1 Forecasting for Operations Dr. Everette S. Gardner, Jr.

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Forecasting for OperationsDr. Everette S. Gardner, Jr.

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Forecasting for operations Why we should forecast with models The importance of forecasting Exponential smoothing in a nutshell Case studies

1. Customer service: U.S. Navy distribution system

2. Inventory investment: Mfg. of snack foods

3. Purchasing workload: Mfg. of water filtration systems

Recommendations: How to improve forecast accuracy

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Paper folding forecast

A sheet of notebook paper is 1/100 of an inch thick.

I fold the paper 40 times.

How thick will it be after 40 folds?

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Fold Inches MilesStart 0.01

1 0.02

5 0.32

10 10.24

20 10,485.76 0.17

25 335,544.32 5.30

30 10,737,418.24 169.47

35 343,597,383.68 5,422.94

40 10,995,116,277.76 173,534.03

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The Importance of Forecasting

Forecasts determine: Master schedules Economic order quantities Safety stocks JIT requirements to both internal and external

suppliers

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The Importance of Forecasting (cont.) Better forecast accuracy always cuts inventory

investment. Example:

Forecast accuracy is measured by the standard deviation of the forecast error

Safety stocks are usually set at 3 times the standard deviation

If the standard deviation is cut by $1, safety stocks are cut by $3

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Exponential smoothing methods Forecasts are based on weighted moving

averages of Level Trend Seasonality

Averages give more weight to recent data

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Origins of exponential smoothing Simple exponential smoothing –

The thermostat model Error = Actual data – forecast New forecast = Old Forecast + (Weight x Error)

Invented by Navy operations analyst Robert G. Brown in 1944

First application: Using sonar data to forecast the tracks of Japanese submarines

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Exponential smoothing at work

“A depth charge has a magnificent laxative effect on a submariner.”

Lt. Sheldon H. Kinney, Commander, USS Bronstein (DE 189)

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Forecast profiles from exponential smoothing

Additive Multiplicative

Nonseasonal Seasonality Seasonality

Constant Level

Linear Trend

Exponential

Trend

Damped Trend

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35

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Automatic Forecasting with the damped trend

In constant-level data, the forecasts emulate simple exponential smoothing:

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20

25

30

35

40

45

50

55

60

In data with consistent growth and little noise, the forecasts usually follow a linear trend:

Automatic Forecasting with the damped trend

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Automatic Forecasting with the damped trend

When the trend is erratic, the forecasts are damped:

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25

30

35

40

45

50 Saturation level

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Automatic Forecasting with the damped trend

The damping effect increases with noise in the data:

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25

30

35

40

45

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Saturation level

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Case 1: U.S. Navy distribution system Scope

50,000 line items stocked at 11 supply centers 240,000 demand series $425 million inventory investment

Decision Rules Simple exponential smoothing Replenishment by economic order quantity Safety stocks set to minimize backorder delay time

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Problems Customer pressure to reduce backorder delay No additional inventory budget available

Characteristics of demand series 90% nonseasonal Frequent outliers and jump shifts in level Trends, usually erratic, in most series

Solution Automatic forecasting with the damped trend

U.S. Navy distribution system (cont.)

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U.S. Navy distribution system (cont.) Research design 1

Random sample (5,000 items) selected Models tested

Random walk benchmark Simple, linear-trend, and damped-trend smoothing

Error measure Mean absolute percentage error (MAPE)

Results 1 Damped trend gave the best MAPE Impact of backorder delay unknown

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U.S. Navy distribution system (cont.) Research design 2

The mean absolute percentage error was discarded Monthly inventory values were computed:

EOQ Standard deviation of forecast error Safety stock Average backorder delay

Results 2 Damped trend gave the best backorder delay Management was not convinced

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U.S. Navy distribution system (cont.) Research design 3

6-year simulation of inventory performance, using actual daily demand and lead time data

Stock levels updated after each transaction Forecasts updated monthly

Results 3 Again, damped trend was the clear winner Results very similar to steady-state predictions Backorder delay reduced by 6 days (19%) with no

additional inventory investment

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Average delay in filling backordersU.S. Navy distribution system

Damped trend

Simple smoothing

Linear trend

Random walk

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30

35

40

45

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370 380 390 400 410 420 430

Inventory investment (millions)

Ba

ck

ord

er

da

ys

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Case 2: Snack-food manufacturer Scope

82 snack foods Food stocks managed by commodity traders Packaging materials managed with subjective

forecasts and inventory levels

Problems Excess stocks of packaging materials Impossible to predict inventory on the balance sheet

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11-Oz. corn chipsMonthly packaging inventory and usage

