Forecasting 4 Forecasting 3 Demand Pooling Ardavan AsefVaziri

Forecasting - 4 Forecasting - 3 Demand Pooling Ardavan Asef-Vaziri Based on Operations management: Stevenson Chapter 7 Operations Management: Jacobs, Chase, and Aquilano Demand Forecasting Supply Chain Management: Chopra and Meindl in a Supply Chain Ardavan Asef-Vaziri 6/4/2009 Measures of Effectiveness 1

Forecasting - 4 Operations Management Session 16: Trend and Seasonality Ardavan Asef-Vaziri 6/4/2009 Measures of Effectiveness 2

Forecasting - 4 Previous Lecture v The importance of forecasting? v Forecast § Forecast is not a single number § Error measure MAD § Moving average § Exponential smoothing § Tradeoff: stability and responsiveness § Static Model for trend and Seasonality Ardavan Asef-Vaziri 6/4/2009 Measures of Effectiveness 3

Forecasting - 4 Today’s Lecture v An application of the exponential smoothing method § Risk-pooling effect again! v Trend forecast v Seasonal forecast Ardavan Asef-Vaziri 6/4/2009 Measures of Effectiveness 4

Forecasting - 4 Forecasts and Probability Distributions: How many to stock? A firm produces Red and Blue T-Shirts Ardavan Asef-Vaziri 6/4/2009 Measures of Effectiveness 5

Forecasting - 4 Forecasts and Probability Distributions ( = 0. 3) Month T-Shirt Demand Forecast January 909. 9 February 616. 7 909. 9 March 1073. 3 821. 94 April 1382. 9 897. 348 May 1359. 5 1043. 014 June 1519. 9 1137. 96 July 344. 9 1252. 542 August 929. 7 980. 2492 September 1328. 5 965. 0844 674 1074. 109 October November Ardavan Asef-Vaziri 6/4/2009 954. 0764 Measures of Effectiveness 6

Forecasting - 4 Forecasts and Probability Distributions v 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? v 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. v What is the probability that the actual demand will be larger than 1, 026? Ardavan Asef-Vaziri 6/4/2009 Measures of Effectiveness 7

Forecasting - 4 There is a Distribution Around the Forecasted Sale Standard Deviation of Error = 1. 25 MAD w Error is assumed to NORMALLY DISTRIBUTED with • A MEAN (AVERAGE) = 0 • STANDARD DEVIATION = 1. 25* MAD Ardavan Asef-Vaziri 6/4/2009 Measures of Effectiveness 8

Forecasting - 4 Forecasts and Probability Distributions ( = 0. 3) Month T-Shirt Demand Forecast AD January 909. 9 February 616. 7 909. 9 293. 2 March 1073. 3 821. 94 251. 36 April 1382. 9 897. 348 485. 552 May 1359. 5 1043. 014 316. 4864 June 1519. 9 1137. 96 381. 9405 July 344. 9 1252. 542 907. 6417 August 929. 7 980. 2492 50. 54916 September 1328. 5 965. 0844 363. 4156 674 1074. 109 400. 1091 October November Ardavan Asef-Vaziri 954. 0764 6/4/2009 Measures of Effectiveness 9

Forecasting - 4 How many to stock Suppose the company desires that the probability of not being able to meet demand is 2. 5% Look-up on normal table (show using book) Ardavan Asef-Vaziri 6/4/2009 Measures of Effectiveness 10

Forecasting - 4 How many to stock Note that MAD=383 in this example. Ardavan Asef-Vaziri 6/4/2009 Measures of Effectiveness 11

Forecasting - 4 The Forecast for a Blue Products ( = 0. 3) Ardavan Asef-Vaziri 6/4/2009 Measures of Effectiveness 12

Forecasting - 4 Blue Product Inventory Level v The stocking level, of the blue product, for period 11 is: 1148+1. 96*(1. 25*237)=1728 v Recall that: amt. stocked = forecast + 1. 96 x 1. 25 x. MAD implies the probability of not satisfying demand is P( demand > amt. stocked ) = 0. 025. Ardavan Asef-Vaziri 6/4/2009 Measures of Effectiveness 13

Forecasting - 4 Total Inventory Level v The total inventory for Red and Blue is: 1892 + 1728 = 3620 v P( Red demand > # of Red T-shirts stocked ) = 0. 025 P( Blue demand > # of Blue T-shirts stocked ) = 0. 025 Ardavan Asef-Vaziri 6/4/2009 Measures of Effectiveness 14

Forecasting - 4 Aggregate Forecasts v Can we more accurately forecast the combined demand? v Suppose we can make Gray Shirt and then dye the T-shirts either red or blue. v What is the Demand for Gray Shirts? v 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 Ardavan Asef-Vaziri 6/4/2009 Measures of Effectiveness 15

Forecasting - 4 Forecast for the Aggregate Demand Inventory of Gray = 2102 + 1. 96*1. 25*614 = 3603 Ardavan Asef-Vaziri 6/4/2009 Measures of Effectiveness 16

Forecasting - 4 Aggregate Demand Forecast Conclusions v By stocking 3603 Gray T-shirts, we ensure P( T-shirt demand > # stocked ) = 0. 025 v Otherwise, we needed to stock 1892 blue T-shirts and 1728 red T-shirts for a combined number of 1892+1728 = 3620 T-shirts to ensure that P( red T-shirt demand > # red shirts stocked) = P( blue T-shirt demand > # blue shirts stocked) = 0. 025 v 3603 < 3620 … we need to stock less T-shirts to ensure a given stockout probability (2. 5% in this example) when we have an aggregate forecast. Ardavan Asef-Vaziri 6/4/2009 Measures of Effectiveness 17