that she used fbr her previous calculations of the optimal order quantity.d) Talia's strategy fbr estimating the demand is overly simplistic. She makes the simplifying assu