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1212

Inventory Management

12-2

Learning ObjectivesLearning Objectives

Define the term inventory, list the major reasons for holding inventories, and list the main requirements for effective inventory management.

Discuss the nature and importance of service inventories

Discuss periodic and perpetual review systems. Discuss the objectives of inventory management. Describe the A-B-C approach and explain how it

is useful.

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Learning ObjectivesLearning Objectives

Describe the basic EOQ model and its assumptions and solve typical problems.

Describe the economic production quantity model and solve typical problems.

Describe the quantity discount model and solve typical problems.

Describe reorder point models and solve typical problems.

Describe situations in which the single-period model would be appropriate, and solve typical problems.

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Independent Demand

A

B(4) C(2)

D(2) E(1) D(3) F(2)

Dependent Demand

Independent demand is uncertain. Dependent demand is certain.

Inventory: a stock or store of goods

InventoryInventory

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Inventory ModelsInventory Models

Independent demand: finished goods, items that are ready to be sold E.g. a computer

Dependent demand: components of finished products E.g. parts that make up the computer

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Types of InventoriesTypes of Inventories

Raw materials and purchased parts Partially completed goods called

work-in-process (WIP)

Finished-goods inventories (manufacturing firms)

or merchandise (retail stores)

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Types of InventoriesTypes of Inventories

Replacement parts, tools, and supplies

Goods-in-transit to warehouses or customers

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Functions of InventoryFunctions of Inventory

To meet anticipated demand

To smooth production requirements

To decouple operations

To protect against stockouts

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Functions of InventoryFunctions of Inventory

To take advantage of order cycles

To help hedge against price increases

To permit operations

To take advantage of quantity discounts

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Objectives of Inventory ControlObjectives of Inventory Control

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

Level of customer service

Costs of ordering and carrying inventory

Inventory turnover is the ratio ofthe annual cost of goods sold tothe average inventory investment.

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A system to keep track of inventory

A reliable forecast of demand

Knowledge of lead times

Reasonable estimates of Holding costs

Ordering costs

Shortage costs

A classification system

Effective Inventory ManagementEffective Inventory Management

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Inventory Counting SystemsInventory Counting Systems

Periodic System Physical count of items made at periodic

intervals

Perpetual Inventory System System that keeps track of removals from inventory continuously, thus monitoringcurrent levels of each item

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Inventory Counting SystemsInventory Counting Systems

Two-bin system: Two containers of inventory; reorder when the first is empty

Universal Product Code (UPC): Bar code printed on a label that hasinformation about the item to which it is attached

Radio Frequency Identification

(RFID) Tags

0

214800 232087768

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Lead time: time interval between ordering and receiving the order

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

Shortage costs: costs when demand exceeds supply of inventory

Key Inventory TermsKey Inventory Terms

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ABC Classification SystemABC Classification System

Classifying inventory according to some measure of importance and allocating control efforts accordingly.

AA - very important

BB - moderately important

CC - least important

Figure 12.1

Annual $ valueof items

AA

BB

CC

High

Low

Low HighPercentage of Items

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Cycle CountingCycle Counting

A physical count of items in inventory

Cycle counting management

How much accuracy is needed?

When should cycle counting be performed?

Who should do it?

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Economic order quantity (EOQ) model

The order size that minimizes total annual cost

Economic production model

Quantity discount model

Economic Order Quantity ModelsEconomic Order Quantity Models

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Only one product is involved

Annual demand requirements 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

Assumptions of EOQ ModelAssumptions of EOQ Model

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The Inventory CycleThe Inventory CycleFigure 12.2

Profile of Inventory Level Over Time

Quantityon hand

Q

Receive order

Placeorder

Receive order

Placeorder

Receive order

Lead time

Reorderpoint

Usage rate

Time

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Total CostTotal Cost

Annualcarryingcost

Annualorderingcost

Total cost = +

TC = Q2

H DQ

S+

Q = Order quantity in unitsH = Holding (carrying) cost per unitD = Demand, usually in units per yearS = Ordering cost

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Cost Minimization GoalCost Minimization Goal

Order Quantity (Q)

The Total-Cost Curve is U-Shaped

Ordering Costs

QO

An

nu

al C

os

t

(optimal order quantity)

TCQH

D

QS

2

Figure 12.4C

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Deriving the EOQDeriving the EOQ

Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q.

