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164

CHAPTER 12 M A N A G I N G I N V E N T O RY

C H A P T E R

Managing Inventory

DISCUSSION QUESTIONS 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—(maintenance, repair, and operating 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 of data acquisition has not decreased in a similar fashion. Business organizations still have many items for which the cost of data acquisition for a “perpetual” inventory system is 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 or customers who never return; the cost of lost good will; ordering cost: the costs associated with ordering, transporting, and 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 instantaneous; quantity discounts are not possible; the 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. Providing   trained personnel to audit the accuracy of inventory 4. Allowing   the cause of errors to be identified and remedial action to be taken 5.  Maintaining accurate inventory records 9. A decrease in setup time decreases the cost per order, 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 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. 12.  If the same costs hold, more will be ordered using an economic production quantity, because the average inventory is less than the corresponding EOQ system. 13.  In a fixed-quantity inventory system, when the quantity on hand reaches the reorder point, an order is placed for the specified quantity. In a fixed-period inventory system, an order is placed at 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 to the square root of the 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 when items are withdrawn. Disadvantage: There is a possibility of stockout during the time between orders.

8.  Advantages of cycle counting: 1. Eliminating   the shutdown and interruption of production necessary for annual physical inventories 2. Eliminating   annual inventory adjustments

ETHICAL DILEMMA Setting service levels to meet inventory demand is a manager’s job. Setting an 85% service level for whole blood is an important

165

CHAPTER 12 M A N A G I N G I N V E N T O RY

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 hospitals 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.

ACTIVE MODEL EXERCISES

END-OF-CHAPTER PROBLEMS 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%. Item Code Number

ACTIVE MODEL 12.1: Economic Order Quantity (EOQ) Model

1289 2347 2349 2363 2394 2395 6782 7844 8210 8310 9111

1.  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 units? $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.

Volume 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 )

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.

1.  What is the optimal production run size for hubcaps? 283

A2 B8 C7 D1 E9 F3 G2 H2 I5 J8

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

→ → → → → → → → → →

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 =

$3,371.50

Item

3.  What is the minimal cost? $70.71

→

Percent of Total $ Volume

The company can make the following classifications:

ACTIVE MODEL 12.2: Production Order Quantity Model

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

Average Dollar

Annual Demand Cost ($) Demand × Cost Classificatio n 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

B C B B 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.

CHAPTER 12 M A N A G I N G I N V E N T O RY 166

12.3  $Value per Case

Inventory Item Fish filets French fries Chickens Prime rib Lettuce (case) Lobster tail Rib eye steak Bacon Pasta Tomato sauce Tablecloths Eggs (case) Oil Trashcan liners Garlic powder Napkins Order pads Pepper Sugar Salt

#Ordere d per Week

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

Total $ Value/Week

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

(52 Weeks) Total = ($*52)

$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

$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

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

Percent of Inventory 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%

Cumulative Percent of Inventory 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  700 ÷  20 = 35 35 A items per day 7,000 × 0.35 = 2,450 2450 ÷  60 = 40.83 41 B items per day 7,000 × 0.55 = 3,850 3850 ÷ 120 = 32 32 C items per day 108 items 2(19,500)(25) = 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

12.5  (a) 

EOQ = Q =

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

12.6 (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 × 240 × S ; or 60 = .4 × 10

480S , or 4

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

12.8  (a)  Economic Order Quantity (Holding cost = $5 per year): 2 × 400 × 40 = = 80 units 5 H where D = annual demand, S = setup or order cost, H = holding cost (b)  Economic Order Quantity (Holding cost = $6 per year): Q=

Q=

2( 8,000) ( 45) EOQ = = 424.26 units 4 (c) If H drops in half, from $2 to $1/unit/month, EOQ =

(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.

3,600 = $30. 12

2 DS

2 DS = H

2 × 400 × 40 = 73 units 6

where D = annual demand, S = setup or order cost, H = holding cost 12.9  D = 15,000, H = $25/unit/year, S = $75 2 DS 2 × 15,000 × 75 = = 300 units H 25 (b)  Annual holding costs = (Q/2) × H = (300/2) × 25 = $3,750 (a) EOQ =

(c)  Annual ordering costs = (D/Q) × S = (15,000/300) × 75 = $3,750  15,000 units (d) ROP = d × L =  ÷ × 2 days = 100 units  300 days 

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CHAPTER 12 M A N A G I N G I N V E N T O R Y

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. 12.11 (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  (a)  EOQ =

