Question

PM computer services assembles customized personal computers from generic parts. Formed and operated by part-time UMass Lowell students Paulette Tyler and Maureen Becker, the company has steady growth since it started. The company assembles computers mostly at night, using part time students. Paulette and Maureen purchase generic computer parts in volume at a discount from a variety of sources whenever they see a good deal. Thus, they need a good forecast of demand for their computers so that they will know how many parts to purchase and stock. they have complied demand data for the last 12 months as reported below.

Month	Demand
January	32
February	35
March	37
April	35
May	42
June	47
July	49
August	42
September	53
October	48
November	52
December	55

Make forecasts for the sales using 4-period moving average method. Use the exponential smoothing method with α=0.2 as a smoothing constant to forecast the sales. Assume that the initial forecast for January is 33. Calculate the error and the absolute error for each forecast and summarize your computations in the table below. Compute the MAD as an accuracy measure for evaluating the performance of forecasting method then decide which forecasting method provides a better forecast? Explain Use the better of the two methods to forecast sales for January.

Answer 1

a. Compute four period moving average forecast using

F_m = (D_m-1 + D_m-2 + D_m-3 + D_m-4) ) / 4 where m is the period (month) number from 5 (May) to 12 (December)

F₅ = (35 + 37 + 35 + 32) / 4 = 139 / 4 = 35

F₆ = (42 + 35 + 37 + 35) / 4 = 149 / 4 = 37

F₇ = (47 + 42 + 35 + 37) / 4 = 161 / 4 = 40

F₈ = (49 + 47 + 42 + 35) / 4 = 173 / 4 = 43

F₉ = (42 + 49 + 47 + 42) / 4 = 180 / 4 = 45

F₁₀ = (53 + 42 + 49 + 47) / 4 = 191 / 4 = 48

F₁₁ = (48 + 53 + 42 + 49) / 4 = 192 / 4 = 48

F₁₂ = (52 + 48 + 53 + 42) / 4 = 195 / 4 = 49

All forecasts have been rounded to the nearest whole number since we are talking about computers forecast which can't be in fractions

b. Compute forecast using exponential smoothening method using

α = 0.2

F₁ = 33

F_m = F_m-1 + α * (D_m-1 - F_m-1) ; where m is the period (month) number from 2 (February) to 12 (December)

F₂ = 33 + 0.2 * (33 - 33) = 33

F₃ = 33 + 0.2 * (35 - 33) = 33

F₄ = 33 + 0.2 * (37 - 33) = 34

F₅ = 34 + 0.2 * (35 - 34) = 34

F₆ = 34 + 0.2 * (42 - 34) = 36

F₇ = 36 + 0.2 * (47 - 36) = 38

F₈ = 38 + 0.2 * (49 - 38) = 40

F₉ = 40 + 0.2 * (42 - 40) = 40

F₁₀ = 40 + 0.2 * (53 - 40) = 43

F₁₁ = 43 + 0.2 * (48 - 43) = 44

F₁₂ = 44 + 0.2 * (52 - 44) = 46

All forecasts have been rounded to the nearest whole number since we are talking about computers forecast which can't be in fractions

c. Compute error and absolute error

using four month moving average

E_m = D_m - F_m      where m is the period (month) number from 5 to 12

E₅ = 42 - 35 = 7

E₆ = 47 - 37 = 10

E₇ = 49 - 40 = 9

E₈ = 42 - 43 = -1

E₉ = 53 - 45 = 8

E₁₀ = 48 - 48 = 0

E₁₁ = 52 - 48 = 4

E₁₂ = 55 - 49 = 6

Absolute value of E_m is positive value of E_m

ABS(E₅) = 7

ABS(E₆) = 10

ABS(E₇) = 9

ABS(E₈) = 1

ABS(E₉) = 8

ABS(E₁₀) = 0

ABS(E₁₁) = 4

ABS(E₁₂) = 6

using Exponential Smoothening

E_m = D_m - F_m      where m is the period (month) number from 1 to 12

E₁ = 32 - 33 = -1

E₂ = 35 - 33 = 2

E₃ = 37 - 33 = 4

E₄ = 35 - 34 = 1

E₅ = 42 - 34 = 8

E₆ = 47 - 36 = 11

E₇ = 49 - 38 = 11

E₈ = 42 - 40 = 2

E₉ = 53 - 40 = 13

E₁₀ = 48 - 43 = 5

E₁₁ = 52 - 44 = 8

E₁₂ = 55 - 46 = 9

Absolute value of E_m is positive value of E_m

ABS(E₁) = 1

ABS(E₂) = 2

ABS(E₃) = 4

ABS(E₄) = 1

ABS(E₅) = 8

ABS(E₆) = 11

ABS(E₇) = 11

ABS(E₈) = 2

ABS(E₉) = 13

ABS(E₁₀) = 5

ABS(E₁₁) = 8

ABS(E₁₂) = 9

d. Compute MAD

using four month moving average

MAD = Σ ABS(E_m) / n   ; where m is the period (month) number from 5 to 12 ; n = number of periods(months)

        = (7 + 10 + 9 + 1 + 8 + 0 + 4 + 6) / 8 = 45 / 8

        = 5.63

MAD using four months moving average forecasting is 5.63

using Exponential Smoothening

MAD = Σ ABS(E_m) / n   ; where m is the period (month) number from 1 to 12 ; n = number of periods(months)

        = (1 + 2 + 4 + 1 + 8 + 11 + 11 + 2 + 13 + 5 + 8 + 9) / 12 = 75 / 12

        = 6.25

MAD using Exponential Smoothening forecasting is 6.25

MAD for Four months moving average is smaller compared to MAD of exponential smoothening forecast. Forecast using four months moving average has lesser deviation and thus is more accurate and better.

e. Forecast for January using four month moving average is

F_January = (55 + 52 + 48 + 53) / 4 = 208 / 4 = 52

Forecast for January using four month moving average method is 52

Summary of all computations