ch-12-operations-management-solution-manual-150311132229-conversion-gate01.pdf

164

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C H A P T E R

Managing Inventory

!ETION DIC!ION " 1.

The four types of inventory are:  





Raw material—items that are to be converted into product Work-in-process (WIP)—items that are in the process of  being converted Finished goods—completed items for which title has not been transferred MRO—(maint MRO—(maintenanc enance, e, repair, repair, and operating operating supplies)— supplies)— items that are necessary to keep the transformation process going

2. The advent of low-cost computing should not be seen as obviating the need for the ABC inventory classification scheme. Although the cost of computing   has decreased considerably, the cost cost of data acquisition  has not decreased in a similar fashion. Business organizations still have many items for which the cost of  data data acquis acquisiti ition on for a “perpe “perpetua tual” l” invent inventory ory system system is still still considerably higher than the cost of the item. 3. The purpose of the ABC system is to identify those items that require more attention due to cost or volume. 4. Types of costs— holding cost : cost of capital invested and space required; shortage cost : the cost of lost sales sales or customers customers who never return; return; the cost of lost good will; ordering cost : the costs associated associated with ordering, ordering, transporti transporting, ng, and receiving receiving the items; unit cost : the actual cost of the item. 5. Assumptions of EOQ model: demand is known and constant over time; lead time is known and constant; receipt of inventory is instan instantan taneou eous; s; quanti quantity ty discou discounts nts are not possib possible le;; the only only variable costs are the costs of placing an order or setting up production and the cost of holding or storing inventory over time and if orders are placed at the right time, stockouts or shortages can be completely avoided.

3. Provid Providing ing trained trained personne personnell to audit audit the accura accuracy cy of  inventory 4. Allowing the cause of errors to be identified and and remedial action to be taken 5. Maintainin Maintaining g accurate accurate inventory inventory records records A decrea decrease se in setup setup time time decrea decreases ses the cost cost per order, order, 9. encourages more and smaller orders, and thus decreases the EOQ.

10. Discount points below the EOQ have higher inventory costs, and the prices are no lower than at the EOQ. Points above the EOQ have higher inventory costs than the corresponding price break point or EOQ at prices that are no lower than either either of the price breaks or the EOQ. (It depends on whether there exists a discount point above the EOQ.) 11. Service level refers to the percent of customers to whom the product or service is delivered when and as promised. costs hold, hold, more more will will be ordered ordered using using an 12. If the same costs economic economic production production quantity, because the average average inventory inventory is less than the corresponding EOQ system.

13. In a  fixed-quantity  fixed-quantity  inventory system, when the quantity on hand reaches the reorder point, an or der is placed for the specified quantity. In a  fixed-period    inventory system, an order is placed at  fixed-period  inventory the end of the period. The quantity ordered is that needed to bring on-hand inventory up to a specified level. 14. The EOQ model gives quite good results under inexact inputs; a 10% error in actual demand alters the EOQ by less than 5%. 15. Safety stock is inventory beyond average demand during lead time, held to control the level of shortages when demand and/or lead time are not constant; inventory carried to assure that the desired service level is reached. 16. The reorder point is a function of: demand per unit of time, lead time, customer service level, and standard deviation of demand.

6. The EOQ increases as demand increases or as the setup cost increases; it decreases as the holding cost increases. The changes in the EOQ are proportional proportional to the square root of the changes changes in the parameters.

17. Most retail stores have a computerized cash register (pointof-sale) system. At the time of purchase, the computer system simultaneously rings up the bill and reduces the inventory level in its records for the products sold.

7. Price times quantity is not variable in the EOQ model, but is in the discount model. When quality discounts are available, the unit purchase price of the item depends on the order quantity.

18. Advantage of a fixed period system: There is no physical count of inventory inventory when items items are withdrawn. withdrawn. Disadvanta Disadvantage: ge: There is a possibility of stockout during the time between orders.

8.

