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 inventories3. Explain periodic and perpetual review systems4. Explain the objectives of inventory management5. Describe the A-B-C approach and explain how it is useful6. Describe the basic EOQ model and its assumptions and solve

typical problems7. Describe the economic production quantity model and solve typical

problems8. Describe the quantity discount model and solve typical problems9. Describe reorder point models and solve typical problems10. Describe situations in which the single-period model would be

appropriate, and solve typical problems

Chapter 13: Learning Objectives

13-1

Inventory 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

13-2

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

13-3

Inventory management has two main concerns: Level of customer service

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

Costs of ordering and carrying inventories The overall objective of inventory management is

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

Measures of performance Customer satisfaction

Number and quantity of backorders Customer complaints

Inventory turnover

Objectives of Inventory Control

13-4

Management has two basic functions concerning inventory: Establish a system for tracking items in

inventory Make decisions about

When to order How much to order

Inventory Management

13-5

Requires: A system keep track of inventory A reliable forecast of demand Knowledge of lead time and lead time

variability Reasonable estimates of

holding costs ordering costs shortage costs

A classification system for inventory items

Effective Inventory Management

13-6

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 Two-bin system

Two containers of inventory; reorder when the first is empty

Inventory Counting Systems

13-7

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

Demand Forecasts and Lead Time

13-8

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

Inventory Costs

13-9

Shortage costs Costs resulting when demand exceeds the

supply of inventory; often unrealized profit per unit

Inventory Costs

13-10

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)

50 to 60 percent of the number of items in inventory but only about 10 to 15 percent of the annual dollar value

ABC Classification System

13-11

ABC Analysis

A Items

B ItemsC Items

Per

cent

of a

nnua

l dol

lar u

sage

80 –70 –60 –50 –40 –30 –20 –10 –

0 – | | | | | | | | | |

10 20 30 40 50 60 70 80 90 100

Percent of inventory items

Class A: 10 to 20% of items, 60-70% annual $ usageClass B: IntermediateClass C: 50 to 60% of items, <= 15% annual $ usage

Cycle counting A physical count of items in inventory

Cycle counting management 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?

Cycle Counting

13-13

Economic order quantity models identify the optimal order quantity by minimizing the sum of annual costs that vary with order size and frequency The basic economic order quantity model The economic production quantity model The quantity discount model

How Much to Order: EOQ Models

13-14

The basic EOQ model is used to find a fixed order quantity that will minimize total annual inventory costs

Assumptions: Only one product is involved Annual demand requirements are known Demand is even throughout the year Lead time does not vary Each order is received in a single delivery There are no quantity discounts

Basic EOQ Model

13-15

The Inventory Cycle

Profile of Inventory Level Over Time

Quantityon hand

Q

Receive order

Placeorder

Receive order

Placeorder

Receive order

Lead time

Reorderpoint

Usagerate

Time

13-16

Average inventory on hand

Q2

Annual Holding cost + Annual Ordering cost

Annual Holding cost (Average inventory) x Holding cost per unit

per year (Q/2) x H

Annual Ordering cost Number of orders placed per year x Cost to

place one order (D/Q) x S

Total Annual Cost

Total Annual Cost

orderper cost Ordering yearper unitsin usually Demand,

yearper usually unit,per cost (carrying) Holding unitsin quantity Order

where

2

Cost Ordering AnnualCost Holding AnnualCost Total

SDHQ

SQDHQ

13-18

Goal: Total Cost Minimization

Order Quantity (Q)

The Total-Cost Curve is U-Shaped

Ordering Costs

QO

Ann

ual C

ost

(optimal order quantity)

Holding Costs

SQDHQTC

2

13-19

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.

