Unit 2

Management of Conversion System

Chapter 10: Inventory Management

Lesson 29 - Inventory Management – Basic EOQ model

Learning Objectives

After reading this lesson you would be able to understand

Importance of inventory management

Different types of inventory

Classifying different types of inventory

Optimal ordering quantity

Good Morning students, today we are going to introduce the

concept of what is known as Inventory Management. We will

explore various approaches to Inventory Management and

focuses on its importance as an indispensable tool in

Production and operations management.

Well dear students, all of us, I guess has a fair bit of an idea about

what inventory is all about. I don’t know about your answer, but as

far as I am concerned, this class has an abundant inventory of,

what you call the skill set and talent i.e. the human capital.

Please allow me to focus on the job at hand in a better and

organized manner.

Inventory management

Inventory management is an important concern for all managers.

Inventory is created when the receipt of materials, parts, or

finished goods exceeds their disbursement. It is depleted when

their disbursement exceeds their receipt. Inventory can serve

important functions that add flexibility to the operations of a firm.

Well, what about the uses of inventory?

Any answers around here?

Inventory-uses

Six uses of inventory are:

1. To provide a stock of goods to meet anticipated demand by

customers.

2. To decouple production from distribution. For example, if

product demand is high only during the summer, a firm may

build up stock during the winter and thus avoid the costs of

shortages and stockouts in the summer. Similarly, if a firm’s

supplies fluctuate, extra raw materials of inventory may be

needed to “decouple” production processes.

3. To take advantage of quantity discounts, since purchases in

larger quantities can substantially reduce the cost of goods.

4. To hedge against inflation and price changes.

5. To protect against shortages that can occur due to weather,

supplier shortages, quality problems, or improper deliveries.

“Safety stocks”, namely, extra goods on hand, can reduce the

risk of stockouts.

6. To permit operations to continue smoothly with the use of

“work-in-process” inventory. This is because it takes time to

make goods and because a pipeline of inventories are stocked

throughout the process.

Let us now try to find dome basis for proper categorization of

inventory.

Types of inventory

There are four types of inventories generally a firm maintains.

These are:-

(1) raw material inventory,

(2) work-in-process inventory,

(3) maintenance/repair/operating supply (MRO) inventory, and

(4) finished goods inventory.

Raw material inventory has been purchased, but not

processed. The items can be used to separate suppliers from the

production process. Work-in-process (WIP) inventory has

undergone some change but is not completed. WIP exists because

of the time it takes for a product to be made (called cycle time).

Reducing the cycle time reduces inventory. MROs are inventories

devoted to maintenance/repair/operating supplies. They exist

because the need and timing for maintenance and repair of some

equipment are unknown. Finished goods inventory is completed

and awaiting shipment. Finished goods may be inventoried

because customer demands for a given time period may be

unknown.

We are now going to look at Inventory management again with a

much broader perspective.

Inventory management-

Operations managers establish systems for managing inventory.

First step is to classify inventory items.

Thousands of items are held in inventory by a typical organization,

but only a small percentage of need management’s closest

attention and tightest control. ABC analysis is the process of

dividing items into three classes according to their value (rupee

usage) so that managers can focus on items that have the highest

value. This method is the equivalent of creating a Pareto chart

except that it is applied to inventory rather than quality. The Pareto

principle states that there are a “critical few and trivial many”. The

idea is to focus resources on the few critical inventory parts and

not the many trivial ones. Figure 10.1 shows, class A items

typically represent only about 20 percent of the items but account

for 80 percent of the rupee usage. Class B items account for

another 30 percent of the items but only 15 percent of the rupee

usage. Finally, 50 percent of the items fall in class C, representing

a mere 5 percent of the rupee usage.

Fig Graphic representation of ABC analysis

The goal of ABC analysis is :-

to identify the inventory levels of class A items and enable

management to control them tightly by using the levels as

discussed. To determine annual rupee volume for ABC analysis,

we measure the annual demand of each inventory item times the

cost per unit.

Dear friends, let us examine our conceptual understanding

now.

With the help of an example, let us understand how the ABC

analysis is done.

Example 10.1

The maintenance department for a small manufacturing firm has

responsibility for maintaining an inventory of spare parts for the

machinery it services. The parts inventory, unit cost, and annual

usage are as follows.

Part Unit Cost

(Rs)

Annual

Usage

1

2

3

4

5

6

7

8

9

60

350

30

80

30

20

10

320

510

90

40

130

60

100

180

170

50

60

10 20 120

The department manager wants to classify the inventory parts

according to the ABC system in order to determine which stocks of

parts should most closely be monitored

The first step is to rank the items according to their total value and

also compute each item’s percentage value and quantity.

