Operations management 12th stevenson ch13 inventory management

Inventory CostsPurchase cost  The amount paid to buy the inventory Holding carrying costs  Cost to carry an item in inventory for a length of time, usually a year Ordering costs 

Inventory Management

Chapter 13

McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc All rights reserved.

Chapter 13: Learning Objectives

 You should be able to:

1. Define the term inventory, list the major reasons for holding

inventories, and list the main requirements for effective inventory

management

2 Discuss the nature and importance of service inventories

3 Explain periodic and perpetual review systems

4 Explain the objectives of inventory management

5 Describe the A-B-C approach and explain how it is useful

6 Describe the basic EOQ model and its assumptions and solve

typical problems

7 Describe the economic production quantity model and solve

typical problems

8 Describe the quantity discount model and solve typical problems

9 Describe reorder point models and solve typical problems

10 Describe situations in which the single-period model would be

appropriate, and solve typical problems

A stock or store of goods

Independent demand items

Items that are ready to be sold or used

Inventory

Inventories are a vital part of business: (1)

necessary for operations and (2) contribute to

customer satisfaction

A “typical” firm has roughly 30% of its

current assets and as much as 90% of its

working capital invested in inventory

Raw materials and purchased parts

Work-in-process (WIP)

Finished goods inventories or merchandise

Tools and supplies

Maintenance and repairs (MRO) inventory

Goods-in-transit to warehouses or customers

(pipeline inventory)

Types of Inventory

Independent demand is uncertain

Dependent demand is certain

Inventory: a stock or store of goodsInventory

Objectives of Inventory Control

Inventory management has two main concerns:

1 Level of customer service

 Having the right goods available in the right quantity in the right place at the right time

2 Costs of ordering and carrying inventories

achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds

Effective Inventory Management

Requires:

1 A system keep track of inventory

2 A reliable forecast of demand

3 Knowledge of lead time and lead time variability

Periodic System

Physical count of items in inventory made at

periodic intervals

Perpetual Inventory System

System that keeps track of removals from

inventory continuously, thus monitoring current levels of each item

 An order is placed when inventory drops to a predetermined minimum level

Demand Forecasts and Lead Time

Forecasts

 Inventories are necessary to satisfy customer demands,

so it is important to have a reliable estimates of the

amount and timing of demand

 Point-of-sale (POS) systems

 A system that electronically records actual sales

 Such demand information is very useful for enhancing

forecasting and inventory management

Lead time

 Time interval between ordering and receiving the order

Inventory Costs

Purchase cost

 The amount paid to buy the inventory

Holding (carrying) costs

 Cost to carry an item in inventory for a length of time,

usually a year

Ordering costs

 Costs of ordering and receiving inventory

Setup costs

 The costs involved in preparing equipment for a job

 Analogous to ordering costs

Shortage costs

 Costs resulting when demand exceeds the supply of

inventory; often unrealized profit per unit

ABC Classification System

 A-B-C approach

 Classifying inventory according to some measure of

importance, and allocating control efforts accordingly

 A items (very important)

 10 to 20 percent of the number of items in inventory and

about 60 to 70 percent of the annual dollar value

 B items (moderately important)

 C items (least important)

of items in inventory but only

about 10 to 15 percent of the

annual dollar value

Cycle Counting

Cycle counting

 A physical count of items in inventory

 How much accuracy is needed?

 A items: ± 0.2 percent

 B items: ± 1 percent

 C items: ± 5 percent

 When should cycle counting be performed?

 Who should do it?

ABC Classification Example

Item

Annual Demand

Unit Cost ($)

Annual $ Value Classification

How Much to Order: EOQ Models

Economic order quantity models identify the

optimal order quantity by minimizing the sum

of annual costs that vary with order size and

frequency

1. The basic economic order quantity model

2. The economic production quantity model

3. The quantity discount model

Basic EOQ Model

The basic EOQ model is used to find a fixed

order quantity that will minimize total

annual inventory costs

Assumptions:

1 Only one product is involved

2 Annual demand requirements are known

3 Demand is even throughout the year

4 Lead time does not vary

5 Each order is received in a single delivery

6 There are no quantity discounts

H: Holding cost

S: Ordering cost

Q: Quantity

TC: Total Inventory Costs

 = Ordering Costs + Holding Costs

Assumptions of EOQ Model

The Inventory Cycle

Profile of Inventory Level Over Time

Quantity

on hand

Q

Receive order

Place order Receive order Placeorder Receive orderLead time

Reorder

point

Usage rate

Time

EOQ Example

Average Inventory

EOQ Total Costs Components

Total Annual Cost

orderper

cost Ordering

yearper

units

in usually Demand,

yearper

usually unit,

per cost

(carrying)Holding

units

in quantity Order

where

2

CostOrdering

AnnualCost

HoldingAnnual

D H

Q

Goal: Total Cost Minimization

Order Quantity (Q)

The Total-Cost Curve is U-Shaped

D H

Q

2

Minimum Total Cost

The total cost curve reaches its

minimum where the carrying and

ordering costs are equal.