2DS = H

2(6,000)(30) = 189.74 units 10

(b)  Average inventory = 94.87 (c)  Optimal number of orders/year = 31.62 (d)  Optimal days between orders =

250 = 7.91 31.62

(e)  C ost 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. 2 DS 2(2500)18.75 = H 1.50 = 250 brackets per order Q 250 = 125 units (b)  Average inventory = = 2 2 Q Annual holding cost = H = 125(1.50) = $187.50 2 D 2500 = = 10 orders /year (c)  Number of orders = 250 Q D Annual order cost = S = 10(18.75) = $187.50 Q Q D (d)  TC = H + S = 187.50 + 187.50 = $375/ year 2 Q

12.13  (a) 

(e) 

Q=

Time between orders=

Working days (D /Q )

250 = = 25 days 10   (f) ROP = dL = 10(2) = 20 units (where 10 = daily demand) 2500 d= = 10 250

12.14  (a) 

Total cost = Order cost + Holding cost =

DS QH + Q 2

1,200 × 25 25 × 24 + = $1,500 25 2 1,200 × 25 40 × 24 For Q = 40: = + = $1,230 40 2 1,200 × 25 50 × 24 + = $1,200 For Q = 50: = 50 2 1,200 × 25 60 × 24 For Q = 60: = + = $1,220 60 2 1,200 × 25 100 × 24 + = $1,500 For Q = 100: = 100 2 For Q = 25: =

(b)  Economic Order Quantity: 2 × 1,200 × 25 = 50 units 24 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). Q=

2 DS = H

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

2 DS = H

2(250)20 = 100 units 1

(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 units to be optimal. 2 DS H 2 H S =Q 2D Q=

2

=

(150) (1) 2(250)

=

22,500 = $45 500

CHAPTER 12 M A N A G I N G I N V E N T O RY 168

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 =  H 1 – pd  

12.18  (a) Production   Order Quantity, noninstantaneous delivery:

 50  d Maximum inventory level= Q  1− ÷ = 671 1− ÷ p 300      1 = 671 1 − ÷ = 559  6 (d)  Days of demand satisfied by each production run = 250 = 13.42 days 18.63 Q 671 = 2.24 Days in production for e ach order = p = 300 Total time = 13.42 days per cycle. Thus, percent of time in production = 2.24 = 16.7% 13.42

 559  = (18.63 × 30) +  × 2÷ = $1,117.90  2  12.17  Production Order Quantity, noninstantaneous delivery. (a)  D = 12,000/yr H = $.10/light-yr S = $50/setup P = $1.00/light 12,000/yr = 40 / day 300 days/yr

2 DS 2(12,000)50 =    d .10 1 − 40÷ H 1− ÷ p 100     = 4,472 lights per run

Q=

(b)

Q   1−  2  

d ÷ = 1,095 p

D 10,000 8.22 = = 1,217 Q Inventorymax D H+ S (d)  TC = 2 Q (c) 

= 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:

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

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, d H  p÷ 

4,472   40  $26,832 1− =  (.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

 (b) Inventorymax = Q 1 − 

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.

p = 100/day

Average holding cost / year=

where D = annual demand, S = setup cost, H = holding cost, d = daily demand rate, p = daily production rate

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

(e)  Cost of inventory, excluding goods

d=

2 × 10,000 × 40   50 0.60 1 − ÷  500

= 1217.2, or 1,217 units

D 12,500 (b)  Number of production runs (N ) = = = 18.63 671 Q (c) 

2 DS =  d H1 − ÷ p 

Q=

2 × 12,500 × 30 = 671 (a)  2 1 – 50   300

(a)  Q =

2 DS = H = 181.42 = 181 units(rounded)

Thus, TC (Total cost) = PD +

HQ SD + 2 Q

35 ×181 = (4,800 × 325) +  2 ÷  

+ 120 × 4,800   181  ÷ 

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

Annual ordering cost =D S ) = 45,000÷ (20 Q(  16,971 = $530.33 169

CHAPTER 12 M A N A G I N G I N V E N T O R Y

However, if Bell Computers orders 200 units, which is optional with the discount model, then     TC = (4,800 × 325) +  35 × 200÷ +  120 × 4,800÷ 2   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. (b) Q1 =

2 DS = H

2 × 4,800 × 120 = 181 units 35

Q2 =

2 DS = H

2 × 4,800 × 120 = 188 units 32.5

Q3 =

2 DS = H

2 × 4,800 × 120 = 196 units 30

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. Thus, T...