COLLEGE OF ENGINEERING & ARCHITECTURE (COEA)
SPRING SEMESTER (2025)
HOMEWORK
COURSE CODE: IEG 311 DUE DATE: 08/05/2025
COURSE TITLE: PRODUCTION AND INVENTORY SYSTEMS TOTAL POINT: 10
INSTRUCTOR: Dr. Wasim Alshammary
Student Name
Student ID Course Section 427/429/473/474
QUES. ASSIGGEND EARNED CLO
SECTION
# POINTS POINTS REF. #
A 3 10 5.1
TOTAL POINTS EARNED
Page 1 of 6
Question 1:
The new office supply discounter, Joe Henry’s shop, sells a certain type of ergonomically.
correct office chair which costs $350. The annual holding cost rate is 35%, annual demand is
750, and the order cost is $25 per order. The lead time is 5 days. Because demand is variable
(standard deviation of daily demand is 2.4 chairs), Joe Henry’s shop has decided to establish a
customer service level of 90%. The store is open 250 days per year.
a. What is the optimal order quantity?
EOQ = √((2 * annual demand * ordering cost) / holding cost per unit)
EOQ = √((2 * 750 * 25) / 122.5) = 18 chairs
EOQ= 18 chairs
b. What is the safety stock?
Safety stock = (Z * standard deviation of daily demand * √lead time)
Safety stock = (1.28 * 2.4 * √5)= 7 chairs
Safety stock= 7 chairs
c. What is the reorder point?
Reorder point = (demand per day * lead time) + safety stock
demand per day = (annual demand) / (number of days store is open)
demand per day = 750 / 250
demand per day = 3 units
Reorder point = (3 * 5) + 7= 22 chairs
Page 2 of 6
Question 2:
Boreki Enterprises has the following 10 items in inventory. Theodore Boreki asks you, a recent
OM graduate, to divide these items into ABC classifications.
Indicate the items which will be classified in each category and find the percentage of value for
each classification.
Calculate Annual Dollar Usage (Value)
Annual Value=Annual Demand×Cost per Unit
Ite Annual Cost/Unit Annual Value
m Demand ($) ($)
A2 3,000 50 150,000
B8 4,000 12 48,000
C7 1,500 45 67,500
D1 6,000 10 60,000
E9 1,000 20 20,000
F3 500 500 250,000
G2 300 1,500 450,000
H2 600 20 12,000
15 1,750 10 17,500
J8 2,500 5 12,500
Sort Items by Annual Value (High to Low)
Ite Annual Value
m ($)
G2 450,000
F3 250,000
Page 3 of 6
A2 150,000
C7 67,500
D1 60,000
B8 48,000
E9 20,000
15 17,500
J8 12,500
H2 12,000
Compute Total Annual Value
Total Value=1,087,500
Compute Cumulative % of Value
Ite Annual Cumulative % of Total
m Value Value Value
G2 450,000 450,000 41.4%
F3 250,000 700,000 64.4%
A2 150,000 850,000 78.2%
C7 67,500 917,500 84.4%
D1 60,000 977,500 89.9%
B8 48,000 1,025,500 94.3%
E9 20,000 1,045,500 96.1%
15 17,500 1,063,000 97.7%
J8 12,500 1,075,500 98.9%
H2 12,000 1,087,500 100.0%
ABC Classification
A items (≈ top 70-80% of value):
o G2, F3, A2
B items (≈ next 15-25% of value):
o C7, D1, B8
C items (≈ last 5-10% of value):
o E9, 15, J8, H2
Clas Items % of Total
s Value
A G2, F3, A2 78.2%
B C7, D1, B8 16.1%
C E9, 15, J8, H2 5.7%
Page 4 of 6
Question 3:
A product has a reorder point of 110 units and is ordered four times a year. The following table
shows the historical distribution of demand values observed during the reorder period.
Demand Probability
100 0.3
110 0.4
120 0.2
130 0.1
Managers have noted that stockouts occur 30 percent of the time with this policy, and question.
whether a change in inventory policy, to include some safety stock, might be an improvement.
The managers realize that any safety stock would increase the service level but are worried about
the increased costs of carrying the safety stock. Currently, stockouts are valued at $25 per unit
per occurrence, while inventory carrying costs are $15 per unit per year. What is your advice?
Do higher levels of safety stock add to total costs, or not? What level of safety stock is best?
Current Policy: No Safety Stock (ROP = 110)
Stockouts occur 30% of the time. With 4 orders per year, expected stockouts = 1.2 times/year.
Expected units short = 13.33 units (based on excess demand during stockout periods).
Stockout cost/year = 1.2 × 13.33 × $25 = $400
Carrying cost = $0
Total cost = $400
Policy: 10 Units Safety Stock (ROP = 120)
Stockouts occur only at 130 units demand = 10% probability.
Expected stockouts/year = 0.4
Expected units short = 10 units
Stockout cost/year = 0.4 × 10 × $25 = $100
Carrying cost/year = 10 × $15 = $150
Total cost = $250 optimal
Page 5 of 6
Policy: 20 Units Safety Stock (ROP = 130)
Stockouts eliminated (maximum demand is 130).
Stockout cost = $0
Carrying cost = 20 × $15 = $300
Total cost = $300
What is your advice?
Advice: Introduce 10 units of safety stock. It reduces total cost from $400 to $250 and improves
the service level significantly.
Do higher safety stock levels add to cost?
Not always. Moderate levels can reduce total cost, but excessive safety stock increases carrying
cost more than it saves in stockout cost.
What level of safety stock is best?
10 units is the optimal balance between service level and cost.
Page 6 of 6
