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

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个人收集整理 勿做商业用途
CHAPTER 19
INVENTORY MANAGEMENT WITH UNCERTAIN DEMAND
Review Questions

19.1-1 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 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。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。
19.3-2 Recent 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.
19.3-3 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 for 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 for 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。
19.5—2 A continuous—review 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.
19.5-3 The traditional method of implementing a continuous-review inventory system was to use a two-bin system。
19。5—4 The common modern method of implementing a continuous—review inventory system is a computerized inventory system.
19。5—5 An （R， Q） inventory policy controls a continuous-review inventory system by using a fixed reorder point R and a fixed order quantity Q。
19。5-6 Except 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。
19.5-7 The EOQ model with planned shortages is used to approximate the optimal order quantity.
19.5—8 The 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。
19.5-9 The 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。5—10 R = m + KLs.
19。6—1 The 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。6—2 Occasionally it is not appropriate to apply a single—product inventory model because of interactions between the products.
19.6—3 A 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。6-4 The echelons of IBM’s 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。
19.6-5 The 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。6—6 The cost savings were about ＄20 million per year through improved operational efficiency and even larger annual savings in holding costs。
19.6—7 A supply chain spans procurement， manufacturing， and distribution。
19。6-8 HP faced inventories mounting into the billions of dollars and alarming customer dissatisfaction with its order fulfillment process。
19.6-9 WINO deals with inventories of finished products as well as inventories of incoming goods and departing goods at each site along the supply chain。
19.6-10 A key intangible benefit was to enhance HP’s reputation as a progressive company that can be counted on by its customers to fill their orders promptly.
Problems

19.1 a) 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）.

Freddie’s most profitable alternative is to order 16 copies.
c) Service level if order 15 copies = 0。4
Service level if order 16 copies = 0。6
Service level if order 17 copies = 0。9
Service level if order 18 copies = 1

Cunder = $1
Cover = ＄1

Optimal service level = Cunder / （Cunder + Cover） = $1 / （$1 + ＄1） = 0.5

Freddie should order 16 copies。
d）

19.2 a） Cunder =＄3 –$1 = ＄2 Cover = $1 – ＄0。50 = ＄0.50
b）

Prepare 4 doughnuts each day to minimize costs。
c） Service level if 0 made = 0.1
Service level if 1 made = 0.25
Service level if 2 made = 0。45
Service level if 3 made = 0.75
Service level if 4 made = 0。9
Service level if 5 made = 1

Optimal service level = Cunder / （Cunder + Cover） = $2 / (＄2 + ＄0。50） = 0。8

Prepare 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
Þ ($2 + g) / （$2.5 + g) > 0.9
Þ g 〉 ＄2。50。

The goodwill cost would need to be at least $2.50 before 5 doughnuts should be prepared。
19。3 a) 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。4 a） Revenue (with shortages) = 500（＄3) = $1，500
b) Average number of loaves sold （without shortages) = 300 + （500–300）/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 = $1,300
d） Average number of loaves not sold = (200–0）/2 = 100.
Average number of day—old loaves obtained over all days = 100 x 0。667 = 66。7。
Average daily revenue from day—old 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。5 a） 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 won’t 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 won't be sold = 62。5。
19.6 a） This problem can be interpreted as an inventory problem with uncertain demand for a perishable product with traveler’s 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。3
Service level for buying 1 = 0。55
Service level for buying 2 = 0.75
Service level for buying 3 = 0。85
Service level for buying 4 = 0。95
Service level for buying 5 = 1

Optimal service level = Cunder / （Cunder + Cover） = $49 / （$49 + ＄3) = 0。94。
Buy 4 additional checks。
d)

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 P(demand ≤ Q） = L。
c） Q = m + KLs = 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。05
Service level for accepting 1 = 0.15
Service level for accepting 2 = 0。3
Service level for accepting 3 = 0.45
Service level for accepting 4 = 0。6
Service level for accepting 5 = 0.75
Service level for accepting 6 = 0.85
Service level for accepting 7 = 0。95
Service level for accepting 8 = 1

Optimal service level = Cunder / （Cunder + Cover） = ＄250 / ($250 + $150) = 0。625.
Accept 5 overbooked reservation。
d）

19.9 a）

Q* is cut in half。 R is unchanged. This will reduce the average monthly holding cost. However, it will i