C9 inventory management

OPM 5339-1

Operations Operations ManagementManagement

Inventory ManagementInventory ManagementChapter 9Chapter 9

OPM 5339-2

Stock of materials Stored capacity Examples

© 1995 Corel Corp.© 1984-1994 T/Maker Co. © 1984-1994 T/Maker Co.

© 1995 Corel Corp.

What is Inventory?

OPM 5339-3

The Functions of InventoryTo ”decouple” or separate various parts of the

production processTo provide a stock of goods that will provide a

“selection” for customersTo take advantage of quantity discountsTo hedge against inflation and upward price

changes

OPM 5339-4

Types of InventoryRaw material (RM)Work-in-progress (WIP)Maintenance/repair/operating supply (MRO)Finished goods (FG)

OPM 5339-5

Higher costs Item cost (if purchased) Ordering (or setup) cost

Costs of forms, clerks’ wages etc. Holding (or carrying) cost

Building lease, insurance, taxes etc.

Difficult to control Hides production problems

Disadvantages of Inventory

OPM 5339-6

Inventory

Process stage

Demand Type

Number & Value Other

Raw Material WIP

Finished Goods

Independent

Dependent

A Items

B Items

C Items

Maintenance Operating

© 1984-1994 T/Maker Co.

Inventory Classifications

OPM 5339-7

1 Run time: Job is at machine and being worked on2 Setup time: Job is at the work station, and the work station is

being "setup."3 Queue time: Job is where it should be, but is not being

processed because other work precedes it.4 Move time: The time a job spends in transit5 Wait time: When one process is finished, but the job is

waiting to be moved to the next work area.6 Other: "Just-in-case" inventory.

The Material Flow Cycle

Other WaitTime

MoveTime

Queue

Time

SetupTime

RunTime

Input

Cycle Time

Output

OPM 5339-8

Divides on-hand inventory into 3 classes A class, B class, C class

Basis is usually annual $ volume $ volume = Annual demand x Unit cost

Policies based on ABC analysis Develop class A suppliers more Give tighter physical control of A items Forecast A items more carefully

ABC Analysis

OPM 5339-9% of Inventory Items

Classifying Items as ABC

0

20

40

60

80

100

0 50 100

% Annual $ Usage

AA

BBCC

Class % $ Vol % Items

A 80 15B 15 30C 5 55

OPM 5339-10

Physically counting a sample of total inventory on a regular basis

Used often with ABC classification A items counted most often (e.g., daily)

Cycle Counting

OPM 5339-11

Advantages of Cycle Counting

Eliminates shutdown and interruption of production necessary for annual physical inventories

Eliminates annual inventory adjustmentsProvides trained personnel to audit the accuracy

of inventoryAllows the cause of errors to be identified and

remedial action to be takenMaintains accurate inventory records

OPM 5339-12

Techniques for Controlling Service Inventory Include:

Good personnel selection, training, and disciplineTight control of incoming shipmentsEffective control of all goods leaving the facility

OPM 5339-13

Independent versus Dependent Demand

Independent demand - demand for item is independent of demand for any other item

Dependent demand - demand for item is dependent upon the demand for some other item

OPM 5339-14

Inventory CostsHolding costs - associated with holding or

“carrying” inventory over time; e.g. obsolescence, insurance, extra staffing, interest, pilferage, damage, warehousing, etc.

Ordering costs - associated with costs of placing order and receiving goods; eg. Supplies, forms, order processing, clerical support, etc.

Setup costs - cost to prepare a machine or process for manufacturing an order; e.g. clean-up costs, re-tooling costs, adjustment costs, etc.

OPM 5339-15

Inventory Holding Costs(Approximate Ranges)

Category

Housing costs (building rent, depreciation, operating cost, taxes, insurance)

Material handling costs (equipment, lease or depreciation, power, operating cost)

Labor cost from extra handling

Investment costs (borrowing costs, taxes, and insurance on inventory)

Pilferage, scrap, and obsolescence

Overall carrying cost

Cost as a % of Inventory

Value6%

(3 - 10%)

3%(1 - 3.5%)

3%(3 - 5%)

11%(6 - 24%)

3% (2 - 5%)26%

OPM 5339-16

Fixed order-quantity modelsEconomic order quantityProduction order quantityQuantity discount

Probabilistic models

Fixed order-period models

Help answer the inventory planning questions!

Help answer the inventory planning questions!

© 1984-1994 T/Maker Co.

