# OPERATIONS MANAGEMENT 4 PROBLEMS ASSIGNMENT (2015)

June 5, 2016

Question
MyOffice consumes 500,000 boxes of specialized sheets of fine ivory paper every year. Each
box of paper costs \$20. Processing an order is an involved and time consuming process and it
costs \$1500 to process each order. Storing this paper requires a specialized facility and holding
costs are 32%. Assume a lead time of one week and that there are 250 working days in a year.
(10 marks)
a.
b.
c.
d.
e.
f.
g.

What order quantity minimizes my total inventory costs?
What is the average inventory held during the year?
What is the time between orders?
What is the reorder point?
How many orders are placed in a year?
If it takes 0.5 cubic foot to store one sheet of paper, how large (in cubic feet) should the
storage space be to accommodate the maximum quantity that I can hold?
How will the total costs change of the supplier to MyOffice supplier can supply a maximum
of 5000 sheets of that paper per day.

The new office supply discounter, Peter Clips Etc. (PCE), sells a certain type of
ergonomically correct office chair that costs \$300. The annual holding cost rate is 40%,
annual demand is 600, and the order cost is \$20 per order. The lead-time is 4 days.
Because demand is variable (standard deviation of daily demand is 2.4), PCE has decided
to establish a customer service level of 93%. The store is open 300 days per year (15
points).
a.
b.
c.
d.
e.
f.
g.

What is
What is
What is
What is
What is
What is
Service

the optimal order quantity?
the safety stock?
the reorder point?
the safety stock, if required service level is increased to 97%?
the safety stock, if required service level is decreased to 88%?
the service level, if safety stock in part b is increased by 2?
level, if safety stock in part b is decreased by 1?

WXYZ is a television station that has 36 thirty-second advertising slots during each evening.
The station is now selling advertising for the first few days in November. They could sell all the
slots now for \$5,000 each, but because November 7 will be an election day, the station may be
able to sell slots to political candidates at the last minute for a price of \$10,000 each. For now,
assume that a slot not sold in advance and not sold at the last minute is worthless to WXYZ (15
marks).
To help make this decision, the sales force has created the following probability distribution for
last-minute sales:
a. How many slots should WZMU sell in advance?
b. Now suppose that if a slot is not sold in advance and is not sold at the last minute, it may be
used for a promotional message worth \$3100. Now how many slots should WXYZ sell in
Demand
(d)

Probability

8
9
10
11
12
13
14
15
16
17
18
19

0.00
0.05
0.10
0.15
0.20
0.10
0.10
0.10
0.10
0.05
.050
0.00

Cumulative
probability
P(D <= d)
0.00
0.05
0.15
0.30
0.50
0.60
0.70
0.80
0.90
0.95
1.00
1.00

Question 2 (10 marks). You are planning the new layout for the local branch of the Sixth Ninth Bank. You are considering separate cashier windows for the three different classes of service. Each class of service would be separate with its own cashiers and customers. Oddly enough, each class of service, while different, has exactly the same demand and service times. People for one class of service arrive every four minutes and arrival times are exponentially distributed (the standard deviation is equal to the mean). It takes seven minutes to service each customer and the standard deviation of the service times is three minutes. You assign two cashiers to each type of service. Show your work please. (15 points)
a.
b.

On average, how long will each line be at each of the cashier windows?
On average how long will a customer spend in the bank (assume they enter, go directly to one line, and leave as soon as service is complete).

You decide to consolidate all the cashiers so they can handle all types of customers without
increasing the service times. Choose the correct response from the choices provided below.