EPT 432 Operations Management
Laboratory Module
LAB 3
INVENTORY MANAGEMENT
1.0
OBJECTIVE
1. Identify ABC analysis, EOQ model and POQ model.
2. Calculate ABC, EOQ and POQ.
3. Develop the methods above using Microsoft Excel.
2.0
INTRODUCTION
Inventory comes in many shape and sizes. Raw material is the purchased items or
extracted materials transformed into components or products. Components are parts or
subassemblies used in final product. Work in progress (WIP) is referring to the items in
process throughout plant. Finished goods are products sold to customers. Distribution
inventory consists of finished goods in the distribution system.
Inventory plays multiple roles in company’s operation. The six functions of inventory are
summarized as below:1. Anticipation inventory or Seasonal inventory
- Items built in anticipation of future demand. Allows company to maintain a level
production strategy.
2. Fluctuation inventory / Safety stock
- Protects against unexpected demand variations. Assures customer service levels
3. Lot size inventory or Cycle stock
- Results from the actual quantity purchased. Allows for lower unit costs.
4. Transportation / Pipeline inventory
- Items in movement between locations. Inventory moves from manufacturer to
distribution facilities.
5. Speculative / Hedge inventory
- Extra inventory built up or purchased to protect against some future event.
Allows for continuous supply.
6. Maintenance, Repair and Operating (MRO) Inventory
- Includes maintenance supplies, spare parts, lubricants, cleaning agents and daily
operating supplies. Facilitates day-to-day operations.
2.1 ABC Analysis
ABC analysis is a business term used to define an inventory categorization technique
often used in materials management. ABC analysis provides a mechanism for identifying
items which will have a significant impact on overall inventory cost whilst also providing
Page 1 of 10
EPT 432 Operations Management
Laboratory Module
a mechanism for identifying different categories of stock that will require different
management and controls
When carrying out an ABC analysis, inventory items are valued (item cost multiplied by
quantity issued/consumed in period) with the results then ranked. The results are then
grouped typically into three bands. These bands are called ABC code
1. "A class" inventory will typically contain items that account for 70% to 80% of
total value
2. "B class" inventory will have around 15% to 25% of total value
3. "C class" inventory will account for the remaining 5%
ABC Analysis is similar to Pareto in that the "A class" group will typically account for a
large proportion of the overall value but a small percentage of the overall volume of
inventory. See example no. 1
2.2 Economic Order Quantity (EOQ) Model
EOQ is an inventory- control technique that minimizes the total of ordering and holding
costs.
This technique is relatively easy to use but is based on several assumptions:1. Demand is known, constant and independent
2. Lead time – that is the time between placement and receipt of the order – is
known and constant
3. Receipt of inventory is instantaneous and complete. In other words, the inventory
from an order arrives in one batch at one time
4. Quantity discounts are not possible
5. The only variable costs are the cost of setting up pr placing an order (setup cost)
and the cost of holding or storing inventory over time (holding or carrying cost).
6. Stock outs (shortages) can be completely avoided if orders are placed at right
time.
Using the following variables, we can determine setup and holding costs and solve for
Q*:
Q
= Number of units per order
Q*
= Optimum number of units per order (EOQ)
D
= Annual demand in units for the inventory item
S
= Setup or ordering cost for each order
H
= Holding or carrying cost per unit per year
Page 2 of 10
EPT 432 Operations Management
Laboratory Module
1. Annual set up cost
= (Number of orders placed per year) x (Set up or order cost per order)
=
Annual demand
(setup or order cost per or
Number of units in each order
= D
(S)
= D S
Q
Q
2. Annual holding cost
= (Average inventory level) x (Holding cost per unit per year)
= Order quantity
(Holding cost per unit per year)
2
= Q
(H) = Q
2
2
H
3. Optimal order quantity is found when annual step cost equals annual holding cost,
namely:
D S
= Q H
Q
2
4. To solve for Q*, simply cross multiply terms and isolate Q on the left of the equal sign:
2 DS = Q²H
Q² = 2DS
H
Q* =
2DS
H
*now we have derived the equation for the optimal order quantity, Q*, it is possible to
solve inventory problems directly. See example no. 2.
Page 3 of 10
EPT 432 Operations Management
Laboratory Module
We can also determined the expected number of orders placed during the year (N) and
the expected time between orders (T), as follows:Expected number of orders = N =
Demand
=
Order quantity
D
Q*
Expected time between orders = T = Number of working days per year
N
As mentioned earlier in this section, the total annual variable inventory cost is sum of
setup and holding cost:
Total Annual Cost (TC) = Setup (order) cost + Holding cost
Also can be express as TC
= D S + Q H
Q
2
Inventory cost may also be expressed to include the actual cost of the material purchased.