Advantages of cycle counting: 1. Eliminati Eliminating ng the shutdown and interruption interruption of production production necessary for annual physical inventories 2. Eliminat Eliminating ing annual inventory inventory adjustment adjustmentss

I#EMMA ETHICA# D Setting service levels to meet inventory demand is a manager’s  job. Setting an 85% service level for whole blood is an important

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 judgment call on the part of the hospital administrator. Another major disaster means a certain shortage, yet any higher level may be hard to cost justify. Many ho spitals do develop joint or regional groups to share supplies. The basic issue is how to put a price tag on lifesaving medicines. This is not an easy question to answer, but it makes for good discussion.

ODE# E %ERCIE ACTIVE M

RO(#EM END&O'&CHAPTER P 12.1 An ABC system generally classifies the top 70% of dollar volume items as A, the next 20% as B, and the remaining 10% as C items. Similarly, A items generally constitute 20% of total number of items, B items are 30%; and C items are 50%. Ite) Co*e N+),er

ACTIVE MODEL 12.1: Economic Order Quantity (EOQ) Model 1.

1289 2347 2349 2363 2394 2395 6782 7844 8210 8310 9111

What is the EOQ and what is the lowest total cost? EOQ 200 units with a cost of $100

2. What is the annual cost of carrying inventory at the EOQ and the annual cost of ordering inventory at the EOQ of 200 un its? $50 for carrying and also $ 50 for ordering 3. From the graph, what can you conclude about the relationship between the lowest total cost and the costs of ordering and carrying inventory? The lowest total cost occurs where the ordering and inventory costs are the same. 4. How much does the total cost increase if the store manager orders 50 more hypodermics than the EOQ? 50 fewer hypodermics? Ordering more increases costs by $2.50 or 2.5%. Ordering fewer increases costs by $4.17 or 4.17% 5. What happens to the EOQ and total cost when demand is doubled? When carrying cost is doubled? The EOQ rises by 82 units (41%) and the total cost rises by $41 (41%) in either case. 6. Scroll through lower setup cost values and describe the changes to the graph. What happens to the EOQ? The curves seem to drop and move to the left. The EOQ decreases. 7. Comment on the sensitivity of the EOQ model to errors in demand or cost estimates. The total cost is not very sensitive to mistakes in forecasting demand or placing orders.

ACTIVE MODEL 12.2: Production Order Quantity Model 1.

What is the optimal production run size for hubcaps? 283

2.

How does this compare to the corresponding EOQ model? The run size is larger than the corresponding EOQ.

3.

What is the minimal cost? $70.71

4.

How does this compare to the corresponding EOQ model? The total cost is less than the cost for the equivalent EOQ model.

Average Do--ar

→ → → → → → → → → → →

400 × 3.75 300 × 4.00 120 × 2.50 75 × 1.50 60 × 1.75 30 × 2.00 20 × 1.15 12 × 2.05 8 × 1.80 7 × 2.00 6 × 3.00

= = = = = = = = = = =

Vo-+)e

Per.ent o/  Tota- 0 Vo-+)e

1,500.00 1,200.00 300.00 112.50 105.00 60.00 23.00 24.60 14.40 14.00 18.00

44.0% 36.0% 9.0% 3.3% 3.1% 1.8% 0.7% 0.7% 0.4% 0.4% 0.5%   100%   (rounded $3,371.50 )

The company can make the following classifications: A: 1289, 2347 (18% of items; 80% of dollar-volume). B: 2349, 2363, 2394, 2395 (36% of items; 17.2% of dollar-volume). C: 6782, 7844, 8210, 8310, 9111 (45% of items; 2.7% of dollarvolume).

12.2 (a) You decide that the top 20% of the 10 items, based on a criterion of demand times cost per unit, should be A items. (In this example, the top 20% constitutes only 58% of the total inventory value, but in larger samples the value would probably approach 70% to 80%.) You therefore rate items F3 and G2 as A items. The next 30% of the items are A2, C7, and D1; they represent 23% of  the value and are categorized as B items. The remaining 50% of  the items (items B8, E9, H2, I5, and J8) represent 19% of the value and become C items. Ann+aIte) De)an* Cot 03 De)an* A2 8 C7 !1 E9 "3 #2 H2 5 8

3,000 4,000 1,500 6,000 1,000 500 300 600 1,750 2,500

50 12 45 10 20 500 1,500 20 10 5

150,000 48,000 67,500 60,000 20,000 250,000 450,000 12,000 17,500 12,500

Cot C-ai.atio n  C   C A A C C C

(b) Borecki can use this information to manage his A and B items more closely and to save ordering costs on his less important C items by ordering only when A or B items are being ordered from the same supplier. (c) A2 could easily move to the A category based on annual dollar volume. In a small sample, 30% of the items can be placed in the A category if deemed appropriate.