Deriving EOQ

cost holdingunit per annualcost)der demand)(or annual(22

O HDSQ

13-20

The batch mode is widely used in production. In certain instances, the capacity to produce a part exceeds its usage (demand rate) Assumptions

Only one item is involved Annual demand requirements are known Usage rate is constant Usage occurs continually, but production occurs

periodically The production rate is constant Lead time does not vary There are no quantity discounts

Economic Production Quantity (EPQ)

13-21

EPQ: Inventory ProfileQ

Qp

Imax

Productionand usage

Productionand usage

Productionand usage

Usageonly

Usageonly

Cumulativeproduction

Amounton hand

Time

13-22

rate Usage ratedelivery or Production

inventory Maximum where

2

Cost SetupCost CarryingTC

max

max

min

up

uppQ

I

SQDHI

p

EPQ – Total Cost

13-23

upp

HDSQp

2

EPQ

13-24

Quantity discount Price reduction for larger orders offered to

customers to induce them to buy in large quantities

Quantity Discount Model

priceUnit where

2

Cost PurchasingCost OrderingCost CarryingCost Total

P

PDSQDHQ

13-25

Quantity DiscountsAdding PD does not change EOQ

13-26

Quantity Discounts

The total-cost curve with quantity discounts is composed of a portion of the total-cost curve for each price

13-27

Reorder point When the quantity on hand of an item drops to

this amount, the item is reordered. Determinants of the reorder point

The rate of demand The lead time The extent of demand and/or lead time variability The degree of stockout risk acceptable to

management

When to Reorder

13-28

) as units timesame(in timeLeadLT per week) day,per period,per (units rate Demand

whereLTROP

dd

d

Reorder Point: Under Certainty

13-29

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

StockSafety timelead duringdemand Expected ROP

13-30

Safety Stock

13-31

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?

13-32

The amount of safety stock that is appropriate for a given situation depends upon: The average demand rate and average lead

time Demand and lead time variability The desired service level

How Much Safety Stock?

demand timelead ofdeviation standard Thedeviations standard ofNumber

where timelead during

demand Expected ROP

LT

LT

d

d

z

z

13-33

Reorder Point: Demand Uncertainty

) as units time(same time Lead LT

) as units time(same periodper demand of stdev. The

per week) day,(per periodper demand Average

deviations standard ofNumber where

LT ROP

d

d

d

z

zLTd

d

d

LTLT dd Note: If only demand is variable, then

13-34

Reorder Point: Lead Time Uncertainty

) as units time(same timelead Average LT

) as units time(same timelead of stddev. Theper week) day,(per periodper Demand

deviations standard ofNumber where

LT ROP

LT

LT

d

ddz

zdd

LTLT dd Note: If only lead time is variable, then

13-35

Reorder Point: Demand and Lead Time Uncertainty

) as units time(same timelead Average LT

) as units time(same timelead of stddev. Theper week) day,(per periodper demand Average

deviations standard ofNumber where

LT ROP

LT

LT

d

dd

z

zdd

222LT LTdd dLT

Note: If both demand and lead time is variable, then

13-36

Fixed-order-interval (FOI) model Orders are placed at fixed time intervals

Reasons for using the FOI model Supplier’s policy may encourage its use Grouping orders from the same supplier can

produce savings in shipping costs Some circumstances do not lend themselves to

continuously monitoring inventory position

How Much to Order: FOI

13-37

Fixed-Quantity vs. Fixed-Interval Ordering

Fixed Interval

Fixed Quantity

13-38

mereorder tiat handon Amount orders)between timeof(length intervalOrder OI

whereLTOILT)OI(

mereorder tiat handon Amount

stockSafety

intervalprotection during

demand Expected

Order toAmount

A

Azd d

FOI Model

13-39

Single-period model Model for ordering of perishables and other

items with limited useful lives Shortage cost

Generally, the unrealized profit per unit Cshortage = Cs = 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

Cexcess = Ce = Cost per unit – Salvage value per unit

Single-Period Model

13-40

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

Single-Period Model

13-41

Stocking Levels

Service level

So Balance Point

Quantity

Cs Ce

So =OptimumStocking Quantity

unitper cost excess unitper cost shortage

where

level Service

e

s

es

s

CC

CCC

13-42

Improving inventory processes can offer significant cost reduction and customer satisfaction benefits Areas that may lead to improvement:

Record keeping Records and data must be accurate and up-to-date

Variation reduction Lead variation Forecast errors

Lean operations Supply chain management

Operations Strategy

13-43