In Class Exercises Solution.pdf

Inventory Management Practice Problems 1. A museum of natural resources opened a gift shop two years ago. Managing inventories has become a problem. Low inventory turnover is squeezing profit margins and causing cash-flow problems. The top- selling items at the museum’s gift shop is a bird feeder. Sales are 18 units per week, and the supplier charges $60 per unit. The cost of placing an order with the supplier is $45. Annual holding cost is 25 percent of a feeder’s value, and the museum operates 52 weeks per year. Management chose a 390-unit lot size so that new orders could be placed less frequently. a) What is the annual total cost of the current policy of using a 390-unit lot size? b) Would a lot size of 468 be better? c) Calculate the EOQ and its total annual cycle -inventory cost. How frequently will order be placed if the EOQ is used?

Solutions: D = (18 units/weeks) (52 weeks/year) = 936 units H = 0.25($60/unit) = $15 per unit per year a) For a 390-unit lot size, 390 936 TC = (H) + ($45) = $2925 + $108 = $3033 2

390

b) For a 468-unit lot size, TC = $3600 →Q = 468 is a more expensive option

c)

𝑄𝑜 = TC = =

√ 75 2

2𝐷𝑆 𝐻

= √

($15) +

2(936)(45)

936 75

15

= 74.94, or 75 units,

($45)

TC = $1,124.10

How frequently will order be placed? Length of order cycle =

𝑄𝑜 𝐷

=

75 936

= 0. 080 year, or 29.2 days

2. A mall-order house uses 18,000 boxes a year. Carrying costs are 60 cents per box a year, and ordering costs are $96. The following price schedule applies. Determine a) The optimal order quantity. b) The number of order per year. Number of Boxes 1,000 to 1,999 2,000 to 4,999 5,000 to 9,999 10,000 or more

Price per Box $1.25 $1.20 $1.15 $1.10

Solution D = 18,000 boxes/yearr. S = $96 H = $.60/box per year. a) Qo =

2DS  H

2(18,000)96  2,400 boxes .60

Since this quantity is feasible in the range 2000 to 4,999, its total cost and the total cost of all lower price breaks (i.e., 5,000 and 10,000) must be compared to see which is lowest. TC2,400 =

2,400 18,000 (.60)  ($96)  $1.20(18,000)  $23,040 2 2,400

TC5,000 =

5,000 18,000 (.60)  ($96)  $1.15(18,000)  $22,545.6 [lowest ] 2 5,000

TC10,000 =

10,000 18,000 (.60)  ($96)  $1.10(18,000)  $22,972.80 2 10,000

Hence, the best order quantity would be 5,000 boxes. Lowest TC TC

  

2,400

5,000

10,000 Quantity

b)

D 18,000   3.6 orders per year Q 5,000

3. The manager of a popular Hotel needs to keep close tabs on all room items, including body wash soap. The daily demand for soap is 275 bars, with standard deviation of 30 bars. This soap is shipped in cases of 24 bars. Ordering cost is $10 and annual holding cost for this soap is $7.20 per case. The lead time from the supplier is 5 days. a. What is the optimum order quantity for this bar of soap? b. What should the reorder point be for the bar of soap if management wants to have a 99 percent service level?

4. A Fish Market buys bluefish daily for $4.20 per pound and sells it for $5.70 per pound. At the end of each business day, any remaining bluefish is sold to a producer of cat food for $2.40 per pound. Daily demand can be approximated by a normal distribution with a mean of 80 pounds and a standard deviation of 10 pounds. What is the optimal stocking level?

Solution Cs = Rev – Cost = $5.70 – $4.20 = $1.50/unit Ce = Cost – Salvage = $4.20 – $2.40 = $1.80/unit SL =

Cs/ Cs + Ce)

= $1.50/ ($1.50 + $1.80)

The corresponding z = –.11 d = 80 lb./day

d = 10 lb./day So = d + z d = 80 – .11(10) = 78.9 lb.

= .4545