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I V E N T O R Y   166 N

12.3 0Va-+e 5er Cae

Inventory Ite) "&' *e+' "ren -r&e' C&en' Pr&/e r& e++ue ('e) o'+er +&* R& ee '+e on P'+  To/+o 'ue  T*e*o+' E' ('e) &*  Tr'n *&ner' #r*& oder &n' rder d' Peer ur *+

  Or*ere *   5er Tota- 0 $2 7ee83 7ee8  Va-+e97ee8  Tota- : 0;$23

143 43 75 166 35 245 135 56 23 23 32 22 28 12 11 12 12 3 4 3

10 32 14 6 24 3 3 5 12 11 5 7 2 3 3 2 2 3 2 2

$1,430 $1,376 $1,050 $996 $840 $735 $405 $280 $276 $253 $160 $154 $56 $36 $33 $24 $24 $9 $8 $6 $8,151

C+)+-ative Per.ent o/ Inventory

Per.ent o/ Ran8  Inventory

$74,360 $71,552 $54,600 $51,792 $43,680 $38,220 $21,060 $14,560 $14,352 $13,156 $8,320 $8,008 $2,912 $1,872 $1,716 $1,248 $1,248 $468 $416 $312 $423,852

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

17.54% 16.88% 12.88% 12.22% 10.31% 9.02% 4.97% 3.44% 3.39% 3.10% 1.96% 1.89% 0.69% 0.44% 0.40% 0.29% 0.29% 0.11% 0.10% 0.07% 100.00%

17.54% 34.43% 47.31% 59.53% 69.83% 78.85% 83.82% 87.25% 90.64% 93.74% 95.71% 97.60% 98.28% 98.72% 99.13% 99.42% 99.72% 99.83% 99.93% 100.00%

(a) Fish filets total $74,360. (b) C items are items 10 through 20 in the above list (although this can be one or two items more or less). (c) Total annual $ volume = $423,852.

12.4 7,000 × 0.10 = 700 7,000 × 0.35 = 2,450 7,000 × 0.55 = 3,850

12.5

(a) EOQ

=Q=

700 ÷ 20 = 35 2450 ÷ 60 = 40.83 3850 ÷ 120 = 32 2(19,500)(25)

35 A items per day 41 B items per day 32 C items per day 108 items

(b) If S were $30, then the EOQ would be 60. If the true ordering cost turns out to be much greater than $30, then the firm’s order policy is ordering too little at a time.

12.8

Q

= 493.71 = 494 units

4 (b) Annual holdings costs = [Q /2] H = [494/2](4) = $988 (c) Annual ordering costs = [ D/Q]S = [19500/494](25) = $987

EOQ =

=

Q

12.9

2 × 240 × S .4

× 10

; or 60 =

=

480S  , or 4

60 = 120S , so solving for S results in S =

3,600 12

 H 

=

2 × 400 × 40 5

2 DS   H 

=

2 × 400 × 40 6

=

= 73 units setup or order cost,  H

2 DS  2 × 15,000 × 75 = = 300 units 25  H  (b) Annual holding costs = (Q /2) × H = (300/2) × 25 = $3,750

=

(c) Annual ordering costs = ( D/Q) × S = (15,000/300)

(d)

= $30.

