Solutions 1.The Cost Of Computing

CHAPTER 12

DISCUSSION QUESTIONS

1. 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.

2. The standard EOQ model assumes instantaneous delivery (delivery of the entire lot is made at one instant of time), whereas the Production Inventory Model assumes that delivery takes place at a constant rate over time.

3. Reasons for an organization to maintain inventory include: n The decoupling function: ¨ inventory can be used to decouple stages in the production process within an organization ¨ inventory can be used to decouple the production process from instabilities or irregularities in supply of raw materials or labor ¨ inventory can be used to decouple the production process from unstable demand and thus (a) allow production scheduling to develop a “smoother” schedule, and (b) avoid shortages or stockouts n Quantity discounts: ¨ inventory can be used to enable the organization to purchase goods in larger lot sizes and take advantage of quantity discounts n A hedge against inflation: ¨ investing in inventory now assures one that the price will not increase

4. Costs that are associated with ordering and maintaining inventory include: n Initial purchase cost of the item n Holding cost (insurance, space, heat, light, security, warehouse personnel, etc.) n Obsolescence or deterioration cost (particularly important in perishable goods or in a product that is undergoing rapid technological evolution) n Ordering or setup cost (cost of forms, clerical processing, etc., or cost of machine setup)

5. The more important assumptions of the basic EOQ model are: n Demand is known and constant over time. n The lead time, that is, the time between the placement of the order and the receipt of the goods, is known and constant. n The receipt of the inventory is instantaneous; i.e., the goods arrive in a single batch, at one instant in time.

Chapter 12: Inventory Management 1 n Quantity discounts are not possible. n The only variable costs are the cost of setting up or placing an order and the cost of holding or storing inventory over time. n If orders are placed at the right time, stockouts or shortages can be completely avoided.

6. The EOQ is relatively insensitive to small changes in demand or setup or carrying costs. If, for example, demand increases by 10%, EOQ will increase by approximately 5%.

9. A decrease in setup time decreases the cost per order, encourages more and smaller orders, and thus decreases the EOQ.

12. If per unit holding costs increase with increasing inventory, total inventory cost will increase; EOQ will decrease.

14. 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.

END-OF-CHAPTER PROBLEMS

12.2 He decides 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%.) He therefore rates 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.

Item Annual Demand Cost ($) Demand ´ Cost Classification A2 3,000 50 150,000 B B8 4,000 12 48,000 C C7 1,500 45 67,500 B D1 6,000 10 60,000 B E9 1,000 20 20,000 C F3 500 500 250,000 A G2 300 1,500 450,000 A H2 600 20 12,000 C I5 1,750 10 17,500 C J8 2,500 5 12,500 C

12.3 Item Annual Demand Cost ($) Demand ´ Cost Classification E102 800 4.00 3,200 C D23 1,200 8.00 9,600 A 27% D27 700 3.00 2,100 C R02 1,000 2.00 2,000 C R19 200 8.00 1,600 C S107 500 6.00 3,000 C S123 1,200 1.00 1,200 C U11 800 7.00 5,600 B 16% U23 1,500 1.00 1,500 C 33% V75 1,500 4.00 6,000 B 17% 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 35 C items per day

2 Instructor’s Solutions Manual t/a Operations Management 108 items

2100062.50 12.5 EOQ   500 units 0.50

28,00045 12.6 EOQ   600 units 2

28,00045 720,000 12.7 300   90,000  H H 720,000 H   $8 90,000

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

2DS 2  400  40 Q    80 units H 5

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

2DS 2  400  40 Q    73 units H 6

where: D = period demand, S = setup or order cost, H = holding cost

12.9 (a) Economic Order Quantity:

2DS 2 1,500 150 Q    100 units H 45

where: D = period demand, S = setup or order cost, H = holding cost QH 100  45 (b) Holding cost    $2,250.00 2 2 DS 1500 150 (c) Order cost    $2,250.00 Q 100 (d) Reorder point: 1,500 Reorder point = demand during lead time  units day  6 days  30 units 300

12.10 Reorder point = demand during lead time  100 units day  21 days  2,100 units

12.11 Reorder point = demand during lead time  500 units day 14 days  7,000 units

2DS 2  4,000  25 Q    149.1 or 149 valves H 0.10  90

where: D = period demand, S = setup or order cost, H = holding cost (b) Average inventory  74.5 valves

Demand 4,000 (c) Number of orders per year    26.8 or 27 orders EOQ 149

Chapter 12: Inventory Management 3 (d) Assuming 250 business days per year, the optimal number of business days between orders is given by:

250 1 Optimal number of days   9 days 27 4

(e) Total annual inventory cost  Order cost  holding cost DS QH 4,000  25 149  0.1 90     Q 2 149 2  671.14  670.50  $1,341.64 Note: Order and carrying costs are not equal due to rounding of the EOQ to a whole number. (f) Reorder point = demand during lead time  16 units day  5 days  80 valves

