DAO2703/DSC2006
NATIONAL UNIVERSITY OF SINGAPORE
DAO2703/DSC2006 – Operations and Technology Management
(Semester 1 – AY2018/2019)
Time Allowed : 2 Hours
Q1 to Q8 are based on the following:
Assume that a manufacturer is trying to set inventory policies for about 4000 different parts
it was carrying. Assume that this manufacturer has an advanced tracking system and monitors
its inventory continuously while trying to set inventory policies for all the parts it is carrying.
Also assume that, among all the parts, the cheapest part has a part ID of GoodLuckEveryone.
The manufacturer purchases part GoodLuckEveryone for $10 each and uses it together with
various other parts for production of an engine model. Based on the demand of the engine
model and other relevant information, the annual demand for GoodLuckEveryone is
estimated to be normally distributed with mean 1000 and standard deviation 200. The
manufacturer orders GoodLuckEveryone from an overseas supplier and faces a two-month
lead time from the initiation to the receipt of an order. The accountant estimates that the fixed
cost to initiate and receive an order is $20, and recommends a 20 percent annual interest rate
for determining holding cost. In other words, the annual inventory holding cost for the part
GoodLuckEveryone is 20 percent of the product cost, that is, 20 percent of $10. The
manufacturer is targeting at a service level of 95 percent for part GoodLuckEveryone.
The following table provides a list of z values for different values of the service level.
Service level
z
90%
1.29
91%
1.34
93%
1.48
95%
1.65
97%
1.88
99%
2.33
Q1. How many units of part GoodLuckEveryone will the manufacturer order each time?
(A) 131
(B) 141
(C) 151
(D) 161
(E) None of the above
Q2. How many units of part GoodLuckEveryone will the manufacturer order each time?
(A) 101
(B) 111
(C) 121
(D) 181
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(E) None of the above
Answer:
K=20
AVG = 1000 (units per year)
h= $2 (per year per unit of GoodLuckEveryone)
Q = [(2*K*AVG)/h]^0.5 = [(2*20*1000)/2]^0.5 = 141.421 ~ 141
Q3. What level of safety stock of part GoodLuckEveryone should the manufacturer carry?
(A) 105
(B) 115
(C) 125
(D) 135
(E) None of the above
Q4. What level of safety stock of part GoodLuckEveryone should the manufacturer carry?
(A) 155
(B) 165
(C) 175
(D) 185
(E) None of the above
Answer:
Z=1.65
STD = 200 (for annual demand)
L = 2 months = 2/12 year = 1/6 year
z*STD*(L)^0.5 = 1.65*200*(1/6)^0.5 = 134.7219 ~=135 (round up to the next integer
if you do not want a service level which is lower than 95%)
Q5. What should its reorder point be?
(A) 302
(B) 312
(C) 322
(D) 332
(E) None of the above
Answer:
Continuous review policy:
Reorder point = L*AVG + z*STD*(L)^0.5
= (1/6)*1000+1.65*200*(1/6)^0.5 = 301.3886 ~=302 (round up to the next integer if
you do not want a service level which is lower than 95%)
Q6. What is the average inventory level?
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(A) 205.5
(B) 215.5
(C) 225.5
(D) 235.5
(E) None of the above
Answer:
Average inventory level = Q/2 + z*STD*(L)^0.5 = 141/2 + 135 = 205.5
Q7. A new manager comes and feels that the continuous review policy is too expensive to
implement, so decides to use a periodic review policy and review the inventory level every
three months. An order is placed after each review. What base-stock level should the manager
use?
(A) 600
(B) 610
(C) 620
(D) 630
(E) None of the above
Answer:
Periodic Review Policy:
r = 3 months = 3/12 year = 0.25 year
L = 2 months = 2/12 year = 1/6 year
L+r = 5/12 year
AVG = 1000 (units per year)
z=1.65
STD = 200 (for annual demand)
Base-stock level = (L+r)*AVG + z*STD*(L+r)^0.5
= (5/12)*1000 + 1.65*200*(5/12)^0.5
= 629.681
~ 630 (round up to the next integer if you do not want a service level which is lower
than 95%)
Q8. The manager is about to place an order and notes that the inventory level is 530 and there
is neither incoming orders nor backorders. How many units of GoodLuckEveryone will he
order?
(A) 100
(B) 200
(C) 300
(D) 400
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(E) None of the above
Answer:
Base stock level – 530 = 630 – 530 = 100
(Yes! I wish you all good luck and score 100 in your final exam! All the best and
enjoy your winter vacation!)