TC
= D S + Q H + PD
Q
Thus, Q*
3.0
=
2
2DS
H
Production Order Quantity (POQ) Model
POQ is an economic order quantity technique applied to production orders. This model is
applicable under 2 situations:1. when inventory continuously flows or build up over a period of time after an
order has been placed.
2. when units are produced and sold simultaneously, we take into account daily
production (or inventory flow) rate and daily demand rate.
The expression for annual inventory holding cost for the production order quantity
model:
Q
= number of units per order
H
= Holding cost per unit per year
p
= daily production rate
d
= daily demand rate, or usage rate
t
= length of the production runs in days
Page 4 of 10
EPT 432 Operations Management
Laboratory Module
1. Annual inventory = (average inventory level) x (holding cost per unit per year)
holding cost
2. (Average inventory level) = (Maximum inventory level) / 2
3.
Maximum
inventory level
=
Total production during
the production run
-
Total used during
the production run
= pt – dt
However, Q = total produced = pt and thus t = Q/p. Therefore:Maximum inventory level = p Q - d
p
=Q
Q =Q– d
p
Q
p
1–d
P
4. Annual inventory holding cost (or simply holding cost) =
Maximum inventory level
(H) = Q
2
1–
2
d
H
p
Using this expression for holding cost and the expression for setup cost developed in the
basic EOQ model, we solve for the optimal number of pieces per order by equating setup
cost and holding cost:
Setup cost
=(D/Q)S
Holding cost
= ½ HQ 1- (d / p)
Set ordering cost equal to holding cost to obtain Q*p:
D S = ½ HQ 1- (d / p)
Q
Q²
=
2DS
H 1 – (d / p)
Q*p =
2DS
H
1 - (d / p)
Page 5 of 10
EPT 432 Operations Management
3.0
Laboratory Module
EXAMPLE
1. L. Houts Plastics is a large manufacturer of injection molded plastic’s in North
Carolina. An investigation of the company’s manufacturing facility in Charlotte yields
the information presented in the table below. How would the plant classify these items
according to an ABC classification system?
1289
2347
Average
Industry
(units)
400
300
2349
2363
2394
2395
6782
7844
8210
8310
9111
120
75
60
30
20
12
8
7
6
Item Code #
Value
($/unit)
3.75
4.00
2.50
1.50
1.75
2.00
1.15
2.05
1.80
2.00
3.00
Solution:
(1) Find the total volume
Page 6 of 10
EPT 432 Operations Management
Laboratory Module
(2) Find the percentage
(3) Find the ABC classification
Page 7 of 10
EPT 432 Operations Management
Laboratory Module
2. William Beeville’s computer training school, in Richmond, stocks workbook with the
following characteristics:
Demand, D
= 19,500 units/year
Ordering Cost, S
= $25/order
Holding cost, H
= $4/unit/year
(a) Calculate the EOQ for the workbooks
(b) What are the annual holding costs for the workbooks?
(c) What are the annual ordering costs?
Solution:
Finding the optimal order size
(a) Calculate EOQ total value
Q* =
2DS
H

Find the value for 2DS/H

√ the total value
Page 8 of 10
EPT 432 Operations Management
Laboratory Module
(b) calculate the annual holding cost
(c) find the annual ordering cost
4.0
EXERCISE
1. Boreki Enterprise has the following 10 items in inventory. Theodore Baski asks you, a
recent OM graduate, to divide these items into ABC classifications. What do your report
back?
ITEM
A2
B8
C7
D1
E9
F3
G2
H2
I5
J8
ANNUAL
DEMAND
3000
4000
1500
6000
1000
500
300
600
1750
2500
COST/UNIT
($)
50
12
45
10
20
500
1500
20
10
5
Page 9 of 10
EPT 432 Operations Management
Laboratory Module
2. Amin’s machine shop uses 2,500 brackets during the course of a year. These brackets
are purchased from a supplier 90 miles away. The following information is known about
the brackets:
Annual demand
Holding cost per bracket per year
Order cost per order
Lead time
Working days per day
2500
$1.50
$18.75
2 days
250
a) Given the above information, what would be the economic order quantity (EOQ)?
b) Given the EOQ, what would be the average inventory? What would be the annual
inventory holding cost?
c) Given the EOQ, how many orders would be made each year? What would be the
annual order cost?
d) Given the EOQ, what is the total annual cost of managing the inventory?
e) What is the time between orders?
f) What is the reorder points (ROP)?
3. Razat Motors is an Indonesian car manufacturer. At its largest manufacturing facility,
in Jakarta, the company produces subcomponents at a rate of 300 per day, and it uses
these subcomponents at a rate of 12,500 per year (of 250 working days). Holding costs
are $2 per item per year, and ordering costs are $30 per order.
(a)
(b)
(c)
(d)
(e)
what is the economic production quantity?
How many production runs per year will be made?
What will the maximum inventory level?
What percentage of time will be the facility b producing components?
What is the annual cost of ordering and holding inventory?
Page 10 of 10