OPMG-UB.0001.02-03
Operations Management
Fall 2015
Homework 7
Due Tuesday, November 24th, 2015
1. B&H is deciding how to manage the inventory of cameras that it sells. The demand for cameras
at B&H is 100 cameras per week. Each time that B&H places an order for a new shipment of
cameras it must pay $90 in ?xed processing fees. A camera costs B&H $80 to purchase. The cost
for B&H to hold a camera in its store for one week is $3.00. Assume that the leadtime for the
delivery of a camera is 0 weeks.
a. Suppose that B&H places orders for cameras in quantities of 50 cameras at a time and places a
new order for cameras each time that it runs out. Draw a graph showing the number of cameras
that B&H has on-hand in inventory at each point in time up until the time when it places its fourth
order. Label the points in time at which B&H places a new order, showing the time at which each
order is placed. Assume that B&H places its ?rst order for 50 cameras on day 0.
b. Suppose again that B&H places orders for 50 cameras at a time. What will be B&H’s average holding costs per week? What will be B&H’s average ?xed ordering costs per week?.
c. What is the optimal number of cameras for B&H to order each time that it places an order? Assuming that B&H orders according to its optimal ordering quantity, what will be B&H’s
average ?xed ordering costs over the course of a week? What will be B&H’s average holding costs
over the course of a week?
d. Suppose now that the leadtime for the delivery of a shipment of cameras increases to 0.5
weeks. Assuming that B&H orders according its optimal order quantity from part c above, what
should be B&H’s reorder point for a shipment of cameras?
e. The demand for cameras at B&H has become more variable and now follows a normal distribution. The average demand for cameras at B&H is still 100 cameras per week but the standard
deviation of the demand is now 40 cameras per week. Leadtime for a shipment of cameras is still
0.5 weeks and all other cost parameters for the problem remain the same. Suppose that B&H
would like to operate at a service level of 69.15%. What should B&H set its new reorder point to
be? Also, what will be the average additional holding costs that B&H incurs over the course of a
week as a result of adjusting its reorder point?
f. Suppose now that the demand for cameras is constant again (no variability) with a demand
rate of 100 cameras per week and assume that B&H orders according to the EOQ level calculated
in part c above. The leadtime for the delivery of cameras is still 0.5 weeks. However, rather than
placing an order when B&H’s inventory of cameras reaches its reorder point calculated in part d
above, B&H decides to place a new order for cameras whenever it has 65 cameras in inventory.
How much additional holding costs (over the EOQ costs) will B&H incur as a result of this ordering
policy?
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2. Every evening, Empire News needs to determine how many copies of the newspaper to purchase for the following morning. A newspaper costs $0.75 to purchase and sells for $2.00. Any
unsold newspapers can be recycled at the end of the day at a value of $0.10 per newspaper. The
following table provides Empire News’ daily demand distribution for newspapers.
Number of newspapers
Probability
160
.10
170
.10
175
.05
185
.30
200
.10
205
.10
210
.20
220
.05
a. Suppose that Empire News is considering purchasing 205 newspapers. What is the marginal
value from a 206th newspaper?
b. What is the optimal number of newspapers for Empire News to purchase each evening?
3. A pastry shop is considering how much hot chocolate to make each morning. Hot chocolate costs $0.05 per oz to make and sells for $0.50 per oz. Customers can buy hot chocolate in any
number of ounces that they wish. Any hot chocolate not sold by the end of the day is discarded.
The daily demand for hot chocolate is normally distributed with a mean of 1,000 oz and a standard
deviation of 150 oz. How much hot chocolate should the pastry shop make each morning?
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