Inventory Inventory

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Inventory - I Items from last class What is inventory Inventory Video Inventory Cost Structure Basic Ideas for Managing Independent

Demand InventoryEconomic Order Quantity Exercise

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Inventory DefinitionInventory Definition

A stock of items held to meet future demand

Question: Goods vs Services?

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Types of Inventory

Inputs• Raw Materials• Purchased parts• Maintenance and

Repair Materials

Outputs• Finished Goods• Scrap and Waste

Process

In Process• Partially Completed

Products and Subassemblies

(in warehouses, or “in transit”)

(often on the factory floor)

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Types of Inventory

Work inprocess

Work inprocess

Work inprocess

Finishedgoods

RawMaterials

Vendors Customer

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Water Tank Analogy for Inventory

Supply RateInventory Level

Demand Rate

Inventory Level

Buffers Demand Rate from Supply Rate

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Independent and Dependent Demand Independent and Dependent Demand InventoryInventory

Independent demand– items demanded by external customers

(Kitchen Tables) Dependent demand

– items used to produce final products (table top, legs, hardware, paint, etc.)

– Demand determined once we know the type and number of final products

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Independent and Dependent Demand Independent and Dependent Demand Inventory ManagementInventory Management

Independent demand– Uncertain / forecasted– Continuous Review / Periodic Review

Dependent demand– “Requirements” / planned– Materials Requirements Planning / Just in

Time

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Reasons To Hold InventoryReasons To Hold Inventory

Meet variations in customer demand:Meet unexpected demandSmooth seasonal or cyclical demand

Pricing related:Temporary price discountsHedge against price increasesTake advantage of quantity discounts

Process & supply surprisesInternal – upsets in parts of or our own processesExternal – delays in incoming goods

Transit

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Reasons To Reasons To NOTNOT Hold Inventory Hold Inventory Carrying cost

Financially calculable Takes up valuable factory space

Especially for in-process inventory Inventory covers up “problems” …

That are best exposed and solved

Driver for increasing inventory turns (finished goods) and lean production/Just in time for work in process

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Inventory Hides Problems

Poor Quality

UnreliableSupplier

MachineBreakdownInefficient

Layout

BadDesign

LengthySetups

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To Expose Problems:Reduce Inventory Levels

Poor Quality

UnreliableSupplier

MachineBreakdownInefficient

Layout

BadDesign

LengthySetups

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Remove Sources of Problems and Repeat the Process

Poor Quality

UnreliableSupplier

MachineBreakdownInefficient

Layout

BadDesign

LengthySetups

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VideoVideo

Inventory concepts that occur in the textbook supply chain

Watch for:Difference between independent and

dependent demand inventory

“How much and when” to order

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Inventory Cost Structures Ordering (or setup) cost Carrying (or holding) cost:

Cost of capitalCost of storageCost of obsolescence, deterioration, and loss

Stock out cost Item costs, shipping costs and other cost

subject to volume discounts

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Typical Inventory Carrying CostsTypical Inventory Carrying Costs

Housing cost:Building rent or depreciationBuilding operating costTaxes on buildingInsurance

Material handling costs:Equipment, lease, or depreciationPowerEquipment operating cost

Manpower cost from extra handling and supervision

Investment costs:Borrowing costsTaxes on inventoryInsurance on inventory

Pilferage, scrap, and obsolescence

Overall carrying cost

6% (3% - 10%)

3% (1% - 4%)

3% (3% - 5%)

10% (6% - 24%)

5% (2% - 10%) (15% - 50%)

Costs as % of Inventory Value

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Inventory Management SystemsInventory Management Systems

Functions of Inventory Management– Track inventory – How much to order– When to order

Prioritization Inventory Management Approach

– EOQ– Continuous / Periodic

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ABC Prioritization

Based on “Pareto” concept (80/20 rule) and total usage in dollars of each item.

Classification of items as A, B, or C often based on $ volume.

Purpose: set priorities for management attention.

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ABC Prioritization ‘A’ items: 20% of SKUs, 80% of dollars ‘B’ items: 30 % of SKUs, 15% of dollars ‘C’ items: 50 % of SKUs, 5% of dollars Three classes is arbitrary; could be any

number. Percents are approximate. Danger: dollar use may not reflect

importance of any given SKU!