Part Total

Value

(Rs)

% Value % Quantity %

Cumulative

9

8

2

1

4

3

6

5

10

7

30,600

16,000

14,000

5,400

4,800

3,900

3,600

3,000

2,400

1,700

85,400

35.9

18.7

16.4

6.3

5.6

4.6

4.2

3.5

2.8

2.0

6.0

5.0

4.0

9.0

6.0

10.0

18.0

13.0

12.0

17.0

6.0

11.0

15.0

24.0

30.0

40.0

58.0

71.0

83.0

100.0

Making an intuitive judgment, it appeared that the first three items

form a group with the highest value, the next three items form a

second group, and the last four items constitute a group. Thus, the

ABC classification for these items is as follows.

Class Items % Value %

Quantity

A

B

C

9, 8, 2

1, 4, 3

6, 5, 10, 7

71.0

16.5

12.5

15.0

25.0

60.0

Criteria other than annual dollar volume can determine item

classification. For instance, anticipated engineering changes,

delivery problems, quality problems, or high unit cost may dictate

upgrading items to a higher classification. The advantage of

dividing inventory items into classes allows policies and controls

to be established for each class.

Can anyone tell the class what factors influence the choice of

this form of analysis?

O.K.Let me help you with this one.

Policies that may be based on ABC analysis include the following:

1. The purchasing resources expended on supplier development

should be much higher for individual A items than for C

items.

2. A items, as opposed to B and C items, should have tighter

physical inventory control.

3. Forecasting A items may warrant more care than forecasting

other items.

Dear friends, at this juncture, let me tell you that the

management of service inventories needs some special

considerations. Although we tend to think of services as not

having inventory, that is not the case. For instance, extensive

inventory is held in wholesale and retail businesses, making

inventory management crucial. In the food service business, for

example, control of inventory can make the difference between

success and failure. Moreover, inventory that is in transit or idle in

a warehouse is lost value.

Similarly, inventory which is damaged or stolen prior to sale is a

loss. The impact on profitability is substantial, consequently

inventory accuracy and control is critical.

The applicable techniques include:

1. Good personnel selection, training, and discipline. These are

never easy, but very necessary in food service, wholesale,

and retail operations where employees have access to directly

consumable merchandise.

2. Tight control of incoming shipments. This is being addressed

by many firms through the use of bar-code systems that read

every incoming shipment and automatically check the tallies

against the purchase order. When properly designed, these

systems are very hard to defeat.

3. Effective control of all goods leaving the facility. This is

done with bar codes or items being shipped, personnel

stationed at the exits and in potentially high-loss areas.

We will now examine a variety of inventory models and the

costs associated with them.

Let us begin.

Inventory models

Inventory control models assume that demand for an item is

independent of, or dependent on, the demand for other items. For

example, the demand for refrigerators is independent of the

demand for toaster ovens. However, the demand for toaster oven

components is dependent on the production requirements of toaster

ovens.

Here we will concentrate on managing independent demand items.

Holding, ordering, and setup costs

Holding costs are the costs associated with holding or carrying

inventory over time. Therefore, holding costs also include costs

related to storage, such as insurance, extra staffing, and interest

payments. Table 10.1 shows the kinds of costs that need to be

evaluated to determine holding costs.

Table 10.1 Determining inventory holding costs

Category Cost as a percent of inventory

value

Housing costs, such as building

rent, depreciation, operating

cost, taxes, insurance

6%

(3 – 10%)

Material handling costs,

including equipment, lease or

depreciation, power, operating

cost

3%

(1 – 3.5%)

Labour cost from extra

handling

3%

(3 – 5%)

Investment costs, such as

borrowing costs, taxes, and

insurance on inventory

11%

(6 – 24%)

Scrap and obsolescence

Overall carrying cost

3%

(2 – 5%)

26%

Ordering cost

Ordering cost includes costs of supplies, forms, order processing,

clerical support, and so forth. When orders are being

manufactured, ordering costs also exist, but they are known as

setup costs.

Setup cost is the cost to prepare a machine or process for

manufacturing an order. In many environments setup cost is highly

correlated with setup time. Setup usually requires a substantial

amount of work prior to an operation actually being accomplished

at the work center.

Inventory models for independent demand

Here we will introduce three inventory models that address two

important questions: when to order and

How much to order.