Q = 2DS

H =

2(Annual Demand)(Order or Setup Cost)

Annual Holding CostOPT

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Minimum Total CostMinimum Total Cost

The total cost curve reaches its minimum where the carrying and ordering costs are equal.

Q2

H DQ

S=

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Production done in batches or lots Capacity to produce a part exceeds the

part’s usage or demand rate Assumptions of EPQ are similar to EOQ

except orders are received incrementally during production

Economic Production Quantity (EPQ)Economic Production Quantity (EPQ)

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Only one item is involved Annual demand is known Usage rate is constant Usage occurs continually Production rate is constant Lead time does not vary No quantity discounts

Economic Production Quantity AssumptionsEconomic Production Quantity Assumptions

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Economic Run SizeEconomic Run Size

QDS

H

p

p u0

2

Q0 = Order quantity in unitsH = Holding (carrying) cost per unitD = Demand, usually in units per yearS = Ordering cost p = Production or delivery rateu = Usage rate

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Total Costs with Purchasing CostTotal Costs with Purchasing Cost

Annualcarryingcost

PurchasingcostTC = +

Q2

H DQ

STC = +

+Annualorderingcost

PD +

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Total Costs with PDTotal Costs with PDC

ost

EOQ

TC with PD

TC without PD

PD

0 Quantity

Adding purchasing costdoesn’t change EOQ

Figure 12.7

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When to Reorder with EOQ OrderingWhen 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

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Determinants of the Reorder PointDeterminants of the Reorder Point

The rate of demand The lead time Demand and/or lead time variability Stockout risk (safety stock)

Reorder PointReorder Point

If demand and lead time are both constant, the reorder point is simply

ROP = d X LT

Where

d = Demand rate (units per day or week)

LT = Lead times in days or weeks

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Safety StockSafety StockFigure 12.12

LT Time

Expected demandduring lead time

Maximum probable demandduring lead time

ROP

Qu

an

tity

Safety stockSafety stock reduces risk ofstockout during lead time

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Reorder PointReorder PointFigure 12.13

ROP

Risk ofa stockout

Service level

Probability ofno stockout

Expecteddemand Safety

stock

0 z

Quantity

z-scale

The ROP based on a normaldistribution of lead time demand

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Orders are placed at fixed time intervals Order quantity for next interval? Suppliers might encourage fixed

intervals May require only periodic checks of

inventory levels Risk of stockout Fill rate: the percentage of demand

filled by the stock on hand

Fixed-Order-Interval ModelFixed-Order-Interval Model

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Tight control of inventory items Items from same supplier may yield

savings in: Ordering Packing Shipping costs

May be practical when inventories cannot be closely monitored

Fixed-Interval BenefitsFixed-Interval Benefits

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Requires a larger safety stock for given risk of stockout

Increases carrying cost Costs of periodic reviews

Fixed-Interval DisadvantagesFixed-Interval Disadvantages

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Single period model: model for ordering of perishables and other items with limited useful lives

Shortage cost: unrealized profits per unit (generally)

Excess cost: difference between purchase cost and salvage value of items left over at the end of a period

Single Period ModelSingle Period Model

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Continuous stocking levels

Identifies optimal stocking levels

Optimal stocking level balances unit shortage and excess cost

Discrete stocking levels

Service levels are discrete rather than continuous

Desired service level is matched or exceeded

Single Period ModelSingle Period Model

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Optimal Stocking LevelOptimal Stocking Level

Service Level

So

Quantity

Ce Cs

Balance point

Service level =Cs

Cs + CeCs = Shortage cost per unitCe = Excess cost per unit

Figure 12.16

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Example 15Example 15

Ce = $0.20 per unit Cs = $0.60 per unit Service level = Cs/(Cs+Ce) = .6/(.6+.2) Service level = .75

Service Level = 75%

Quantity

Ce Cs

Stockout risk = 1.00 – 0.75 = 0.25

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Too much inventory Tends to hide problems Easier to live with problems than to

eliminate them Costly to maintain

Wise strategy Reduce lot sizes Reduce safety stock

Accurate and up-to-date inventory records

Operations StrategyOperations Strategy