1DSCI 3123

Inventory

• Stock of items held to meet future demand– Tangible goods– Intangible goods

• Inventory management answers two questions– How much to order?– When to order?

2DSCI 3123

Types of Inventory

• Raw materials• Purchased parts and supplies• Labor• In-process (partially completed) products• Component parts• Working capital• Tools, machinery, and equipment• Finished goods

3DSCI 3123

Reasons To Hold Inventory

• Meet unexpected demand

• Smooth seasonal or cyclical demand

• Meet variations in customer demand

• Take advantage of price discounts

• Hedge against price increases

• Quantity discounts

4DSCI 3123

Two Forms Of Demand

• Dependent– items used to produce final products

• Independent– items demanded by external customers

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Inventory Costs

• 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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Inventory Control Systems

• Fixed-order-quantity system (Continuous)– constant amount ordered when inventory declines

to predetermined level

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

passage of time

7DSCI 3123

ABC Classification System

• Demand volume & value of items vary• Classify inventory into 3 categories

Class % of Units % of Dollars

A 5 - 15 70 - 80

B 30 1515

C 50 - 60 5 - 10

8DSCI 3123

ABC Classification ExampleCost Usage Part Value Value Quantity Cumulative

60 90 9 30,600 35.8 6.0 6.0350 40 8 16,000 18.7 5.0 11.0

30 130 2 14,000 16.4 4.0 15.080 60 1 5,400 6.3 9.0 24.030 100 4 4,800 5.6 6.0 30.020 180 3 3,900 4.6 13.0 43.010 170 6 3,600 4.2 18.0 61.0

320 50 5 3,000 3.5 10.0 71.0510 60 10 2,400 2.8 12.0 83.0

20 120 7 1,700 2.0 17.0 100.085,400$

Class Items % Value % UnitsA 9,8,2 71 15B 1, 4, 3 16.5 25C 6, 5, 10, 7 12.5 60

9DSCI 3123

Assumptions Of Basic EOQ Model

• Demand is known with certainty

• Demand is relatively constant over time

• No shortages are allowed

• Lead time for the receipt of orders is constant

• The order quantity is received all at once

10DSCI 3123

The Inventory Order CycleDemand rate

0 TimeLead time

Lead time

Order Placed

Order Placed

Order Received

Order Received

Inve

ntor

y L

evel

Reorder point, R

Order qty, Q

11DSCI 3123

EOQ Cost Model

CO - cost of placing order D - annual demand

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

Annual ordering cost =

Annual carrying cost =

Total cost = +

CoD

QCcQ

2CoD

Q

CcQ

2

12DSCI 3123

EOQ Model

TC=CoD

Q+CcQ

2

CoD

Q=CcQ

2

∂TC

∂Q=−

CoD

Q2 +Cc

2 Q2 =

2CoD

Cc

0=−CoD

Q2 +Cc

2 Qopt=

2CoD

Cc

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Total Cost at Q*

Qopt=2CoD

Cc

TCmin =CoD

Qopt

+CcQopt

2

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EOQ Model Cost CurvesSlope = 0

Total Cost

Ordering Cost = CoD/Q

Order Quantity, Q

Annualcost ($)

Minimumtotal cost

Optimal order Qopt

Carrying Cost = CcQ/2

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EOQ Example

CC = $0.75 per yard

CO = $150

D = 10,000 yards

Find EOQ, TC at Q*, # of order/year, and cycle time

NOTE: store days = 311

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EOQ Example

Qopt=2CoD

Cc

=2(150)(10,000)

(0.75)=2,000yards

TCmin =CoD

Qopt

+CcQopt

2

=(150)(10,000)

2,000+

(0.75)(2,000)

2=$750+750=$1,500

17DSCI 3123€

Number of orders per year =D

Qopt

=10,000

2,000= 5

Order cycle time =311

D/Qopt

=311

5= 62.2 store days

Orders per/yr and Cycle Time

18DSCI 3123

EOQ With Noninstantaneous Receipt

Q(1-d/p)

Inventorylevel

(1-d/p)Q2

Time0

Orderreceipt period

BeginOrderreceipt

EndOrderreceipt

Maximuminventory level

Averageinventory level

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EOQ With Noninstantaneous Receipt

p = production rate d = demand rate

€

Max inv level = Q -Q

pd = Q 1 -

d

p

⎛

⎝ ⎜

⎞

⎠ ⎟

Avg inv level =1

2Q 1 -

d

p

⎛

⎝ ⎜

⎞

⎠ ⎟

⎡

⎣ ⎢

⎤

⎦ ⎥=Q

21 -

d

p

⎛

⎝ ⎜

⎞

⎠ ⎟

Total carrying cost =CcQ

21 -

d

p

⎛

⎝ ⎜

⎞

⎠ ⎟

20DSCI 3123

EOQ With Noninstantaneous Receipt

€

TC=CoD

Q+CcQ

21-

d

p

⎛

⎝ ⎜ ⎞

⎠ ⎟

Qopt=2CoD

Cc 1-d

p

⎛

⎝ ⎜ ⎞

⎠ ⎟

21DSCI 3123

Production Quantity Example

CC = $0.75 per yard

CO = $150

D = 10,000 yards

d = 10,000/311 = 32.2 yards per day

p = 150 yards per day

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Optimum Q - Q*

Qopt=2CoD

Cc 1-d

p

⎛

⎝ ⎜ ⎞

⎠ ⎟

=2(150)(10,000)

0.751-32.2

150

⎛

⎝ ⎜ ⎞

⎠ ⎟

=2,256.8 yards

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Total Cost

€

TCmin=CoD

Q+CcQ

21-

d

p

⎛

⎝ ⎜ ⎞

⎠ ⎟

=(150)(10,000)

2,256.8+

(0.75)2,256.8

21-

32.2

150

⎛

⎝ ⎜ ⎞

⎠ ⎟

=$1,329

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Production Run and Max Inv. Levels

Production run = Q/p

= 2,256.8/150

= 15.05 yards

Number of production runs = D/Q

= 10,000/2,256.8

= 4.43

Max inv level=Q 1-d

p

⎛

⎝ ⎜ ⎞

⎠ ⎟ =2,256.8 1-

32.2

150

⎛

⎝ ⎜ ⎞

⎠ ⎟ =1,722yards

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Safety Stocks

• 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

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Inputs and Outputs to Aggregate Production Planning

AggregateProductionPlanning

CompanyPolicies

FinancialConstraints

StrategicObjectives

Units or dollarssubcontracted,backordered, or

lost

CapacityConstraints

Size ofWorkforce

Productionper month

(in units or $)

InventoryLevels

DemandForecasts

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Hierarchical Planning ProcessItems

Product lines or families

Individual products

Components

Manufacturing operations

Resource level

Plants

Individual machines

Critical work centers

Production Planning Capacity Planning

Resource Requirements Plan

Rough-Cut Capacity Plan

Capacity Requirements Plan

Input/Output Control

Aggregate Production Plan

Master Production Schedule

Material Requirements Plan

Shop Floor Schedule

All work centers