Copyright © 2011 The McGraw-Hill Companies, All Rights Reserved Chapter 17 Inventory Control.

Copyright © 2011 The McGraw-Hill Companies, All Copyright © 2011 The McGraw-Hill Companies, All Rights ReservedRights Reserved

Chapter 17Inventory Control

Learning Objectives1. Explain the different purposes for keeping

inventory.2. Understand that the type of inventory system

logic that is appropriate for an item depends on the type of demand for that item.

3. Calculate the appropriate order size when a one-time purchase must be made.

4. Describe what the economic order quantity is and how to calculate it.

5. Summarize fixed–order quantity and fixed–time period models, including ways to determine safety stock when there is variability in demand.

6. Discuss why inventory turn is directly related to order quantity and safety stock.

Inventory You should visualize inventory as stacks

of money sitting on forklifts, on shelves, and in trucks and planes while in transit

For many businesses, inventory is the largest asset on the balance sheet at any given time

Inventory is often not very liquid It is a good idea to try to get your

inventory down as far as possible The average cost of inventory in the United

States is 30 to 35 percent of its value

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Definition of Inventory Inventory: the stock of any item or resource

used in an organization and can include: raw materials, finished products, component parts, supplies, and work-in-process Manufacturing inventory: refers to items that

contribute to or become part of a firm’s product Inventory system: the set of policies and

controls that monitor levels of inventory and determines what levels should be maintained, when stock should be replenished, and how large orders should be

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Purposes of Inventory1. To maintain independence of

operations2. To meet variation in product demand3. To allow flexibility in production

scheduling4. To provide a safeguard for variation in

raw material delivery time5. To take advantage of economic

purchase-order size

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Inventory Costs1. Holding (or carrying) costs

Costs for storage, handling, insurance, and so on

2. Setup (or production change) costs Costs for arranging specific equipment

setups, and so on3. Ordering costs

Costs of placing an order4. Shortage costs

Costs of running out

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Independent Versus Dependent Demand Independent demand: the demands for

various items are unrelated to each other For example, a workstation may produce

many parts that are unrelated but meet some external demand requirement

Dependent demand: the need for any one item is a direct result of the need for some other item Usually a higher-level item of which it is

part

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Inventory Control-System Design Matrix: Framework Describing Inventory Control Logic

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Inventory Systems Single-period inventory model

One time purchasing decision (Example: vendor selling t-shirts at a football game)

Seeks to balance the costs of inventory overstock and under stock

Multi-period inventory models Fixed-order quantity models

Event triggered (Example: running out of stock)

Fixed-time period models Time triggered (Example: Monthly sales call by

sales representative)

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Multi-Period Models There are two general types of multi-

period inventory systems1. Fixed–order quantity models

Also called the economic order quantity, EOQ, and Q-model

Event triggered2. Fixed–time period models

Also called the periodic system, periodic review system, fixed-order interval system, and P-model

Time triggered

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Key Differences To use the fixed–order quantity model,

the inventory remaining must be continually monitored

In a fixed–time period model, counting takes place only at the review period

The fixed–time period model Has a larger average inventory Favors more expensive items Is more appropriate for important items Requires more time to maintain

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Fixed-Order Quantity Model Models Demand for the product is constant and

uniform throughout the period Lead time (time from ordering to

receipt) is constant Price per unit of product is constant Inventory holding cost is based on

average inventory Ordering or setup costs are constant All demands for the product will be

satisfied

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Basic Fixed–Order Quantity Model

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Basic Fixed-Order Quantity (EOQ) Model Formula

