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Chapter 12 Inventory Management Discussion 1. A large bakery buys flour in 25- pound bags. The bakery uses an average of 4,860 bags a year. Preparing an order and receiving a shipment of flour involves a cost of $ 10 per order. Annual carrying costs are $ 75 per bag. a. Determine the economic order quantity. b. What is the average number of bags on hand? c. How many orders per year will there be? d. Compute the total cost of ordering and carrying flour. e. If ordering costs were to increase by $ 1 per order, how much would that affect the minimum total annual cost? 2. A large law firm uses an average of 40 boxes of copier paper a day. The firm operates 260 days a year. Storage and handling costs for the paper are $ 30 a year per box, and it costs approximately $ 60 to order and receive a shipment of paper. a. What order size would minimize the sum of annual ordering and carrying costs? b. Compute the total annual cost using your order size from part a. c. Except for rounding, are annual ordering and carrying costs always equal at the EOQ? 3. A chemical firm produces sodium bisulfate in 100- pound bags. Demand for this product is 20 tons per day. The capacity for producing the product is 50 tons per day. Setup costs $ 100, and storage and handling costs are $ 5 per ton a year. The firm operates 200 days a year. ( Note: 1 ton = 2,000 pounds.) a. How many bags per run are optimal? b. What would the average inventory be for this lot size? c. Determine the approximate length of a production run, in days. d. About how many runs per year would there be? e. How much could the company save annually if the setup cost could be reduced to $ 25 per run? 4. Offwego Airlines has a daily flight from Chicago to Las Vegas. On average, 18 ticket holders cancel their reservations, so the company intentionally overbooks the flight. Cancellations can be described by a normal distribution with a mean of 18 passengers and a standard deviation of 4.55 passengers. Profit per passenger is $ 99. If a passenger arrives but cannot board due to overbooking, the company policy is to provide a cash payment of $ 200. How many tickets should be overbooked to maximize expected profit? 5. Given this information: Expected demand during lead time = 300 units Standard deviation of lead time demand = 30 units Determine each of the following, assuming that lead time demand is distributed normally: a. The ROP that will provide a risk of stockout of 1 percent during lead time. b. The safety stock needed to attain a 1 percent risk of stockout during lead time. c. Would a stock-out risk of 2 percent require more or less safety stock than a 1 percent risk? Explain. Would the ROP be larger, smaller, or unaffected if the acceptable risk was 2 percent instead of 1 percent? Explain.

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Answer Keys 1. D = 4,860 bags/yr. S = $10 H = $75 a.

Q

2DS 2(4,860)10  36 bags H 75

b. Q/2 = 36/2 = 18 bags c.

D 4,860 bags  135 orders Q 36 bags / orders D

d. TC Q / 2H  Q S 

36 4,860 (75)  (10) 1,350  1,350  $2,700 2 36

e. Using S = $5, Q =

2(4,860)(11) 37.757 75

4,860 37.757 (11) 1,415.89  1,415.90 $2,831.79 (75)  37.757 2 Increase by [$2,831.79 – $2,700] = $131.79 TC 

2.

D = 40/day x 260 days/yr. = 10,400 packages S = $60 H = $30 a.

Q0 

b.

TC 



2DS 2(10,400)60   203.96  204 boxes H 30 Q D H S 2 Q

10,400 204 (60)  3,060  3,058.82 $6,118.82 (30)  204 2

c. Yes

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3. p = 50/ton/day u = 20 tons/day D= 20 tons/day x 200 days/yr. = 4,000 tons/yr. 200 days/yr. S = $100 , H = $5/ton per yr. a.

Q0 

2DS p  H p u

b.

I max 

Q 516.4 (p  u)  (30)  309.84 tons [approx. 6,196.8 bags] P 50

Average is

2(4,000)100 5

50  516.40 tons[10,328bags] 50  20

I max 309.48 154.92 tons [approx. 3,098 bags] : 2 2

c. Run length =

Q 516.4  10.33 days P 50 D

4,000

d. Runs per year: Q  516.4  7.75 [approx. 8] e. Q = 258.2, TC =

D I max H S, Q 2

TCorig. = $1,549.00 TCrev. = $ 774.50 Savings would be 4.

$774.50

Cu = $99, Co = $200, 99___ = 0.3311. => z = −0.44. 99 + 200 Overbook: 18 – 0.44(4.55) = 15.998, or 16 tickets. Service level=

5.

Expected demand during LT = 300 units dLT = 30 units a. Z = 2.33, ROP = exp. demand + ZdLT 300 + 2.33 (30) = 369.9 ≈ 370 units b. 70 units (from a.) c. smaller Z , less safety stock ROP smaller:

Basic EOQ Formulas:

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Economicorder quantity : EOQ  TC 

Q D H S, 2 Q

2DS H

Length of order cycle 

Q , D

Reorder Point, ROP  L  d

Continuous review under uncertain demand and constant lead time Optimal Order Quantity 

2E[D]S H

If demand is normally distributed with mean of  and standard deviation of reorder point is ROP=  L  z * L L *   z * L *

 , then

Economic Production quantity: 2DS H

EPQ Optimal run or order size  TC 

Imax D H  S , 2 Q

cycle time

Q , u

p , p u

I max 

Run time 

Q ( p  u) p

Q p

Single Period Model: Service Level

C underage C underage  C overage

1  Pr(stockout) .

If demand is normally distributed with a mean of  and standard deviation of  , then the optimal stocking quantity =   z *  which minimizes the sum of underage and overage costs.

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