Question

You are the store manager for a Bomberland store. One of your products is a study desk. This desk comes in two colors: maple and cherry. Weekly demand for each desk color follows a Normal distribution with mean 100 and standard deviation 50. The demands for the two colors are independent. You order inventory replenishments weekly, the lead-time from your supplier is 3 weeks and your supplier is quite reliable, i.e., you always receive your entire order in three weeks. You use the order up-to model to decide your order quantities.

24. Suppose your order up-to level S is 400 for maple. After receiving your weekly delivery from your supplier at the beginning of a week, you note that you have 250 units of the maple desk on-hand, 100 maple desks still on-order and no maple desks backordered. How many maple desks will you order this week?

a. 0

b. 50

c. 100

d. 150

e. 200

25. Suppose your order up-to level is 500 for maple desks. With a 3-week lead time, what is your expected ending inventory of maple desks? Choose the closest number.

a. 98

b. 108

c. 208

d. 308

e. 408

26. If the order-up-to level for maple is S = 500, what is the approximate fill rate?

a. 92.00%

b. 95.00%

c. 98.75%

d. 99.56%

e. 100.00%

27. Suppose the ordering cost for maple desk is $100 and the unit holding cost is $5 per day. If there are 5 working days each week, the length of the review period using the economic order quantity model is (Hint: use the economic order quantity in Chapter 7 to figure out the length of a review period. The review period is the average flow time of one order cycle.)

a. Less than 1 day

b. Between 1 day and 2 days

c. At least a week

d. Two weeks or longer

Answer 1

24.

Order up-to level = 400; On hand = 250; On order = 100
So, order quantity = 400 - 250 - 100 = 50

25.

P = review period = 1 week
L = average lead time = 3 weeks
d = weekly average demand = 100
s = std. dev. of weekly demand = 50

Optimum order up to level (T*) = d*(P+L) + Z*s*SQRT(P+L)
or, 500 = 100*(1+3) + Z*50*SQRT(1+3)
or, Z = 100/100 = 1 i.e. L(z) = 0.083 (from loss function tables)

Expected shortage per cycle (ESC) = L(z) x s*SQRT(P+L) = 0.083*50*SQRT(1+3) = 8.3

Exp. Inventory at the end of cycle = T* - d(P+L) + ESC = 500 - 100*(1+3) + 8.3 = 108.3 or 108 (rounded off).

(26)

L(z) = 0.083

Fill Rate = 1 - L(z)*s*SQRT(P+L)/(d*(P+L)) = 1 - 0.083*50*SQRT(1+3)/(100*(1+3)) = 98% (so, option 'c' may be correct)

(27)

D = daily demand = 100/5=20; S = ordering cost=$100; H=carrying cost per day = $5
EOQ = (2.D.S/H)^1/2 = SQRT(2*20*100/5) = 28 units

Lenght of the review period = EOQ/D = 28/20 = 1.4 days (i.e. between 1 and 2 days)