Inventory Control !!

8/11/2019 Inventory Control !!

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Inventory Management


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Elements of Inventory Management Inventory Control Systems Economic Order Quantity Models Quantity Discounts

Reorder Point Order Quantity for a Periodic Inventory

System

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Stock of items kept to meet future demand Purpose of inventory management

how many units to order

when to order

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Bullwhip effect demand information is distorted as it moves awayfrom the end-use customer

higher safety stock inventories to are stored tocompensate

Seasonal or cyclical demand Inventory provides independence from

vendors Take advantage of price discounts Inventory provides independence between

stages and avoids work stoppages

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Customers usually perceive quality service asavailability of goods they want when theywant them

Inventory must be sufficient to provide high-

quality customer service in QM

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Raw materials Purchased parts and supplies

Work-in-process (partially completed)products (WIP)

Items being transported Tools and equipment

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Dependent Demand for items used to produce final

products

Tires for autos are a dependent demand item

Independent Demand for items used by external

customers

Cars, appliances, computers, and houses areexamples of independent demand inventory

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Carrying cost cost of holding an item in inventory

Ordering cost cost of replenishing inventory

Shortage cost temporary or permanent loss of sales when

demand cannot be met

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Continuous system (fixed-order-quantity) constant amount ordered when inventory declines

to predetermined level

Periodic system (fixed-time-period) order placed for variable amount after fixed

passage of time

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Class A 5 15 % of units

70 80 % of value

Class B

30 % of units 15 % of value

Class C 50 60 % of units

510 % of value

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1 $ 60 902 350 403 30 130

4 80 605 30 1006 20 1807 10 1708 320 50

9 510 6010 20 120

PART UNIT COST ANNUAL USAGE


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13-12

Example 10.1

9 $30,600 35.9 6.0 6.08 16,000 18.7 5.0 11.02 14,000 16.4 4.0 15.01 5,400 6.3 9.0 24.0

4 4,800 5.6 6.0 30.03 3,900 4.6 10.0 40.06 3,600 4.2 18.0 58.05 3,000 3.5 13.0 71.0

10 2,400 2.8 12.0 83.0

7 1,700 2.0 17.0 100.0

TOTAL % OF TOTAL % OF TOTAL

PART VALUE VALUE QUANTITY % CUMMULATIVE

A

B

C

$85,400


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Example 10.1

% OF TOTAL % OF TOTALCLASS ITEMS VALUE QUANTITY

A 9, 8, 2 71.0 15.0B 1, 4, 3 16.5 25.0

C 6, 5, 10, 7 12.5 60.0


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EOQ optimal order quantity that will

minimize total inventory costs

Basic EOQ model

Production quantity model

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Demand is known with certainty and isconstant over time No shortages are allowed Lead time for the receipt of orders is constant

Order quantity is received all at once

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Demandrate

TimeLeadtime

Leadtime

Orderplaced

Orderplaced

Orderreceipt

Orderreceipt

Inve

ntory

Level

Reorder point, R

Order quantity, Q

0

Averageinventory

Q

2


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Co- cost of placing order D- annual demandC

c- annual per-unit carrying cost Q- order quantity

Annual ordering cost =C

oD

Q

Annual carrying cost =C

cQ

2

Total cost = +C

oD

Q

CcQ

2


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TC = +C

oD

Q

CcQ

2

= +C

oD

Q2

Cc

2

TC

Q

0 = +C

0D

Q2

Cc

2

Qopt=

2CoD

Cc

Deriving Qopt Proving equality ofcosts at optimal point

=C

oD

Q

CcQ

2

Q2 =2CoD

Cc

Qopt=2C

oD

Cc


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Order Quantity, Q

Annualcost ($) Total Cost

Carrying Cost =C

cQ

2

Slope = 0

Minimum

total cost

Optimal orderQopt

Ordering Cost =C

oD

Q


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Cc= $0.75 per gallon Co= $150 D= 10,000 gallons

Qopt=2C

oD

Cc

Qopt=2(150)(10,000)

(0.75)

Qopt= 2,000 gallons

TCmin= +C

oD

Q

CcQ

2

TCmin= +(150)(10,000)

2,000

(0.75)(2,000)

2

TCmin= $750 + $750 = $1,500

Orders per year = D/Qopt

= 10,000/2,000

= 5 orders/year

Order cycle time = 311 days/(D/Qopt)

