forecasting 6 pooldemand

8/12/2019 Forecasting 6 PoolDemand

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Measures of Ef fect iveness 1Ard avan As ef-Vaziri 6/4/2009

Forecast ing - 4

Chapter 7

Demand Forecasting

in a Supply Chain

Forecasting - 3Demand Pooling

Ardavan Asef-Vaziri

Based on

Operations management: Stevenson

Operations Management: Jacobs, Chase, and AquilanoSupply Chain Management: Chopra and Meindl


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Operations Management

Session 16: Trend and Seasonality


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Previous Lecture

The importance of forecasting?

Forecast

Forecast is not a single number

Error measure MAD

Moving average

Exponential smoothing Tradeoff: stability and responsiveness

Static Model for trend and Seasonality


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Forecasts and Probability Distributions: How many

to stock?

A firm produces Red and Blue T-Shirts

Month/demand Red Shirts Blue Shirts

January 909.9 1185.0

February 616.7 546.2

March 1073.3 1229.5

April 1382.9 1248.7

May 1359.5 1337.9

June 1519.9 1539.6

July 344.9 1300.8

AugustSeptember

October


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Forecasts and Probability Distributions (= 0.3)

Month T-Shirt Demand ForecastJanuary 909.9February 616.7 909.9March 1073.3 821.94

April 1382.9 897.348May 1359.5 1043.014June 1519.9 1137.96July 344.9 1252.542August 929.7 980.2492September 1328.5 965.0844October 674 1074.109November 954.0764

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Forecasts and Probability Distributions

Suppose the company stocks 954 T-shirts, the forecasted

number. What is the probability the company will have a

stockout, that is, that there will not be enough T-shirts to satisfy

demand?

The company does not want to have unsatisfied demand, as that

would be lost revenue. So the company overstocks. Suppose

the company stocks 1,026 units.

What is the probability that the actual demand will be larger than1,026?

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There is a Distribution Around the Forecasted Sale

Standard Deviation of Error = 1.25 MAD

Error is assumed to NORMALLY DISTRIBUTED with

A MEAN (AVERAGE) = 0

STANDARD DEVIATION = 1.25* MAD

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9/17Measures of Ef fect iveness 9Ard avan As ef-Vaziri 6/4/2009

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Forecasts and Probability Distributions (= 0.3)

Month T-Shirt Demand Forecast ADJanuary 909.9February 616.7 909.9 293.2March 1073.3 821.94 251.36April 1382.9 897.348 485.552May 1359.5 1043.014 316.4864June 1519.9 1137.96 381.9405July 344.9 1252.542 907.6417August 929.7 980.2492 50.54916September 1328.5 965.0844 363.4156October 674 1074.109 400.1091November 954.0764

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How many to stock

96.1MAD1.25

954-stockedamt.when

025.0

MAD1.25

954-stockedamt.N(0,1)P

stocked)amt.MAD)N(954,1.25(stocked)amt.demandNov.(

P

P

Suppose the company desires that the probability ofnot being able to meet demand is 2.5%

Look-up on normal table(show using book)

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How many to stock

1892954MAD1.251.96stockedAmt.

implies

96.1MAD1.25

549stockedAmt.

Note that MAD=383 in this example.

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The Forecast for a Blue Products (= 0.3)

January 1185.0

February 546.2 1185.0 638.7429

March 1229.5 993.3 236.1592

April 1248.7 1064.2 184.5132

May 1337.9 1119.5 218.4141

June 1539.6 1185.1 354.516

July 1300.8 1291.4 9.349969

August 1084.4 1294.2 209.8464

Septembe 1211.8 1231.3 19.48862October 965.6 1225.4 259.8598

1147.5 236.7656

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Blue Product Inventory Level

The stocking level, of the blue product, for period

11 is:

1148+1.96*(1.25*237)=1728Recall that:

amt. stocked = forecast + 1.96x1.25xMAD

implies the probability of not satisfying demand is

P( demand > amt. stocked ) = 0.025.

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Total Inventory Level

The total inventory for Red and Blue is:

1892 + 1728 = 3620

P( Red demand > # of Red T-shirts stocked ) = 0.025

P( Blue demand > # of Blue T-shirts stocked ) = 0.025

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Aggregate Forecasts

Can we more accurately forecast the combined demand?

Suppose we can make Gray Shirt and then dye the T-shirtseither red or blue.

What is the Demand for Gray Shirts?

We look at the sum of the demands in the past We forecast the demand for the two products combined

We compute the MAD for the aggregate forecast

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Forecast for the Aggregate Demand

Month/demand Red Shirts

January 909.9

February 616.7

March 1073.3

April 1382.9May 1359.5

June 1519.9

July 344.9

August 929.7

September 1328.5

October 674.0November

Blue Shirts

1185.0

546.2

1229.5

1248.71337.9

1539.6

1300.8

1084.4

1211.8

965.6

Gray Shirts Forecast AD

2094.9

1162.9 2094.9 931.9782

2302.8 1815.292 487.4767

2631.6 1961.535 670.10022697.5 2162.565 534.888

3059.5 2323.031 736.4826

1645.7 2543.976 898.2896

2014.1 2274.489 260.3722

2540.3 2196.378 343.9045

1639.5 2299.549 660.0016

2101.549 613.722

Inventory of Gray = 2102 + 1.96*1.25*614 = 3603

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Aggregate Demand Forecast Conclusions

By stocking 3603 Gray T-shirts, we ensure

P( T-shirt demand > # stocked ) = 0.025

Otherwise, we needed to stock 1892 blue T-shirts

and 1728 red T-shirts for a combined number of1892+1728 = 3620 T-shirts to ensure that

P( red T-shirt demand > # red shirts stocked)

= P( blue T-shirt demand > # blue shirts stocked)

= 0.0253603 < 3620 we need to stock less T-shirts to

ensure a given stockout probability (2.5% in thisexample) when we have an aggregate forecast.

forecasting 6 pooldemand

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