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INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke
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INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Mar 29, 2015

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Page 1: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

INVENTORY MANAGEMENT

Operations Management

Dr. Ron Tibben-Lembke

Page 2: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Purposes of Inventory

Meet anticipated demand Demand variability Supply variability

Decouple production & distribution permits constant production quantities

Take advantage of quantity discounts Hedge against price increases Protect against shortages

Page 3: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

2006 13.81 1857 24.0% 446 801 58 1305 9.92007

Page 4: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

US Inventory, GDP ($B)

-

2,000

4,000

6,000

8,000

10,000

12,000

14,000

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

Business Inventories US GDP

Page 5: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

US Inventories as % of GDP

0.0%

5.0%

10.0%

15.0%

20.0%

25.0%

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

Year

% o

f G

DP

Source: CSCMP, Bureau of Economic Analysis

Page 6: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Two Questions

Two main Inventory Questions: How much to buy? When is it time to buy?Also:Which products to buy?From whom?

Page 7: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Types of Inventory

Raw Materials Subcomponents Work in progress (WIP) Finished products Defectives Returns

Page 8: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Inventory Costs

What costs do we experience because we carry inventory?

Page 9: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Inventory Costs

Costs associated with inventory: Cost of the products Cost of ordering Cost of hanging onto it Cost of having too much / disposal Cost of not having enough (shortage)

Page 10: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Shrinkage Costs

How much is stolen? 2% for discount, dept. stores, hardware,

convenience, sporting goods 3% for toys & hobbies 1.5% for all else

Where does the missing stuff go? Employees: 44.5% Shoplifters: 32.7% Administrative / paperwork error: 17.5% Vendor fraud: 5.1%

Page 11: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Inventory Holding Costs

Category % of ValueHousing (building) cost 4%Material handling 3%Labor cost 3%Opportunity/investment 9%Pilferage/scrap/obsolescence 2%

Total Holding Cost 21%

Page 12: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Inventory Models

Fixed order quantity models How much always same, when changes Economic order quantity Production order quantity Quantity discount

Fixed order period models How much changes, when always same

Page 13: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Economic Order Quantity

Assumptions Demand rate is known and constant No order lead time Shortages are not allowed Costs:

S - setup cost per order H - holding cost per unit time

Page 14: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

EOQ

Time

Inventory Level

Q*OptimalOrderQuantity

Decrease Due toConstant Demand

Page 15: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

EOQ

Time

Inventory Level

Q*OptimalOrderQuantity

InstantaneousReceipt of OptimalOrder Quantity

Page 16: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

EOQ

Time

Inventory Level

Q*

Lead Time

ReorderPoint(ROP)

Page 17: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

EOQ

Time

Inventory Level

Q*

Lead Time

ReorderPoint(ROP)

Average Inventory Q/2

Page 18: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Total Costs

Average Inventory = Q/2 Annual Holding costs = H * Q/2 # Orders per year = D / Q Annual Ordering Costs = S * D/Q Cost of Goods = D * C Annual Total Costs = Holding + Ordering +

CoG

DCQ

DS

QHQTC **

2*)(

Page 19: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

How Much to Order?

Annual Cost

Order Quantity

Holding Cost= H * Q/2

Page 20: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

How Much to Order?

Annual Cost

Order Quantity

Holding Cost= H * Q/2

Ordering Cost= S * D/Q

Page 21: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

How Much to Order?

Annual Cost

Order Quantity

Total Cost= Holding + Ordering

Page 22: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

How Much to Order?

Annual Cost

Order Quantity

Total Cost= Holding + Ordering

Optimal Q

Page 23: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Optimal Quantity

Total Costs =

2*

2 Q

DS

H

Take derivative with respect to Q =

Solve for Q:

22 Q

DSH

Set equal to zero0

H

DSQ

22 H

DSQ

2

DCQ

DS

QH **

2*

Page 24: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Adding Lead Time

Use same order size

Order before inventory depleted R = * L where:

= average demand rate (per day) L = lead time (in days) both in same time period (wks, months,

etc.)