2DS 2  5,000  30 Q    77.46 or 78 units H 50

where: D = period demand, S = setup or order cost, H = holding cost 78 (b) Average inventory   39 units 2 Demand 5,000 (c) Number of orders per year    64.1 or 64 orders EOQ 78 (d) Assuming 250 business days per year, the optimal number of business days between orders is given by:

250 Optimal number of days   3.91 days 64

(e) Total cost  order cost  holding cost DS QH 5,000  30 78  50     Q 2 78 2  1,923.02 1,950  $3,873.08 Note: Order and carrying costs are not equal due to rounding of the EOQ to a whole number. If an EOQ of 77.46 is used, the order and carrying costs calculate to $1,936.49 for a total cost of $3,872.98. (f) Reorder point:

5,000 units Reorder point = demand during lead time  10 days  200 units 250 days

This is not to say that we reorder when there are 200 units on hand (as there never are). The ROP indicates that orders are placed several cycles prior to their actual demand.

2DS 2 1,200  25 Q    50 units H 24

where: D = period demand, S = setup or order cost, H = holding cost DS QH (b) Total cost = order cost + holding cost   Q 2

4 Instructor’s Solutions Manual t/a Operations Management 1,200  25 25  24 For Q  25:    $1,500 25 2 1,200  25 40  24 For Q  40 :    $1,230 40 2 1,200  25 50  24 For Q  50 :    $1,200 50 2 1,200  25 60  24 For Q  60 :    $1,220 60 2 1,200  25 100  24 For Q  100 :    $1,500 100 2

As expected, small variations in order quantity will not have a significant effect on total costs.

DS QH 12.15 (a) Total cost = order cost + holding cost   Q 2 For Q  50 :

600  60 50  20   720  500  $1,220 50 2

(b) Economic Order Quantity:

2DS 2  600  60 Q    60 units H 20

where: D = period demand, S = setup or order cost, H = holding cost For Q  60 :

600  60 60  20   600  600  $1,200 60 2

(c) Reorder point: 600 units Reorder point = demand during lead time  10 days  24 units 250 days

12.16 Economic Order Quantity, noninstantaneous delivery: 2DS 2 10000  200 Q    2309.4 units H[1  (d / p)  50  1.00 1   200

where: D = period demand, S = setup or order cost, H = holding cost, d = daily demand rate, p = daily production rate

12.17 Economic Order Quantity, noninstantaneous delivery: 2DS 2  8000 100 Q    1651.4 units H[1  (d / p)  40  0.80 1   150 

where: D = period demand, S = setup or order cost, H = holding cost, d = daily demand rate, p = daily production rate

12.18 (a) Economic Order Quantity, noninstantaneous delivery:

Chapter 12: Inventory Management 5 2DS 2 10000  40 Q    1217.2 units H[1  (d / p)  50  0.60 1   500

where: D = period demand, S = setup or order cost, H = holding cost, d = daily demand rate, p = daily production rate  d  50       (b) I  Q1     1217.21     1095.5 units max   p    500 

D 10,000 (c)   8.22 Q 1,217 I D (d) T.C. max H  S  328.50  328.80  657.30 2 Q

12.19 Economic Order Quantity:

2DS Q  H

where: D = period demand, S = setup or order cost, H = holding cost, P  price/unit (a) Economic Order Quantity, standard price:

2  2,000 10 Q   200 units 1 Total cost  order cost  holding cost  purchase cost DS QH 2,000 10 200 1    PD    2,000 1  100 100  2,000  $2,200 Q 2 200 2

(b) Quantity Discount:

Total cost  order cost  holding cost  purchase cost DS QH 2,000 10 2,000 1    PD    2,000  0.75 Q 2 2,000 2  10 1,000 1,500  $2,510

Note: No, EOQ with 200 units and a total cost of $2,200 is better.

12.20 Under present price of $50.00 per unit, Economic Order Quantity:

2DS Q  H 2 1,000  40 Q   80 units 0.25  50

where: D = period demand, S = setup or order cost, H = holding cost, P  price/unit

6 Instructor’s Solutions Manual t/a Operations Management Total cost  order cost  holding cost  purchase cost DS QH 1,000  40 80  0.25  50    PD    1,000  50 Q 2 80 2  500.00  500.00  50,000  $51,000 Under the quantity discount price reduction of 3%:

Total cost  order cost  holding cost  purchase cost DS QH 1,000  40 200  0.25  50  0.97    PD   1,000  50  0.97 Q 2 200 2  200.00 1212.50  48,500  $49,912.50

Therefore, the pumps should be ordered in batches of 200 units and the quantity discount taken.

