Operations Management

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The University of Alabama

Culverhouse College of Business
OM 423: Inventory Management

Fall 2020

Practice Problem: Exam 2 Preparation

1. You work for Company Z and are tasked with the purchase of a product. Your plant
operates 45 weeks out of the year and the demand for the product is 1,575 units per week.
Holding cost is 30% of unit cost per year. The supplier charges $400 per order. The
supplier offers an all-units quantity discount scheme based on the price schedule described
in the table below.

a. Based on this price schedule, how much would you order at a time?
b. What would be the total annual cost?
c. If the replenishment lead time is six weeks, determine the reorder level.

2. You have been tasked with developing the best ordering policy for the following two items,

given that the company only wants to use an average of 4,500 square feet of storage space.
The manager of the company suggested you to consider an additional cost factor C = 2.
This additional cost factor is used to reduce the order size from EOQ in such a way that the
average storage space constraint is respected.

The company operates 50 weeks per year.

a. Is this a reasonable value for C? Justify your answer.
b. Assuming that we allocate 2400 square feet and 2100 square feet to items 1 and 2,

respectively. What would be your ordering policy recommendation for these
items? For each item, explain how the TRC based on this new policy compares to
the case with no space limitations. Justify your answers.

Cost per Unit Lower Quantity Upper Quantity

$8.79 0 1,999
$8.77 2,000 3,999
$8.75 4,000 5,999
$8.72 6,000

Item Unit Cost
(v)

Weekly
Demand

Order Cost
(A)

Space per unit
(s) (𝐟𝐟𝐟𝐟𝟐𝟐)

Holding Cost %
per month

1 $9 600 $120 6 14%
2 $11.5 350 $110 1 8%

3. A small electronics company sells two types of subcomponents. The management desires
to construct an inventory policy for each one of these items that minimizes the cost of
managing cycle inventory when backorders are allowed:

Item 1
Demand per Week 30
Item cost, v 20
Setup cost, A 50
Holding cost, h% 15%
Backorder cost, b% 300%
Lead Time, LT 5 weeks
**The company operates 50 weeks per year

For each item, determine the following:
– Economic order quantity and planned backorders
– Total relevant cost and total annual cost
– Reorder level