H

DSQ

2

dd

Page 25: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

A Question:

If the EOQ is based on so many horrible assumptions that are never really true, why is it the most commonly used ordering policy? Profit function is very shallow Even if conditions don’t hold perfectly,

profits are close to optimal Estimated parameters will not throw you off

very far

Page 26: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Quantity Discounts

How does this all change if price changes depending on order size?

Holding cost as function of cost: H = I * C

Explicitly consider price:

Q2DS

I C

Page 27: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Discount Example

D = 10,000 S = $20 I = 20%

Price Quantity EOQc = 5.00 Q < 500

6334.50 501-999

6663.90 Q >= 1000 716

Page 28: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Discount Pricing

Total Cost

Order Size500 1,000

Price 1 Price 2 Price 3

X 633

X 666

X 716

Page 29: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Discount Pricing

Total Cost

Order Size500 1,000

Price 1 Price 2 Price 3

X 633

X 666

X 716

Page 30: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Discount Example

Order 666 at a time:Hold 666/2 * 4.50 * 0.2= $299.70Order 10,000/666 * 20 = $300.00Mat’l 10,000*4.50 = $45,000.00

45,599.70

Order 1,000 at a time:Hold 1,000/2 * 3.90 * 0.2= $390.00Order 10,000/1,000 * 20 =$200.00Mat’l 10,000*3.90 = $39,000.00

39,590.00

Page 31: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Discount Model

1. Compute EOQ for next cheapest price2. Is EOQ feasible? (is EOQ in range?)

If EOQ is too small, use lowest possible Q to get price.

3. Compute total cost for this quantity4. Repeat until EOQ is feasible or too big.5. Select quantity/price with lowest total

cost.

Page 32: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

INVENTORY MANAGEMENT-- RANDOM DEMAND

Page 33: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Random Demand

Don’t know how many we will sell Sales will differ by period Average always remains the same Standard deviation remains constant

Page 34: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Impact of Random Demand

How would our policies change? How would our order quantity change? How would our reorder point change?

Page 35: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Mac’s Decision

How many papers to buy? Average = 90, st dev = 10 Cost = 0.20, Sales Price = 0.50 Salvage = 0.00 Cost of overestimating Demand, CO

CO = 0.20 - 0.00 = 0.20 Cost of Underestimating Demand, CU

CU = 0.50 - 0.20 = 0.30

Page 36: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Optimal Policy

G(x) = Probability demand <= xOptimal quantity:

Mac: G(x) = 0.3 / (0.2 + 0.3) = 0.6From standard normal table, z = 0.253=Normsinv(0.6) = 0.253Q* = avg + zs = 90+ 2.53*10 = 90 +2.53 =

93

uo

u

CC

C

Q)Pr(D

Page 37: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Optimal Policy

If units are discrete, when in doubt, round up

If u units are on hand, order Q - u units Model is called “newsboy problem,”

newspaper purchasing decision By time realize sales are good, no time to

order more By time realize sales are bad, too late,

you’re stuck Similar to the problem of # of Earth Day

shirts to make, lbs. of Valentine’s candy to buy, green beer, Christmas trees, toys for Christmas, etc., etc.

Page 38: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Random Demand – Fixed Order Quantity

If we want to satisfy all of the demand 95% of the time, how many standard deviations above the mean should the inventory level be?

Page 39: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Probabilistic Models

Safety stock = xm

From statistics,

From normal table z.95 = 1.65

Safety stock = zsL= 1.65*10 = 16.5

R = m + Safety Stock

Therefore, z = Safety stock & Safety stock = zsLsL

=350+16.5 = 366.5 ≈ 367

L

xz

Page 40: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Random Example

What should our reorder point be? demand over the lead time is 50 units, with standard deviation of 20 want to satisfy all demand 90% of the time (i.e., 90% chance we do not run out)

To satisfy 90% of the demand, z = 1.28 Safety stock = zσL= 1.28 * 20 = 25.6 R = 50 + 25.6 = 75.6

Page 41: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

St Dev Over Lead Time

What if we only know the average daily demand, and the standard deviation of daily demand? Lead time = 4 days, daily demand = 10, standard deviation = 5,

What should our reorder point be, if z = 3?