12.21 Under present price of $7.00 per unit, Economic Order Quantity:

2DS Q  H 2  6,000  20 Q   478.1 or 478 units 0.15  7

where: D = period demand, S = setup or order cost, H = holding cost, P  price/unit

Total cost  order cost  holding cost  purchase cost DS QH 6,000  20 478  0.15  7    PD    7  6,000 Q 2 478 2  251.05  250.95  42,000  $42,502.00

Note: Order and carrying costs are not equal due to rounding of the EOQ to a whole number. Under the quantity discount price of $6.65 per unit:

Total cost  order cost  holding cost  purchase cost DS QH 6,000  20 3,000  0.15  6.65    PD    6,000  6.65 Q 2 3,000 2  40.00 1,496.25  39,900  $41,436.25

Therefore, the new policy, with a total cost of $41,436.25, is preferable.

2DS Q  H

where: D = period demand, S = setup or order cost, H = holding cost, P  price/unit (a) Economic Order Quantity, standard price:

2  45 10 Q   30 units 0.05  20

Chapter 12: Inventory Management 7 Total cost  order cost  holding cost  purchase cost DS QH 45 10 30  0.05  20    PD    45  20 Q 2 30 2  15 15  900  $930

(b) Quantity Discount, 75 units or more. Economic Order Quantity, discount over 75 units:

2  45 10 Q   31.19 or 31 units 0.05 18.50

Because EOQ = 31 and a discount is given only on orders of 75 or more, we must calculate the total cost using a 75-unit order quantity:

Total cost  order cost  holding cost  purchase cost DS QH 45 10 75  0.05 18.50    PD    45 18.50 Q 2 75 2  6  34.69  832.50  $873.19

(c) Quantity Discount, 100 units or more; Economic Order Quantity, discount over 100 units:

2  45 10 Q   33.81 or 34 units 0.05 15.75

EOQ = 34 and a discount is given only on orders of 100 or more, thus we must calculate the total cost using a 100-unit order quantity. Calculate total cost using 100 as order quantity:

Total cost  order cost  holding cost  purchase cost DS QH 45 10 100  0.05 15.75    PD    45 15.75 Q 2 100 2  4.5  39.38  708.75  $752.63

Based purely upon cost, the decision should be made to order in quantities of 100, for a total cost of $752.63. It should be noted, however, that an order quantity of 100 implies that an order will be placed roughly every two years. When orders are placed that infrequently, obsolescence may become a problem.

2DS Q  H

where: D = period demand, S = setup or order cost, H = holding cost, P  price/unit (a) Order quantity 9 sheets or less, unit price = $18.00

2 100  45 Q   50 units 0.20 18

8 Instructor’s Solutions Manual t/a Operations Management Total cost  order cost  holding cost  purchase cost DS QH 100  45 50  0.20 18    PD    18 100 Q 2 50 2  90  90 1,800  $1,980 see note at end of problem re. actual price

(b) Order quantity 10 to 50 sheets: unit price = $17.50

2 100  45 Q   50.7 units or 51 units 0.20 17.50 Total cost  order cost  holding cost  purchase cost DS QH 100  45 51 0.20 17.50    PD    17.50 100 Q 2 51 2  88.23  89.25 1750.00  1927.48

Note: Order and carrying costs are not equal due to rounding the EOQ to a whole number. See note at end of problem regarding price. (c) Order quantity more than 50 sheets: unit price = $17.25

2 100  45 Q   51.1 units or 51 units 0.20 17.25 Total cost  order cost  holding cost  purchase cost DS QH 100  45 51 0.20 17.25    PD    17.25 100 Q 2 51 2  88.24  87.98 1,725.00  $1,901.22

Therefore, order 51 units. Note: Order and carrying costs are not equal due to rounding of the EOQ to a whole number. Important Note: Calculations of total cost under (a) and (b) are actually inappropriate because the original assumptions as to lot size would not be satisfied by the calculated EOQs.

12.24 D  700 12 , H  5, S  50

Allen 1–499 $16.00 500–999 $15.50 1000+ $15.00

Baker 1–399 $16.10 400–799 $15.60 800+ $15.10

2DS 28,40050 Q    409.88  410 H 5

Vendor: Allen

410 8,400 at 410, TC  5  50  8,40016  $136,449.36 2 410

Chapter 12: Inventory Management 9 500 8,400 at 500, TC  5  50  8,40015.5  $132,290 2 500

1,000 8,400 at 1000, TC  5  50  8,40015  $128,920 BEST 2 1,000

Vendor: Baker

410 8,400 at 410, TC  5  50  8,40015.60  $133,089.39 2 410 800 8,400 at 800, TC  5  50  8,40015.10  $129,365 2 800

10 Instructor’s Solutions Manual t/a Operations Management