Inventory Models

OPM 5339-17

Known and constant demand Known and constant lead time Instantaneous receipt of material No quantity discounts Only order (setup) cost and holding cost No stockouts

1. EOQ Assumptions

OPM 5339-18

Inventory Usage Over Time

Time

Inve

ntor

y Le

vel

AverageInventory

(Q*/2)

0

Minimum inventory

Order quantity = Q (maximum inventory level)

Usage Rate

OPM 5339-19

EOQ ModelHow Much to Order?

Order quantity

Annual Cost

Holding Cost CurveTotal Cost Curve

Order (Setup) Cost Curve

Optimal Order Quantity (Q*)

Minimum total cost

OPM 5339-20

More units must be stored if more are ordered

Purchase OrderDescription Qty.Microwave 1

Order quantity


Order quantity

Why Holding Costs Increase

OPM 5339-21

Cost is spread over more units

Example: You need 1000 microwave ovens





1 Order (Postage $ 0.33) 1000 Orders (Postage $330)

Order quantity

Purchase Order

Description Qty.Microwave 1000

Why Order Costs Decrease

OPM 5339-22

Deriving an EOQ1. Develop an expression for setup or ordering

costs

2. Develop an expression for holding cost

3. Set setup cost equal to holding cost

4. Solve the resulting equation for the best order quantity

OPM 5339-23

Optimal Order Quantity

Expected Number of Orders

Expected Time Between Orders Working Days / Year

Working Days / Year

= =× ×

= =

= =

=

= ×

Q*D S

H

ND

Q*

TN

dD

ROP d L

2

D = Demand per year

S = Setup (order) cost per order

H = Holding (carrying) cost

d = Demand per day

L = Lead time in days

EOQ Model Equations

OPM 5339-24

The Reorder Point (ROP) Curve

Q*

ROP (Units)

Slope = units/day = d

Lead time = L

Time (days)

Inve

ntor

y le

vel

(uni

ts)

OPM 5339-25

Answers how much to order and when to order Allows partial receipt of material

Other EOQ assumptions apply Suited for production environment

Material produced, used immediately Provides production lot size

Lower holding cost than EOQ model

2. Production Order Quantity Model

OPM 5339-26

Reasons for Variability in Production

Most variability is caused by waste or by poor management. Specific causes include: employees, machines, and suppliers produce

units that do not conform to standards, are late or are not the proper quantity

inaccurate engineering drawings or specifications production personnel try to produce before

drawings or specifications are complete customer demands are unknown

OPM 5339-27

D = Demand per year

S = Setup cost

H = Holding cost

d = Demand per day

p = Production per day

POQ Model Equations

Optimal Order Quantity

Setup Cost

Holding Cost

= =

-

= *

= *

=

Q

H*d

p

Q

D

QS

p*

1

(

0.5 * H * Q -d

p1

)-d

p1

( )

2*D*S

( )Maximum inventory level

OPM 5339-28

Answers how much to order & when to order

Allows quantity discounts Reduced price when item is purchased in larger

quantities Other EOQ assumptions apply

Trade-off is between lower price & increased holding cost

3. Quantity Discount Model

Inventory Usage Over Time

29Figure 12.3Figure 12.3

Order Order quantity = Q quantity = Q (maximum (maximum inventory inventory

level)level)

Inve

nto

ry le

vel

Inve

nto

ry le

vel

TimeTime

Usage rateUsage rate Average Average inventory inventory on handon hand

QQ22

Minimum Minimum inventoryinventory

Minimizing Costs

30

Objective is to minimize total costsObjective is to minimize total costs

Table 11.5Table 11.5

An

nu

al c

ost

An

nu

al c

ost

Order quantityOrder quantity

Curve for total Curve for total cost of holding cost of holding

and setupand setup

Holding cost Holding cost curvecurve

Setup (or order) Setup (or order) cost curvecost curve

Minimum Minimum total costtotal cost

Optimal Optimal order order

quantityquantity

The EOQ Model

31

QQ = Number of pieces per order= Number of pieces per orderQ*Q* = Optimal number of pieces per order (EOQ)= Optimal number of pieces per order (EOQ)DD = Annual demand in units for the Inventory item= Annual demand in units for the Inventory itemSS = Setup or ordering cost for each order= Setup or ordering cost for each orderHH = Holding or carrying cost per unit per year= Holding or carrying cost per unit per year

