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13 In our discussion of Winter's method, a monthly seasonality of (say) 0.80 for January means that during January, air conditioner sales are expected to be 80% of the sales during an average month. An alternative approach to modeling seasonality is to let the seasonality factor for each month represent how far above average air conditioner sales will be during the current month. For instance, if sJan - 50, then air conditioner sales during January are expected to be 50 less than air conditioner sales during an average month. If sjuly = 90, then air conditioner sales during July are expected to be 90 more than air conditioner sales during an average month. Let s, = the seasonality for month t after month t demand is observed L, = the estimate of base after month t demand is observed T, = the estimate of trend after month i demand is observed Then the Winter's method equations given in the text are modified to be as follows (* indicates multiplication): L, = a * (I) + (1 – a) * (L--1 + T,-1) T, = B * (L, – L,-1) + (1 – B) * T,-1 s, = y * (II ) + (1 – y) * s1-12 a What should I and II be? b Suppose that month 13 is a January, L12 = 30, T12 = -3, s1 = -50, and s2 = -20. Let a = y = B = 0.5. Suppose 12 air conditioners are sold during month 13. At the end of month 13, what is the predic- tion for air conditioner sales during month 14?

13 In our discussion of Winter's method, a monthly seasonality of (say) 0.80 for January means that during January, air conditioner sales are expected to be 80% of the sales during an average month. An alternative approach to modeling seasonality is to let the seasonality factor for each month represent how far above average air conditioner sales will be during the current month. For instance, if sJan - 50, then air conditioner sales during January are expected to be 50 less than air conditioner sales during an average month. If sjuly = 90, then air conditioner sales during July are expected to be 90 more than air conditioner sales during an average month. Let s, = the seasonality for month t after month t demand is observed L, = the estimate of base after month t demand is observed T, = the estimate of trend after month i demand is observed Then the Winter's method equations given in the text are modified to be as follows (* indicates multiplication): L, = a * (I) + (1 – a) * (L--1 + T,-1) T, = B * (L, – L,-1) + (1 – B) * T,-1 s, = y * (II ) + (1 – y) * s1-12 a What should I and II be? b Suppose that month 13 is a January, L12 = 30, T12 = -3, s1 = -50, and s2 = -20. Let a = y = B = 0.5. Suppose 12 air conditioners are sold during month 13. At the end of month 13, what is the predic- tion for air conditioner sales during month 14?

Operations Research : Applications and Algorithms
Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter24: Forecasting Models
Section24.4: Winter’s Method: Exponential Smoothing With Seasonality
Problem 13P
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13 In our discussion of Winter's method, a monthly seasonality of (say) 0.80 for January means that during January, air conditioner sales are expected to be 80% of the sales during an average month. An alternative approach to modeling seasonality is to let the seasonality factor for each month represent how far above average air conditioner sales will be during the current month. For instance, if sJan - 50, then air conditioner sales during January are expected to be 50 less than air conditioner sales during an average month. If sjuly = 90, then air conditioner sales during July are expected to be 90 more than air conditioner sales during an average month. Let s, = the seasonality for month t after month t demand is observed L, = the estimate of base after month t demand is observed T, = the estimate of trend after month i demand is observed Then the Winter's method equations given in the text are modified to be as follows (* indicates multiplication): L, = a * (I) + (1 – a) * (L--1 + T,-1) T, = B * (L, – L,-1) + (1 – B) * T,-1 s, = y * (II ) + (1 – y) * s1-12 a What should I and II be? b Suppose that month 13 is a January, L12 = 30, T12 = -3, s1 = -50, and s2 = -20. Let a = y = B = 0.5. Suppose 12 air conditioners are sold during month 13. At the end of month 13, what is the predic- tion for air conditioner sales during month 14?
Transcribed Image Text:13 In our discussion of Winter's method, a monthly seasonality of (say) 0.80 for January means that during January, air conditioner sales are expected to be 80% of the sales during an average month. An alternative approach to modeling seasonality is to let the seasonality factor for each month represent how far above average air conditioner sales will be during the current month. For instance, if sJan - 50, then air conditioner sales during January are expected to be 50 less than air conditioner sales during an average month. If sjuly = 90, then air conditioner sales during July are expected to be 90 more than air conditioner sales during an average month. Let s, = the seasonality for month t after month t demand is observed L, = the estimate of base after month t demand is observed T, = the estimate of trend after month i demand is observed Then the Winter's method equations given in the text are modified to be as follows (* indicates multiplication): L, = a * (I) + (1 – a) * (L--1 + T,-1) T, = B * (L, – L,-1) + (1 – B) * T,-1 s, = y * (II ) + (1 – y) * s1-12 a What should I and II be? b Suppose that month 13 is a January, L12 = 30, T12 = -3, s1 = -50, and s2 = -20. Let a = y = B = 0.5. Suppose 12 air conditioners are sold during month 13. At the end of month 13, what is the predic- tion for air conditioner sales during month 14?
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