= 311/5

= 62.2 store days


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Order is received gradually, as inventory issimultaneously being depleted AKA non-instantaneous receipt model

assumption that Q is received all at once is

relaxed

p - daily rate at which an order is receivedover time, a.k.a. production rate

d - daily rate at which inventory isdemanded

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Q(1-d/p)

Inventorylevel

(1-d/p)Q

2

Time0

Orderreceipt period

Beginorder

receipt

Endorder

receipt

Maximuminventorylevel

Averageinventorylevel


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p= production rate d= demand rate

Maximum inventory level = Q- d

= Q1 -

Q

p

d

p

Average inventory level = 1 -Q

2d

p

TC= + 1 - dp

CoDQ CcQ2

Qopt=2CoD

Cc 1 -

d

p


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Cc= $0.75 per gallon C

o= $150 D= 10,000 gallons

d= 10,000/311 = 32.2 gallons per day p= 150 gallons per day

Qopt= = = 2,256.8 gallons

2CoD

Cc

1 - dp

2(150)(10,000)

0.75 1 - 32.2150

TC= + 1 - = $1,329d

p

CoD

Q

CcQ

2

Production run = = = 15.05 days per orderQ

p

2,256.8

150


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Number of production runs = = = 4.43 runs/yearDQ

10,0002,256.8

Maximum inventory level = Q 1 - = 2,256.8 1 -

= 1,772 gallons

d

p32.2150


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The optimal order

size, Q, in cell D8


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The formula for Qin cell D10

=(D4*D5/D10)+(D3*D10/2)*(1-(D7/D8))

=D10*(1-(D7/D8))


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Price per unit decreases as orderquantity increases

TC= + + PDC

oD

Q

CcQ

2

where

P= per unit price of the itemD= annual demand


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Qopt

Carrying cost

Ordering cost

Inventoryc

ost($)

Q(d1 ) = 100 Q(d2 ) = 200

TC (d2 = $6 )

TC(d1 = $8 )

TC = ($10 )ORDER SIZE PRICE

0 - 99 $10

100 199 8 (d1)

200+ 6 (d2)


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QUANTITY PRICE

1 - 49 $1,400

50 - 89 1,100

90+ 900

Co= $2,500

Cc= $190 per TV

D= 200 TVs per year

Qopt= = = 72.5 TVs2CoD

Cc

2(2500)(200)

190

TC= + + PD = $233,784C

oD

Qopt

CcQopt

2

For Q= 72.5

TC= + + PD = $194,105C

oD

Q

CcQ

2

For Q= 90


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=(D4*D5/E10)+(D3*E10/2)+C10*D5=IF(D10>B10,D10,B10)


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Inventory level at which a new order is placed

R= dLwhere

d= demand rate per periodL= lead time


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Demand = 10,000 gallons/yearStore open 311 days/year

Daily demand = 10,000 / 311 = 32.154

gallons/dayLead time = L = 10 days

R = dL = (32.154)(10) = 321.54 gallons


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Safety stock buffer added to on hand inventory during lead

time

Stockout an inventory shortage

Service level probability that the inventory available during

lead time will meet demand

P(Demand during lead time


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Reorderpoint, R

Q

LT

Time

LT

Inve

ntory

level

0


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Reorderpoint, R

Q

LTTime

LT

Inventory

level

0

Safety Stock


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R= dL+ zd L

where

d= average daily demand

L= lead timed= the standard deviation of daily demandz= number of standard deviations

corresponding to the service level

probabilityzd L = safety stock


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Probability ofmeeting demand duringlead time = service level

Probability ofa stockout

R

Safety stock

dLDemand

zd L


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The paint store wants a reorder point with a 95%service level and a 5% stockout probability

d= 30 gallons per dayL= 10 days

d= 5 gallons per day

For a 95% service level, z= 1.65

R= dL+ zd L

= 30(10) + (1.65)(5)( 10)= 326.1 gallons

Safety stock = zd L

= (1.65)(5)( 10)= 26.1 gallons


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The reorder point

formula in cell E7


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Q= d(tb+ L) + zd tb+ L - I

where

d = average demand ratetb = the fixed time between ordersL = lead timed = standard deviation of demand

zd tb+ L = safety stock

I = inventory level


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d= 6 packages per dayd= 1.2 packagestb= 60 daysL= 5 days

I= 8 packagesz= 1.65 (for a 95% service level)

Q= d(tb+ L) + zd tb+ L -I

= (6)(60 + 5) + (1.65)(1.2) 60 + 5 - 8

= 397.96 packages


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Formula for ordersize, Q, in cell D10

Inventory Control !!

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