Actual Inventory from

subjective forecasts

Monthly Usage

Month

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Snack-food manufacturer (cont.) Solutions

Automatic forecasting with the damped trend Replenishment by economic order quantity Safety stocks set to meet target probability of

shortage

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Damped-trend performance11-oz. corn chips

$200,000

$250,000

$300,000

$350,000

$400,000

$450,000

$500,000

Actual

ForecastOutlier

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Investment analysis: 11-oz. corn chipsForecast annual usage $4,138,770

Economic order quantity $318,367

Standard deviation of forecast errors $34,140

Nbr. shortages

per 1,000 Probability Safety Order Maximum

order cycles of shortage stock quantity investment

100.0000 0.1000 $43,758 $318,367 $362,12550.0000 0.0500 $56,167 $318,367 $374,5341.0000 0.0010 $105,510 $318,367 $423,8770.0100 0.0000 $145,601 $318,367 $463,9680.0001 0.0000 $177,496 $318,367 $495,863

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Safety stocks vs. shortages11-oz. corn chips

$0

$20,000

$40,000

$60,000

$80,000

$100,000

$120,000

$140,000

$160,000

$180,000

$200,000

0 10 20 30 40 50 60 70 80 90 100

Shortages per 1,000 order cycles

Saf

ety

stoc

k

Target

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Safety stocks vs. forecast errors11-oz. corn chips

($200,000)

($150,000)

($100,000)

($50,000)

$0

$50,000

$100,000

$150,000

$200,000Safety stock

Forecast errors

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11-Oz. corn chipsTarget vs. actual packaging inventory

Actual Inventory from

subjective forecasts

Month

$0

$500,000

$1,000,000

$1,500,000

$2,000,000

$2,500,000

Target maximum inventory based on damped trend

Actual Inventory from

subjective forecasts

Monthly Usage

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How to forecast regional demand Forecast total units with the damped trend Forecast regional percentages with simple

exponential smoothing

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Damped-trend performance11-oz. corn chips

$200,000

$250,000

$300,000

$350,000

$400,000

$450,000

$500,000

Actual

ForecastOutlier

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Regional sales percentages: Corn chips

0%

10%

20%

30%

40%

50%

Mar Jun Sep Dec Mar Jun Sep Dec

South

West

North

East

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Case 3: Water filtration systems company Scope

Annual sales of $15 million Inventory of $5.8 million, with 24,000 stock records

Inventory system Reorder monthly to maintain 3 months of stock Numerous subjective adjustments

Forecasting system 6-month moving average No update to average if demand = 0 Numerous subjective adjustments

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Problems Purchasing and receiving workload

70,000 orders per year

Forecasting Total forecasts on the stock records = $28 million

Annual sales = $15 million

Frequent stockouts due to forecast errors

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Solutions Develop a decision rule for what to stock Implement the damped trend Use the forecasts to do an ABC classification Replace monthly orders with:

Class A JIT Class B EOQ/safety stock Class C Annual buys

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What to stock?

Cost to stock Average inventory balance x holding rate +

Number of stock orders x transportation cost

Cost to not stock Number of customer orders x drop-ship transportation cost

Note: Transportation costs for not stocking may be bothin-and out bound, depending on whether we choose todrop-ship from the vendor

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Water filtration company: Inventory status

4,202 with inadequate

demand to stock18%

2,928 substitute items13%

2,200 obsolete9%

7,526 with no hits in 12 months

33%

6,336 active items27%

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ABC classification based ondamped-trend forecasts for the next yearClass Sales forecast System Items Dollars

A > $36,000 JIT 3% 75%

B $600 - $35,999 EOQ 49% 18%

C < $600 Annual buy 48% 7%

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Inventory control system recommendations

Control SystemInventory

ClassProduction Schedule

Lead-time Behavior

JIT A, B Level Certain

MRP A, B Variable Reliable

EOQ / Safety stock A, B Variable Variable

Annual buy C Any Any

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Annual purchasing workloadTotal savings = 58,000 orders (76%)

JIT

EOQ

JIT

EOQ

Annual buys

0

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000

A B C

Monthly orderingABC system

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Inventory investmentTotal savings = $591,000 (15%)

JIT

EOQ

JIT

EOQ

Annual buys

0

500,000

1,000,000

1,500,000

2,000,000

2,500,000

3,000,000

A B C

Monthly orderingABC system

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Recommendations Benchmark the forecasts with a random walk Judge forecast accuracy in operational terms

Customer service measures Average backorder delay time Percent of time in stock Probability of stockout Average dollars backordered

Inventory investment on the balance sheet Purchasing workload or production setups

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www.bauer.uh.edu/gardner