Page 42: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

St Dev Over LT

If the average each day is 10, and the lead time is 4 days, then the average demand over the lead time must be 40.

What is the standard deviation of demand over the lead time?

Std. Dev. ≠ 5 * 4

404*10* Ld

Page 43: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

St Dev Over Lead Time

Standard deviation of demand =

R = 40 + 3 * 10 = 70

daydaysL L

1054

daydaysL LzLdzLdR **

Page 44: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Service Level Criteria

Type I: specify probability that you do not run out during the lead time Probability that 100% of customers go

home happy Type II: proportion of demands met from

stock Percentage that go home happy, on

average Fill Rate: easier to observe, is commonly

used G(z)= expected value of shortage, given z.

Not frequently listed in tables

RateFillQ

zGL

1)(

Page 45: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Two Types of Service

Cycle DemandStock-Outs

1 1800

2 750

3 23545

4 1400

5 1800

6 20010

7 1500

8 900

9 160010 400

Sum 1,45055

Type I: 8 of 10 periods80% service

Type II:1,395 / 1,450 =

96%

Page 46: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

FIXED-TIME PERIOD MODELS

Page 47: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Fixed-Time Period Model

Every T periods, we look at inventory on hand and place an order

Lead time still is L. Order quantity will be different,

depending on demand

Page 48: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Fixed-Time Period Model: When to Order?

Time

Inventory Level Target maximum

Period

Page 49: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Fixed-Time Period Model: : When to Order?

Time

Inventory Level Target maximum

PeriodPeriod

Page 50: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Fixed-Time Period Model:When to Order?

Time

Inventory Level Target maximum

PeriodPeriod

Page 51: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Fixed-Time Period Model: When to Order?

Time

Inventory Level Target maximum

Period PeriodPeriod

Page 52: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Fixed-Time Period Model: When to Order?

Time

Inventory Level Target maximum

Period PeriodPeriod

Page 53: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Fixed-Time Period Model: When to Order?

Time

Inventory Level Target maximum

Period PeriodPeriod

Page 54: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Fixed Order Period

Standard deviation of demand over T+L =

T = Review period length (in days) σ = std dev per day Order quantity (12.11) =

IzLTdq LT )(

LTLT

Page 55: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Inventory Recordkeeping

Two ways to order inventory: Keep track of how many delivered, sold Go out and count it every so oftenIf keeping records, still need to double-check Annual physical inventory, or Cycle Counting

Page 56: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Cycle Counting

Physically counting a sample of total inventory on a regular basis

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

Advantages Eliminates annual shut-down for physical

inventory count Improves inventory accuracy Allows causes of errors to be identified

Page 57: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Fixed-Period Model

Answers how much to order Orders placed at fixed intervals

Inventory brought up to target amount Amount ordered varies

No continuous inventory count Possibility of stockout between intervals

Useful when vendors visit routinely Example: P&G rep. calls every 2 weeks

Page 58: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

ABC Analysis

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

Page 59: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

Classifying Items as ABC

0

20

40

60

80

100

0 50 100 150

% of Inventory Items

% Annual $ Volume

A

B C

Items %$Vol %ItemsA 80 15B 15 30C 5 55

Page 60: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

ABC Classification Solution

Stock # Vol. Cost $ Vol. % ABC

206 26,000 $ 36 $936,000 71.1

105 200 600 120,000 9.1

019 2,000 55 110,000 8.4

144 20,000 4 80,000 6.1

207 7,000 10 70,000 5.3

Total 1,316,000 100.0

Page 61: INVENTORY MANAGEMENT Operations Management Dr. Ron Tibben-Lembke.

ABC Classification Solution

Stock # Vol. Cost $ Vol. % ABC

206 26,000 $ 36 $936,000 71.1 A

105 200 600 120,000 9.1 A

019 2,000 55 110,000 8.4 B

144 20,000 4 80,000 6.1 B

207 7,000 10 70,000 5.3 C

Total 1,316,000 100.0