Annual setup cost Annual setup cost == ((Number of orders placed per yearNumber of orders placed per year) ) x (x (Setup or order cost per orderSetup or order cost per order))

Annual demandAnnual demand

Number of units in each orderNumber of units in each orderSetup or order Setup or order cost per ordercost per order

==

= (= (SS))DDQQ

Annual setup cost = SDQ

The EOQ Model

32


Annual holding cost Annual holding cost == ((Average inventory levelAverage inventory level) ) x (x (Holding cost per unit per yearHolding cost per unit per year))


22= (= (Holding cost per unit per yearHolding cost per unit per year))

= (= (HH))QQ22


Annual holding cost = HQ2

The EOQ Model

33


Optimal order quantity is found when annual setup cost Optimal order quantity is found when annual setup cost equals annual holding costequals annual holding cost


Annual holding cost = HQ2

DDQQ

SS = = HHQQ22

Solving for Q*Solving for Q*22DS = QDS = Q22HHQQ22 = = 22DS/HDS/H

Q* = Q* = 22DS/HDS/H

An EOQ Example

34

Determine optimal number of needles to orderDetermine optimal number of needles to orderD D = 1,000= 1,000 units unitsS S = $10= $10 per order per orderH H = $.50= $.50 per unit per year per unit per year

Q* =Q* =22DSDS

HH

Q* =Q* =2(1,000)(10)2(1,000)(10)

0.500.50= 40,000 = 200= 40,000 = 200 units units

An EOQ Example

35

Determine optimal number of needles to orderDetermine optimal number of needles to orderD D = 1,000= 1,000 units units Q* Q* = 200= 200 units unitsS S = $10= $10 per order per orderH H = $.50= $.50 per unit per year per unit per year

= N = == N = =Expected Expected number of number of

ordersorders

DemandDemandOrder quantityOrder quantity

DDQ*Q*

N N = = 5= = 5 orders per year orders per year 1,0001,000200200

An EOQ Example

36

Determine optimal number of needles to orderDetermine optimal number of needles to orderD D = 1,000= 1,000 units units Q*Q* = 200= 200 units unitsS S = $10= $10 per order per order NN = 5= 5 orders per year orders per yearH H = $.50= $.50 per unit per year per unit per year

= T == T =Expected Expected

time between time between ordersorders

Number of working Number of working days per yeardays per year

NN

T T = = 50 = = 50 days between ordersdays between orders250250

55

An EOQ Example

37

Determine optimal number of needles to orderDetermine optimal number of needles to orderD D = 1,000= 1,000 units units Q*Q* = 200= 200 units unitsS S = $10= $10 per order per order NN = 5= 5 orders per year orders per yearH H = $.50= $.50 per unit per year per unit per year TT = 50= 50 days days

Total annual cost = Setup cost + Holding costTotal annual cost = Setup cost + Holding cost

TC = S + HTC = S + HDDQQ

QQ22

TC TC = ($10) + ($.50)= ($10) + ($.50)1,0001,000200200

20020022

TC TC = (5)($10) + (100)($.50) = $50 + $50 = $100= (5)($10) + (100)($.50) = $50 + $50 = $100

An EOQ Example with safety stock

38

Determine optimal number of needles to orderDetermine optimal number of needles to orderD D = 1,000= 1,000 units units Q*Q* = 200= 200 units unitsS S = $10= $10 per order per order NN = 5= 5 orders per year orders per yearH H = $.50= $.50 per unit per year per unit per year TT = 50= 50 days daysSafety Stock (ss) = 10 unitsSafety Stock (ss) = 10 unitsTotal annual cost = Setup cost + Holding costTotal annual cost = Setup cost + Holding cost

TC = S + TC = S + (( + ss + ss))HHDDQQ

QQ22

TC TC = ($10) + (100 + )($.50)= ($10) + (100 + )($.50)1,0001,000200200

20020022

TC TC = (5)($10) + (200)($.50) = $50 + $100 = $150= (5)($10) + (200)($.50) = $50 + $100 = $150

Reorder Points

39

EOQ answers the “how much” questionEOQ answers the “how much” question

The reorder point (ROP) tells when to The reorder point (ROP) tells when to orderorder

ROP ROP ==Lead time for a Lead time for a

new order in daysnew order in daysDemand Demand per dayper day

== d x L d x L

d = d = DDNumber of working days in a yearNumber of working days in a year

Reorder Point Curve

40

Q*Q*

ROP ROP (units)(units)In

ven

tory

lev

el (

un

its)