Deriving EOQ

Using calculus, we take the derivative of the total

cost function and set the derivative (slope) equal

to zero and solve for Q.

The total cost curve reaches its minimum where

the carrying and ordering costs are equal

cost holding

unit per

annual

cost) der

demand)(or annual

( 2

2

H DS Q

EOQ Example 1

Annual Demand: D = 9,600 tires

Carrying Cost: H = $16/unit/year

Ordering Cost: S = $75/order

Annual Number of Business days: 288

Q: What is EOQ?

A:

tires H

DS

16

) 75 )(

600 ,

9 )(

2 (

2







days X

year D

Q

9

288 32

1 32

1 600

, 9

300 600

, 9

The batch mode is widely used in production In

certain instances, the capacity to produce a part

exceeds its usage (demand rate)

 Assumptions

1 Only one item is involved

2 Annual demand requirements are known

3 Usage rate is constant

4 Usage occurs continually, but production occurs periodically

5 The production rate is constant

6 Lead time does not vary

7 There are no quantity discounts

Economic Production Quantity

(EPQ)

EPQ: Inventory Profile

Q

Production and usage

Production and usage

Production and usage

Usage only

Usage only

Cumulative production

Amount

on hand

Time

EPQ Example 1

Given:

D = 1,000,000 units per year

p = 8,000 units per day

u = 4,000 units per day

H = $2/unit/year

S = $200 per setup

Q = 20,000 units

EPQ Example 1

Q: At what rate the inventory is built up?

A: p – u = 8000 – 4000 = 4000 per day

Q: What is the Run Time? This is the

production phase of the cycle (the length

of the production time per cycle)

A: 20,000/8000 = 2.5 days = Q/p

Q: What is the maximum inventory?

A: (4000 units per day) X (2.5 days) = 10,000

units = Imax = (p – u)(Q/p)

EPQ – Total Cost

 

rateUsage

ratedelivery

or Production

inventoryMaximum

where

2

CostSetup

CostCarrying

TC

max

max min

u

p p Q I

S Q

D H

I

p

EPQ Example 1

Given:

D = 1,000,000 units per year

p = 8,000 units per day

u = 4,000 units per day

H = $2/unit/year

S = $200 per setup

Q = 20,000 units

EPQ Example 1

Q: What is the number of runs per year?

1,000,000/20,000 = 50 = D/Q

Q: What is the annual setup cost?

(50 setups) X ($200 per setup) = $10,000

=(D/Q)S

Q: What is the cycle time?

20,000/4,000 = 5 days = Q/u

u p

p H

DS

Q p



Quantity discount

Price reduction for larger orders offered to

customers to induce them to buy in large

quantities

Quantity Discount Model

priceUnit

where

2

CostPurchasing

CostOrdering

CostCarrying

CostTotal

D H

Q

EPQ Model Example 2

Given:

D = 48,000 units per year

p = 800 units per day

u = 200 units per day

H = $1/unit/year

S = $45 per setup

EPQ Model Example 2

Optimal run size (Q) is:

EPQ Model Example 2

Total minimum cost:

TC = ((2400)/(2x800))(800-200)x1 +

(48000/2400)x45 = $900 + $900 =

$1,800

Quantity Discounts

Adding PD does not change EOQ

Quantity Discount Model

When price reduction for large orders

is offered the economic order quantity may change.

Example

Price $1.8/unit: Q 552 8units

) 8 1 )(

2 (.

) 5 5 )(

000 , 10 )(

2 (.

) 5 5 )(

000 , 10 )(

2 (.

) 5 5 )(

000 , 10 )(

2

(



Total Costs with

Purchasing Cost

Annual carrying cost

Purchasing cost

PD

+

order 524.4

order 399

Total Costs

Compare Total Costs

The lowest cost is obtained with an

order size of 700 units

Quantity Discounts Procedure (H = percentage of

price)

Beginning with the lowest price,

determine the EOQ for each price range until a feasible EOQ is found.

If the feasible EOQ is for the lowest price range it is the optimal order quantity

If the feasible EOQ is not for the lowest price, compare the total cost (TC) of the feasible

EOQ to the total cost of the lowest price breaks The order quantity with the minimum

TC is optimal

Quantities to investigate

Figure 12.9

Quantities to investigate

Total Costs

Total Costs

Figure 13-9

Total Costs

Total Costs

Total Costs

Identify the quantity range which

contains the minimum point Only one

of the unit prices will have the

minimum point in its feasible range.

