Question

Quarter	Gallons of Chemical Solution
1	550
2	490
3	510
4	590
5	595
6	550
7	565
8	610
9	635
10	565
11	572
12	655

Using the data conduct the following:

a. Starting with a forecast of 550 for quarter 1, forecast the demand for quarter 13 using exponential smoothing with α = 0.6. Plot the actual data and the exponentially smoothed forecasts on the same graph. SHOW FORMULA

b. Forecast demand from quarter 2 to quarter 13 using the naïve approach. Plot your forecasts on the graph developed in part a. SHOW FORMULA

c. Looking at the graph in part b, which forecasting method seems to be more appropriate?

d. Determine the MAD (disregard quarter 1 from computations) to confirm your answer in part c. SHOW FORMULA IF USED.

Answer 1

EXPONENTIAL SMOOTHING

F(T) = F(T-1) + (ALPHA * (A(T-1) - F(T-1)))

FORECAST 2 = 550 + (0.6 * (550 - 550)) = 550

FORECAST 3 = 550 + (0.6 * (490 - 550)) = 514

FORECAST 4 = 514 + (0.6 * (510 - 514)) = 512

FORECAST 5 = 512 + (0.6 * (590 - 512)) = 559

FORECAST 6 = 559 + (0.6 * (595 - 559)) = 581

FORECAST 7 = 581 + (0.6 * (550 - 581)) = 562

FORECAST 8 = 562 + (0.6 * (565 - 562)) = 564

FORECAST 9 = 564 + (0.6 * (610 - 564)) = 592

FORECAST 10 = 592 + (0.6 * (635 - 592)) = 618

FORECAST 11 = 618 + (0.6 * (565 - 618)) = 586

FORECAST 12 = 586 + (0.6 * (572 - 586)) = 578

FORECAST 13 = 578 + (0.6 * (655 - 578)) = 624

MAD

PERIOD	ACTUAL DEMAND	FORECAST	DEVIATIONS	ABSOLUTE DEVIATION
1	550
2	490	550	-60	60
3	510	514	-4	4
4	590	512	78	78
5	595	559	36	36
6	550	581	-31	31
7	565	562	3	3
8	610	564	46	46
9	635	592	43	43
10	565	618	-53	53
11	572	586	-14	14
12	655	578	77	77
SIGMA				445

MAD = SIGMA(ABS DEV) / N

MAD = 445 / 11 = 40.45

NAIVE FORECAST

FORECAST = DEMAND FOR PREVIOUS PERIOD

PERIOD	DEMAND	NAIVE FORECAST
1	550
2	490	550
3	510	490
4	590	510
5	595	590
6	550	595
7	565	550
8	610	565
9	635	610
10	565	635
11	572	565
12	655	572
13		655

MAD

PERIOD	ACTUAL DEMAND	FORECAST	DEVIATIONS	ABSOLUTE DEVIATION
1	550
2	490	550	-60	60
3	510	490	20	20
4	590	510	80	80
5	595	590	5	5
6	550	595	-45	45
7	565	550	15	15
8	610	565	45	45
9	635	610	25	25
10	565	635	-70	70
11	572	565	7	7
12	655	572	83	83
SIGMA				455

MAD = 455 / 11 = 41.36

BASED ON THE MAD, THE EXPONENTIAL SMOOTHING FORECAST IS BETTER.