These independent demand models are:

1. Basic economic order quantity (EOQ) model

2. Production order quantity model

3. Quantity discount model

Figure 29.1 Inventory usage over time

The basic economic order quantity model

The economic order quantity (EOQ) is one of the oldest and most

commonly known inventory control techniques. This technique is

relatively easy to use but is based on several assumptions:

1. Demand is known and constant

2. Lead time, that is, the time between the placement of the order

and the receipt of the order, is known and constant

3. Receipt of inventory is instantaneous. 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 or placing an

order (setup cost) and the cost of holding or storing inventory

over time (holding or carrying cost)

6. Stockouts (shortages) can be completely avoided if orders are

placed at the right time

Figure 29.1 shows the inventory usage over time under these

assumptions. Q represents the amount that is ordered. If this

amount is 500 dresses, all 500 dresses arrive at one time (when an

order is received). Thus, the inventory level jumps from 0 to 500

dresses. In general, an inventory level increases from 0 to Q units

when an order arrives.

Because demand is constant over time, inventory drops at a

uniform rate over time. When the inventory level reaches 0 the

new order is placed and received, and the inventory level again

jumps to Q units. This process continues indefinitely over time.

The objective of most inventory models is to minimize the total

costs. Under the assumptions considered, the significant costs are

the setup (or ordering) cost and the holding (or carrying) cost. All

other costs, such as the cost of the inventory itself, are constant.

Thus, if we minimize the sum of the setup and holding costs, we

will also be minimizing the total costs. Figure 10.2 illustrates total

cost as a function of order quantity, Q. The optimal order size, Q*,

will be the quantity that minimizes the total costs. As the quantity

ordered increases, the total number of orders placed per year will

decrease. Thus, as the quantity ordered increases, the annual setup

or ordering cost will decrease. But as the order quantity increases,

the holding cost will increase due to larger average inventories that

are maintained.

The optimal order quantity occurred at the point where the

ordering cost curve and the carrying cost curve intersected. With

the EOQ model, the optimal order quantity will occur at a point

where the total setup cost is equal to the total holding cost.

The necessary steps in developing the model are:

1. Develop an expression for setup or ordering cost

2. Develop an expression for holding cost

3. Set setup cost equal to holding cost

4. Solve the equation for the best order quantity

Using the following variables we can determine setup and

holding costs and solve for Q*:

Q = Number of pieces per order

Q* = Optimum number of pieces 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

1. Annual setup cost = Number of orders placed per year x

Setup or order cost per order

= (Annual demand / Number of units in

each order) x Setup or

order cost per order

= (D / Q) S

2. Annual holding cost = Average inventory level x Holding

cost per unit per year

= (Order quantity / 2) Holding cost per

unit per year

= (Q / 2) H

3. Optimal order quantity is found when annual setup cost

equals annual holding cost, namely,

(D/Q) S = (Q/2) H

4. To solve for Q*, simply cross-multiply terms and isolate Q

on the left of the equal sign.

2DS = Q2H

Q2 = (2DS/H)

Q* = √(2DS)/H

The total annual inventory cost is the sum of the setup and

holding costs:

Total annual cost = setup cost + Holding cost

In terms of variables the total cost TC can be expressed as:

TC = (D/Q) S + (Q/2) H

Wee friends, this calls for an example.

Example 10.2

Electronic Village stocks and sells a particular brand of personal

computer. It costs the store Rs450 each time it places an order

with the manufacturer for the personal computers. The annual

cost of carrying the PCs in inventory is Rs170. The store

manager estimates that annual demand for the PCs will be 1200

units. Determine the optimal order quantity and the total

minimum inventory cost.

Solution:

D = 1200 personal computer

H = Rs170

S = Rs450

Q* = √(2DS)/H

= √(2 (450)(1200) / 170)

= 79.7 personal computers

TC = (D/Q) S + (Q/2) H

= 450 (1200/79.7) + 170 (79.7/2)

= Rs13,549.91

Moving over to Reorder points then.

Reorder points

Once we have decided how much to order, now we will look at

the second inventory question, when to order. The time

between the placement and receipt of an order, called the lead

time or delivery time, can be as short as a few hours to as long

as months. Thus, when-to-order decision is usually expressed in

terms of a reorder point, the inventory level at which an order

should be placed.

The reorder point (ROP) is given as:

ROP = (Demand per day) x (Lead time for a new order in

days)

= d x L

This equation for ROP assumes that demand is uniform and

constant. When this is not the case, extra stock, often called

safety stock, should be added.