If the feasible minimum point is on the lowest

price range, that is the optimum order quantity

If the feasible EOQ is not for the lowest price,

compare the total cost (TC) of the feasible

minimum point to the total cost of the lowest

price breaks The order quantity with the

minimum TC is optimal

) 5 5 )(

000 , 10 )(

Quantity Discounts

The total-cost curve with quantity discounts

is composed of a portion of the total-cost curve for each price

When to Reorder

Reorder point

 When the quantity on hand of an item drops to this

amount, the item is reordered.

 Determinants of the reorder point

1 The rate of demand

2 The lead time

3 The extent of demand and/or lead time variability

4 The degree of stockout risk acceptable to

management

When to Reorder with EOQ Ordering

Reorder Point - When the quantity on

hand of an item drops to this amount, the item is reordered

Safety Stock - Stock that is held in

excess of expected demand due to

variable demand rate and/or lead

time.

Service Level - Probability that

demand will not exceed supply during lead time.

ROP Factors

Demand rate (d)

Length of lead time (LT)

Variability and uncertainty of demand

and lead time

The degree of stock-out risk acceptable

to management

Stock

Reorder Point: Under Certainty

( Constant Demand and Lead Time

Model)

)asunits time

same(in

timeLead

LT

per week)day,

per period,

per (units

rateDemand

where

LTROP

d d

Constant Demand and Lead

Time Model

Demand rate (d) : constant

Lead Time (LT) : constant

ROP = (d)(LT) (no safety stock)

Example: A Order for 81/2”X11” letter size paper is delivered 7 days after the order is placed The usage rate is 10,00 sheets per day The reorder point is:

ROP = (1,000)(7) = 7,000 sheets

Demand or lead time uncertainty creates the

possibility that demand will be greater than

available supply

To reduce the likelihood of a stockout, it becomes

necessary to carry safety stock

 Safety stock

 Stock that is held in excess of expected demand due

to variable demand and/or lead time

Reorder Point: Under Uncertainty

Stock

Safety time

lead during

demand Expected

Safety Stock

As the amount of safety stock carried

increases, the risk of stockout decreases.

 This improves customer service level

Service level

 The probability that demand will not exceed supply

during lead time

 Service level = 100% - Stockout risk

Safety Stock?

The amount of safety stock that is

appropriate for a given situation depends

upon:

1. The average demand rate and average lead

time

2. Demand and lead time variability

3. The desired service level

How Much Safety Stock?

demand time

lead of

deviation standard

The

deviations standard

of Number

where

time lead

during

demand

Expected ROP

For example 95% service level implies that the

probability that demand will not exceed supply during lead time is 95% There is a 5% chance that demand will exceed supply during the lead time

Reorder Point: Demand

Uncertainty

Note: If only demand is variable, then

) as units time

(same time

Lead LT

) as units time

(same period

per demand

of stdev.

The

per week) day,

(per period

per demand

Average

level service

or risk stockout

by determined is

and deviations

standard of

Number

where

LT ROP

d

d d

z

z LT d

Variable Demand Rate Constant Lead Time Example

Assume that the demand rate for a

product is normally distributed with a

mean of 10 tons and the standard

deviation of 2 tons Lead time is 4 days.

Q: What is the expected demand during

lead time?

( )( d LT ) ( )( )  10 4  40 tons

Reorder Point: Lead Time

(same time

lead Average

LT

) as units time

(same time

lead of

stddev.

The

per week) day,

(per period

per Demand

deviations standard

of Number

where

LT ROP

LT

LT

d

d d

z

zd d

Variable Demand and Lead

Time

Demand Rate: Random Variable

Lead Time: Random Variable

Mean d

d

:

: Standad Deviation 

Single-Period Model

Single-period model

 Model for ordering of perishables and other items with

limited useful lives

 Shortage cost

 Generally, the unrealized profit per unit

C shortage = C s = Revenue per unit – Cost per unit

 Excess cost

 Different between purchase cost and salvage value of

items left over at the end of the period

C excess = C e = Cost per unit – Salvage value per unit

Single-Period Model

The goal of the single-period model is to identify

the order quantity that will minimize the long-run

excess and shortage costs

Two categories of problem:

 Demand can be characterized by a continuous

distribution

 Demand can be characterized by a discrete distribution

Stocking Levels

Service level

So Balance Point

Quantity

So =Optimum Stocking Quantity

unitper

cost excess

unitper

cost shortage

where

levelService

e s

s

C

C

C C

C

ordering of perishables and other

items with limited useful lives

unrealized profits per unit

Cs = Revenue per unit – Cost per unit

purchase cost and salvage value of

items left over at the end of a

period

 Ce = Original cost per unit – Salvage value per unit

Single Period Model

Continuous stocking levels

Identifies optimal stocking levels

Optimal stocking level balances unit

shortage and excess cost

Examples 15 & 16; pages 589, 590

Discrete stocking levels

Service levels are discrete rather than

continuous

Desired service level is equaled or exceeded

Examples 17 & 18; pages 591 & 592

Single Period Model

Operations Strategy

Improving inventory processes can offer

significant cost reduction and customer