= 80 units

 D = 15,000, H = $25/unit/year, S = $75

(a) EOQ

2 ( 8,000) ( 45)

= 848.53 units 1 12.7 (a) This problem reverses the unknown of a standard EOQ problem to solve for S . 60 =

=

2 DS 

where D = annual demand, S holding cost

2 ( 8,000) ( 45)

= 424.26 units 4 (c) If  H  drops in half, from $2 to $1/unit/month, EOQ

=

where D = annual demand, S = setup or order cost,  H = holding cost (b) Economic Order Quantity (Holding cost = $6 per year):

2(8,000)(45) = 600 units 2 (b) If H doubles, from $2 to $4/unit/month,

12.6 (a) EOQ

(a) Economic Order Quantity (Holding cost = $5 per year):

× 75 = $3,750  15,000 units  ROP = d × L =  ÷ × 2 days = 100 units  300 days  

=

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12.10 (a) Reorder point = Demand during lead time = 100 units/day × 21 days = 2,100 units (b) If demand during lead time doubles to 200 units/day,  ROP = 200 units/day × 21 days = 4,200 units. (c) If demand during lead time drops to 50 units/day,  ROP = 50 units/day × 21 days = 1,050 units.

12.14

For Q = 25: = For Q = 40: =

12.11 (a) D = 10,000  Number of business days = 300  Lead time = 5 days  ROP = [Demand/Day](Lead time) = [10,000/300](5) = 166.67 ≅ 167 units. (b) This number is important because it helps Duncan keep enough inventory to prevent stockouts while she waits for the new order to arrive. 12.12

2 DS  =  H 

(a)  EOQ =

2(6,000)(30) 10

For Q = 50: = For Q = 60: =

Q

= 7.91

(e) Cost of inventory management, excluding cost of goods = (31.62 × 30) + (94.87 × 10) = $1,897.30 (f) Total annual inventory cost = $601,897.30 (including the $600,000 cost of goods) Note: Rounding occurs in answers.

12.13

2 DS 

(a) Q =

2(2500)18.75

=

1.50 = 250 brackets per order  H 

Q

(b) Average inventory =

250

= 125 units 2 2 Q Annual holding cost =  H  = 125(1.50) = $187.50 2  D 2500 = = 10 orders /year (c) Number of orders = 250 Q Annual order cost (d) TC =

(e)

Q  H 2

+

D Q

=

 D Q

=

dL

2500 250

=

Working days

=

250

=  10(2) =

demand) d  =

S  = 10(18.75) = $187.50

S = 187.50 + 187.50 = $375/ year

Time between orders

(f) ROP

=

( D/Q)

= 25 days 10 20 units (where 10

=  daily

40 1,200 × 25 50 1,200 × 25

25 × 24

+ + +

60 1,200 × 25 100

2 40 × 24 2 50 × 24 2 60 × 24

+

QH 

2

= $1,500 = $1,230 = $1,200 = $1,220

2 100 × 24 2

Q

+

= $1,500

2 DS 

=

 H 

=

2 × 1,200 × 25 24

= 50 units

where  D = annual demand, S = setup or order cost,  H = holding cost As expected, small variations in order quantity will not have a significant effect on total costs. If we order twice as many (e.g., Q  goes from 25 to 50), TC increases by only $300 (see part a).

(c) Optimal number of orders/year = 31.62

31.62

25 1,200 × 25

+

 DS

(b) Economic Order Quantity:

= 189.74 units

250

1,200 × 25

For Q = 100: =

(b) Average inventory = 94.87

(d) Optimal days between orders =

= Order cost + Holding cost =

(a) Total cost

12.15

(a) The EOQ assumptions are met, so the optimal order quantity is EOQ

2 DS  =  H 

=

2(250)20 1

= 100 units

(b) Number of orders per year =  D/Q = 250/100 = 2.5 orders per year. Note that this would mean in one year the company places 3 orders and in the next it would only need 2 orders since some inventory would be carried over from the previous year. It averages 2.5 orders per year. (c) Average inventory = Q /2 = 100/2 = 50 units (d) Given an annual demand of 250, a carrying cost of  $1, and an order quantity of 150, Patterson Electronics must determine what the ordering cost would have to be for the order policy of 150 units to be optimal. To find the answer to this problem, we must solve the traditional economic order quantity equation for the ordering cost. As you can see in the calculations that follow, an ordering cost of $45 is needed for the order quantity of 150 un its to be optimal. 2 DS 