The demand per day, d, is found by dividing the annual

demand, D, by the number of working days in a year:

d = D / (Number of working days in a year)

We will take an example to demonstrate how to calculate

reorder point.

Example 10.3

The I-75 Discount Carpet Store is open 311 days per year. If

annual demand is 10,000 yards of Super Shag Carpet and the

lead time to receive an order is 10 days, determine the reorder

point for carpet.

Solution:

r = dL

= (10,000/ 311) 10

= 321.54

Thus, when the inventory level falls to approximately 321 yards

of carpet, a new order is placed. Notice that the reorder point is

not related to the optimal order quantity or any of the inventory

costs.

Friends, the next model lined up for today’s discussion is:-

Production order quantity model

In the EOQ inventory model, we assumed that the entire

inventory order was received at one time. There are times,

however, when the firm may receive its inventory over a period

of time. Such cases require a different model, one that does not

require the instantaneous receipt assumption. This model is

applicable when inventory continuously flows or builds up over

a period of time after an order has been placed or when units are

produced and sold simultaneously. Under these circumstances,

we take into account the daily production (or inventory flow)

rate and the daily demand rate. Figure 29.2 shows inventory

levels as a function of time.

Figure 29.2 Inventory levels over time for the production model

Because this model is especially suitable for the production

environment, it is commonly called the production order

quantity model. It is useful when inventory continuously builds

up over time and the traditional economic order quantity

assumptions are valid. We derive this model by setting ordering or

setup costs equal to holding costs and solving for Q*. Using the

following symbols, we can determine the expression for annual

inventory holding cost for the production run model:

Q = Number of pieces 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 run in days

1. Annual inventory holding cost = (Average inventory level) x

(Holding cost per unit per year)

= (Average inventory level) x H

2. Average inventory level = (Maximum inventory level) /2

3. Maximum inventory level = (Total produced during the

production run) – (Total used during

the production run)

= pt – dt

But Q = total produced = pt, and thus t = Q/p. Therefore,

Maximum inventory level = p(Q/p) – d(Q/p)

= Q – (d / p) Q

= Q (1 – d / p)

4. Annual inventory holding cost (or simply holding cost) =

(Maximum inventory level / 2) H = (Q / 2) ( 1 – (d / p) ) H

Using the expression for holding cost above 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 = (1/2) HQ (1 – (d / p) )

Set ordering cost equal to holding cost to obtain Q*p:

(D / Q) S = (1/2) HQ(1 – (d / p))

Q2 = 2DS / (H (1 – (d / p))

Q*p = √ 2DS / (H (1 – (d / p))

We can use the above equation, Q*p, to solve for the

optimum order or production quantity when inventory is consumed

as it is produced.

We will take an example to see how to use it.

Example 10.4

We now assume that I-75 Outlet Store has its own manufacturing

facility in which it produces Super Shag carpet. We further assume

that the ordering cost is the cost of setting up the production

process to make Super Shag carpet. Estimated annual demand is

10,000 meters of carpet, and annual carrying cost is Rs0.75 per

meter. The manufacturing facility operates the same days the store

is open (i.e., 311 days) and produces 150 meters of the carpet per

day. Determine the optimal order size, total inventory cost, the

length of time to receive an order, the number of orders per year,

and the maximum inventory level.

Solution:

S = Rs150

H = Rs0.75

D = 10,000 meters

d = 10,000 / 311 = 32.2 meters per day

p = 150 meters per day

The optimal order size is determined as follows:

Q* = √ 2DS / (H (1 – (d / p))

= √(2 (150) (10,000) / (0.75 (1 – (32.2 / 150) ) ) )

= 2,256.8 meters

This value is substituted into the following formula to determine

total minimum annual inventory cost:

TC min = (D / Q) S + (D / 2) H ( 1 – d / p)

= ( (150)(10,000) / 2,256.8) + (0.75 (2,256.8) / 2) (1 –

32.2/150) )

= Rs1,329

The length of time to receive an order for this type of

manufacturing operation is commonly called the length of the

production run. It is computed as follows:

Production run length = Q/p

= 2,256.8 / 150 = 15.05 days per order

The number of orders per year is actually the number of production

runs that will be made:

Number of production runs (from orders) = D/Q

= 10,000 / 2,256.8

= 4.43 runs per year

Finally, the maximum inventory level is

Maximum inventory level = Q (1 – d / p)

= 2,256.8 (1 – 32.2 / 150)

= 1,772 meters.

With that, we have come to the end of today’s discussions. I hope it has been an enriching and satisfying experience. Points to ponder