Inve

nto

ry l

evel

(u

nit

s)

Time (days)Time (days)Figure 12.5Figure 12.5 Lead time = LLead time = L

Slope = units/day = dSlope = units/day = d

Reorder Point Example

41

Demand Demand = 8,000= 8,000 DVDs per year DVDs per year250250 working day year working day yearLead time for orders is Lead time for orders is 33 working days working days

ROP =ROP = d x L d x L

d =d = DD

Number of working days in a yearNumber of working days in a year

= 8,000/250 = 32= 8,000/250 = 32 units units

= 32= 32 units per day x units per day x 33 days days = 96= 96 units units

Reorder point with Safety Stock

42

Annual Demand = 25,000 units Annual Demand = 25,000 units Number of working days in a year 250 daysNumber of working days in a year 250 daysLead time = 5 daysLead time = 5 daysSafety stock (ss) = 2 days usageSafety stock (ss) = 2 days usage

ROP = d x l + ssROP = d x l + ss

d= D / Number of days work in a yeard= D / Number of days work in a year

d= 25,000 / 250 = 100 units d= 25,000 / 250 = 100 units

ss= 2 days x 100 = 200ss= 2 days x 100 = 200

ROP = 100 x 5 + 200 = 700 unitsROP = 100 x 5 + 200 = 700 units

Quantity Discount Models

43

Reduced prices are often available when Reduced prices are often available when larger quantities are purchasedlarger quantities are purchased

Trade-off is between reduced product cost Trade-off is between reduced product cost and increased holding costand increased holding cost

Total cost = Setup cost + Holding cost + Product costTotal cost = Setup cost + Holding cost + Product cost

TC = S + + PDTC = S + + PDDDQQ

QHQH22


44

Discount Number Discount Quantity Discount (%)

Discount Price (P)

1 0 to 999 no discount $5.00

2 1,000 to 1,999 4 $4.80

3 2,000 and over 5 $4.75


A typical quantity discount scheduleA typical quantity discount schedule


45

1.1. For each discount, calculate Q*For each discount, calculate Q*

2.2. If Q* for a discount doesn’t qualify, If Q* for a discount doesn’t qualify, choose the smallest possible order size choose the smallest possible order size to get the discountto get the discount

3.3. Compute the total cost for each Q* or Compute the total cost for each Q* or adjusted value from Step 2adjusted value from Step 2

4.4. Select the Q* that gives the lowest total Select the Q* that gives the lowest total costcost

Steps in analyzing a quantity discountSteps in analyzing a quantity discount


46

1,0001,000 2,0002,000

To

tal

cost

$T

ota

l co

st $

00


Q* for discount 2 is below the allowable range at point a Q* for discount 2 is below the allowable range at point a and must be adjusted upward to 1,000 units at point band must be adjusted upward to 1,000 units at point b

aabb

1st price 1st price breakbreak

2nd price 2nd price breakbreak

Total cost Total cost curve for curve for

discount 1discount 1

Total cost curve for discount 2Total cost curve for discount 2

Total cost curve for discount 3Total cost curve for discount 3

Figure 12.7Figure 12.7

Quantity Discount Example

47

Calculate Q* for every discountCalculate Q* for every discount Q* =2DSIP

QQ11* * = = 700= = 700 cars order cars order2(5,000)(49)2(5,000)(49)

(.2)(5.00)(.2)(5.00)


(.2)(4.80)(.2)(4.80)


(.2)(4.75)(.2)(4.75)


48

Calculate Q* for every discountCalculate Q* for every discount Q* =2DSIP


(.2)(5.00)(.2)(5.00)


(.2)(4.80)(.2)(4.80)


(.2)(4.75)(.2)(4.75)

1,0001,000 — adjusted — adjusted

2,0002,000 — adjusted — adjusted


49

Discount Number

Unit Price

Order Quantity

Annual Product

Cost

Annual Ordering

Cost

Annual Holding

Cost Total

1 $5.00 700 $25,000 $350 $350 $25,700

2 $4.80 1,000 $24,000 $245 $480 $24,725

3 $4.75 2,000 $23.750 $122.50 $950 $24,822.50


Choose the price and quantity that gives Choose the price and quantity that gives the lowest total costthe lowest total cost

Buy Buy 1,0001,000 units at units at $4.80$4.80 per unit per unit

C9 inventory management

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