Q

=

S

= Q2

= 10 =   =

 H   H 

2 D

(150)2 (1) 2(250) 22,500 500

= $45

CHAPTER 12

12.16  D = 12,500/year, so d  = (12,500/250) = 50/day,  p = 300/day, S  = $30/order, H  = $2/unit/year Q=

2 DS  d   H  1 –  p



=



 D Q

=

12,500 671

Q

= 18.63

(e) Cost of inventory, excluding goods

559   = (18.63 × 30) +  × 2÷ = $1,117.90  2   Production Order Quantity, noninstantaneous delivery.  H = $.10/light-yr S = $50/setup P = $1.00/light  p = 100/day

Q

=

300 days/yr 2 DS 

 d   H 1 − ÷   p 



0.60 1 −



 50 500÷ 

 

(b) Inventory max (c)

 D Q

   = Q 1 − d ÷ = 1,095   p 

= 10,000 = 8.22

(d) TC =

1,217 Inventorymax H 2

+  D S

 

Q

= 328.50 + 328.80 = $657.30 12.19

At the Economic Order Quantity, we have: EOQ

=

(2 × 36,000 × 25) /0.45

= 2,000 units.

The total costs at this quantity are: Holding cost = Q /2 × H = 1,000 × .45 = $450 Ordering cost = D/Q × S = 36,000/2,000 × 25 = $450 Purchase cost = D × P = 36,000 × 0.85 = $30,600 Total cost = $900 + $30,600 = $31,500 At the quantity discount, we have: Holding cost = Q /2 × H = 3,000 × .45 = $1,350 Ordering cost = D/Q × S = 36,000/6,000 × 25 = $150 Purchase cost = D × P = 36,000 × 0.82 = $29,520 Total cost = $1,500 + $29,520 = $31,020

(a)  D = 12,000/yr

12,000/yr

d   p÷  

2 × 10,000 × 40

production rate

 d    50   Maximum inventory level = Q 1 − ÷ = 671 1 − ÷  300    p   1  = 6711 − ÷ = 559  6 

d  =

 

=

= 1217.2, or 1,217 units where  D = annual demand, S = setup cost,  H = holding cost, d = daily demand rate,  p = daily

(d) Days of demand satisfied by each production run = 250 = 13.42 days 18.63

12.17

2 DS 

=

 H 1 −

Q 671 = 2.24 Days in production for each order =  p = 300 Total time = 13.42 days per cycle. 2.24 Thus, percent of time in production = = 16.7% 13.42

I V E N T O R Y   16= N

(a) Production Order Quantity, noninstantaneous delivery:

2 × 12,500 × 30 = 671 (a) 2 1 – 50   300

(b) Number of production runs ( N ) =

(c)

12.18

MANAGING

= 40 /day =

2(12,000)50



.10 1 −



   40 ÷ 100 

The quantity discount will save $480 on this item. The company should also consider some qualitative aspects of the decision, such as available space, the risk of obsolescence of disks, and the risk  of deterioration of the storage medium over time, as 6,000 represents one-sixth of the year’s needs.

12.20  D (Annual demand) = 400 ×  12 = 4,800, P (Purchase price/Unit) = $350/unit,  H   (Holding cost /Unit) = $35/unit/year, S (Ordering cost/Order) = $120/order. So,

= 4,472 lights per run Q

 d   Average holding cost / year = 1 −  ÷  H  2    p  (b)     $26,832 = 4,472 1 −  40   (.10) = 200 = $134.16 2   100÷    D   12,000  (c) Average setup cost /year =  Q÷ S  =  4,472÷ 50       = $134.16   (d) Total cost (including cost of goods)

= PD + $134.16 + $134.16 = ($1 × 12,000) + $134.16 + $134.16 = $12,268.32/year

(a)

=

2

=

Thus, TC (Total cost) = PD +

 HQ

2

+

SD Q

 35 × 181 + ÷   2  

= (4,800 × 325) + 

120 × 4,800  ÷ 181 

= $1,560,000+ 3,168 + 3,182 = $1,566,350, where Price = $325/unit.