H 2

Q + S

Q

D + DC = TC H

2

Q + S

Q

D + DC = TC

Total Total Annual =Annual =

Cost Cost

AnnualAnnualPurchasePurchase

CostCost

AnnualAnnualOrderingOrdering

CostCost

AnnualAnnualHoldingHolding

CostCost++ ++

TC=Total annual TC=Total annual

costcost

D =DemandD =Demand

C =Cost per unitC =Cost per unit

Q =Order quantityQ =Order quantity

S =Cost of placing S =Cost of placing

an order or setup an order or setup

costcost

R =Reorder pointR =Reorder point

L =Lead timeL =Lead time

H=Annual holding H=Annual holding

and storage cost and storage cost

per unit of inventoryper unit of inventory

TC=Total annual TC=Total annual

costcost

D =DemandD =Demand

C =Cost per unitC =Cost per unit

Q =Order quantityQ =Order quantity

S =Cost of placing S =Cost of placing

an order or setup an order or setup

costcost

R =Reorder pointR =Reorder point

L =Lead timeL =Lead time

H=Annual holding H=Annual holding

and storage cost and storage cost

per unit of inventoryper unit of inventory

Annual Product Costs, Based on Size of the Order

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Deriving the EOQ

Using calculus, we take the first derivative of the total cost function with respect to Q, and set the derivative (slope) equal to zero, solving for the optimized (cost minimized) value of Qopt

Using calculus, we take the first derivative of the total cost function with respect to Q, and set the derivative (slope) equal to zero, solving for the optimized (cost minimized) value of Qopt

Q = 2DS

H =

2(Annual D em and)(Order or Setup Cost)

Annual Holding CostOPTQ =

2DS

H =

2(Annual D em and)(Order or Setup Cost)

Annual Holding CostOPT

Reorder point, R = d L_

Reorder point, R = d L_

d = average daily demand (constant)

L = Lead time (constant)

_We also need a We also need a reorder point to reorder point to tell us when to tell us when to place an orderplace an order

We also need a We also need a reorder point to reorder point to tell us when to tell us when to place an orderplace an order

EOQ Example Example Data

Annual Demand = 1,000 unitsAnnual Demand = 1,000 unitsDays per year considered in average Days per year considered in average

daily demand = 365daily demand = 365Cost to place an order = $10Cost to place an order = $10

Holding cost per unit per year = $2.50Holding cost per unit per year = $2.50Lead time = 7 daysLead time = 7 daysCost per unit = $15Cost per unit = $15

Given the information below, what are the EOQ and Given the information below, what are the EOQ and reorder point and Total Inventory Cost?reorder point and Total Inventory Cost?

Given the information below, what are the EOQ and Given the information below, what are the EOQ and reorder point and Total Inventory Cost?reorder point and Total Inventory Cost?

Establishing Safety Stock Levels Safety stock: amount of inventory

carried in addition to expected demand Safety stock can be determined based on many

different criteria A common approach is to simply keep a

certain number of weeks of supply A better approach is to use probability

Assume demand is normally distributed Assume we know mean and standard deviation To determine probability, we plot a normal

distribution for expected demand and note where the amount we have lies on the curve

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Fixed–Order Quantity Model with Safety Stock

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Fixed–Order Quantity Model with Safety Stock

timelead during usage ofdeviation Standard

yprobabilit service afor deviations standard ofNumber z

daysin timeLead L

demanddaily Average d

unitsin point Reorder R

L

LzLdR

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Fixed–Time Period Inventory Model

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Inventory Control and Supply Chain Management

SS

SS

2Q

DturnInventory

2

Qinventory Average

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Price Break Models Selling price varies with order size Steps

Determine Q Determine if feasible or not Calculate TC Choose min TC

Example : The Data and Order Quantities

D = 10,000 S = $20 i = 20 percent Cost per unit…

1-499 $5.00 500-999 $4.50 1,000 and up $3.90

716

90.320.0

20000,102

66750.420.0

20000,102

63300.520.0

20000,102

2

000,1

999500

4991

Q

Q

Q

iC

DSQ

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ABC Classification

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Inventory Accuracy and Cycle Counting Inventory accuracy: refers to how well

the inventory records agree with physical count

Cycle counting: a physical inventory-taking technique in which inventory is counted on a frequent basis rather than once or twice a year

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Any Questions?