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ABC Analysis Example

1010 2020 3030 4040 5050 6060 7070 8080 9090 100100

Percentage of itemsPercentage of items

Per

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f d

oll

ar v

alu

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100 100 —

90 90 —

80 80 —

70 70 —

60 60 —

50 50 —

40 40 —

30 30 —

20 20 —

10 10 —

0 0 —

+Class C

Class A

+Class B

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Annual Usage of Items by Dollar Value

ItemAnnual Usage in

Units Unit Cost Dollar Usage

Percentage of Total Dollar

Usage1 5,000 1.50$ 7,500$ 2.9%2 1,500 8.00 12,000 4.7%3 10,000 10.50 105,000 41.2%4 6,000 2.00 12,000 4.7%5 7,500 0.50 3,750 1.5%6 6,000 13.60 81,600 32.0%7 5,000 0.75 3,750 1.5%8 4,500 1.25 5,625 2.2%9 7,000 2.50 17,500 6.9%10 3,000 2.00 6,000 2.4%

Total 254,725$ 100.0%

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ABC Chart For Previous Slide

0.0%

5.0%

10.0%

15.0%

20.0%

25.0%

30.0%

35.0%

40.0%

45.0%

3 6 9 2 4 1 10 8 5 7

Item No.

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0.0%

20.0%

40.0%

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80.0%

100.0%

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Percentage of Total Dollar Usage Cumulative Percentage

A B C

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Inventory Management Approaches A-items

– Track carefully (e.g. continuous review)– Sophisticated forecasting to assure

correct levels C-items

– Track less frequently (e.g. periodic review)

– Accept risks of too much or too little (depending on the item)

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Economic Order Quantity (EOQ)Model

Demand rate D is constant, recurring, and known Amount in inventory is known at all times Ordering (setup) cost S per order is fixed Lead time L is constant and known. Unit cost C is constant (no quantity discounts) Annual carrying cost is i time the average $ value of

the inventory No stockouts allowed. Material is ordered or produced in a lot or batch and

the lot is received all at once

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EOQ Lot Size Choice

There is a trade-off between lot size and inventory level.Frequent orders (small lot size): higher

ordering cost and lower holding cost.

Fewer orders (large lot size): lower ordering cost and higher holding cost.

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EOQ Inventory Order CycleEOQ Inventory Order Cycle

Demand rate

0 TimeLead time

Lead time

Order Placed

Order Placed

Order Received

Order Received

Inve

nto

ry

Lev

el

Reorder point, R

Order qty, Q

As Q increases, average inventory level increases, but number of orders placed decreases

ave = Q/2

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Total Cost of Inventory – EOQ Model

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Answer to Inventory Management Answer to Inventory Management Questions for EOQ ModelQuestions for EOQ Model

Keeping track of inventoryImplied that we track continuously

How much to order?Solve for when the derivative of total cost with respect

to Q = 0: -SD/Q^2 + iC/2 = 0Q = sqrt ( 2SD/iC)

When to order?Order when inventory falls to the “Reorder Point-level” R

so we will just sell the last item as the new order comes in:

R = DL

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Re-order Point ExampleRe-order Point Example

Demand = 10,000 yds/year

Lead time = L = 10 days

When inventory falls to R, we order so as not to run out before the new order comes in.

R = ?

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Re-order Point ExampleRe-order Point Example

Demand = 10,000 yds/year

Daily demand = 10,000 / 365 = 27.4 yds/day

Lead time = L = 10 days

R = D*L = (27.4)(10) = 274 yds

(usually can neglect issues of working days vs weekends, etc.)

Don’t forget to convert to consistent time units!

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EOQ SummaryEOQ Summary

How much to order?Q = sqrt(2DS/iC)

When to order?R = DL

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EOQ ExerciseEOQ Exercise Now you do it See Excel Spreadsheet:

Excel_Inv_Examples.xls, EOQ tab Compute the values of R and Q and

compare to the simulation Next see what happens when you have

volume discounts (EOQ w Discount Tab)

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EOQ ExampleEOQ ExampleUnit Cost C $0.45 /unitHolding cost factor i 25% /yearOrdering cost S $15.00 /orderDemand rate D 10000 units/yearLead time L 0.0192 year

Solutions:Re-order point R units (rounded)Q = sqrt(2SD/(iC)) units (rounded)