   

Annual ordering cost =

 45,000   D ( S ) =  (200) Q  16,971÷ 

= $530.33

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However, if Bell Computers orders 200 units, which is optional with the discount model, then

 35 × 200 + ÷   2  

TC  = (4,800 × 325) + 

 120 × 4,800 200  ÷

   

= 1,440,000 + 3,500 + 2,880 = $1,446,380. Bell Computers should order 200 units for a minimum total cost of $1,446,380. 2 DS 

(b) Q1 =

 H 

Q2 = Q3 =

2 DS   H 

2 DS   H 

=

=

=

2 × 4,800 × 120 35

EOQ (adjusted) = 300 units Because this last economic order quantity is below the discounted price, we must adjust the order quantity to 300 units. The adjusted EOQ for 300 units is used to compute total cost. Total cost (with discount) = Cost of goods+ Ordering cost + Carrying cost = $380(1,400) +

= 188 units

32.5

30

= 30.3 units

= 181 units

2 × 4,800 × 120

2 × 4,800 × 120

300($380)(0.2) 2 = $532, 000 + $117 + $11, 400

= 196 units

Thus, TC (188 units) = PD +  HQ + SD Q 2

 32.5 × 188 + 120 × 4,800    ÷   ÷  2 188   

= $543,517 The optimal strategy is to order 300 units at a total cost of  $543,517.

12.22  D = 45,000, S = $200, I = 5% of unit price, H = IP Best option must be determined first. Since all solutions yield Q values greater than 10,000, the best option is the $1.25 price.

= (325 × 4,800)+ 

(a) Q* =

= 1,560,000 + 3,055 + 3,064 = $1,566,119  HQ

2

+

SD Q

 IP

= 16,970.56 Q

2

 16,971  (.05) (1.25) ÷  2  

( IP ) = 

= $530.33

 30 × 200 + 120 × 4,800    ÷  200  ÷    2  

(c)

= 1,440,000 + 3,000 + 2,880 = $1,445,880 The minimum order quantity is 200 units yet again because the overall cost of $1,445,880 is less than ordering 188 units, which has an overall cost of $1,566,119.

12.21 The solution to any quantity discount model involves determining the total cost of each alternative after quantities have been computed and adjusted for the original problem and every discount. We start the analysis with no discount: 2(1,400)(25) 0.2(400)

= 29.6 units Total cost (no discount) = Cost of goods + Ordering cost + Carrying cost  

2 DS 

(b) Annual holding cost =

= (300 × 4,800) + 

EOQ (no discount) =

1,400(25) 300

+

181 units would not  be bought at $350. 196 units cannot be bought at $300, hence that isn’t possible either. So, EOQ = 188 units.

TC (200 units) = PD +

2(1,400)(25) 0.2($380)

EOQ (with discount) =

= $400(1,400) + 1,400(25) 29.6

29.6($400)(0.2) 2 = $560, 000 + $1,183 + $1,183

+

= $562,366 The next step is to compute the total cost for the discount:

Annual ordering cost =

D ( S) Q

45,000  =  ÷ ( 200)  16,971  = $530.33

(d) Unit costs = P × D = ($1.25) (45,000) = $56,250 (e) Total cost = $530.33 + $530.33 + 56,250.00 = $57,310.66

12.23

(a)  D = 20,000/yr  I  = 20 percent of purchase price per year in holding costs, where H = IP S = $40/order P = $20/tire if fewer than 500 are ordered; $18/tire if between 500 and 999 are ordered; and $17/tire if 1,000 or more are ordered

CHAPTER 12

Q20

=

2 DS/ H

 

= (2 × 20,000 × 40) /(.2 × 20) = 632.5 (not valid) Over 500, $18 discount would apply. Q18

=

 

= (2 × 20,000 × 40) /(.2 × 18)

2 DS/ H

 

= 666.7 (valid) ≈ 667 Q17

=

 

= (2 × 20,000 × 40) /(.2 × 17)

2 DS/ H

 

= 686 (not valid) Cannot buy 686 at $17.

MANAGING

I V E N T O R Y   1