Question

The Actual demands in the last 4 periods are given. Which of the following statement is not true?

Period	Ai	Weight
1	10
2	20	0.3
3	30	0.3
4	20	0.4

	A.	F5=23.33 using Moving Average and n=3
	B.	F5=20 using Naive Approach
	C.	When the business environment is more dynamic, we tend to choose smaller smoothing constant value.
	D.	F5=23 using Weighted Moving Average when n=3 and the weight is 0.4, 0.3, and 0.3 for period 4, 3, and 2 with respectively.

The Actual Demand in the past 5 periods is given.  Let F1=100 and Smoothing Constant equals to 0.8. Which of the following statement is not true?

Period	Ai
1	120
2	130
3	100
4	150
5	170

	A.	F3=127.20
	B.	F2=116.00
	C.	F6=189.58
	D.	F4=105.44

The actual demand and forecast in the last 8periods are given. Which of the following statement is not true?

Period	Ai	Fi
1	175	177
2	168	180
3	177	168
4	175	170
5	180	184
6	242	233
7	338	335
8	117	110

	A.	MAPE is 3.63%
	B.	MSE is 51.13
	C.	MSE tends to exaggerate the error of the worst-performing data point , therefore, it is useless.
	D.	MAD is 6.38

The monthly demands between 2019 and 2021 are given. If the annual demand forecasting for 2022 is 1500. Using the seasonality index, which of the following statement isnottrue?

Month		2019	2020	2021
1		114	105	98
2		95	98	97
3		118	116	108
4		119	107	97
5		110	114	98
6		115	120	117
7		110	105	118
8		97	97	105
9		119	120	108
10		97	119	113
11		104	114	101
12		100	118	113
		A.	Seasonality Index for May is 0.99
		B.	Seasonality Index for January is 0.97.
		C.	The forecasting for December 2022 is 114.88.
		D.	On average, the monthly demand in June is about 108% of the grand average monthly demand.

Answer 1

1)

formula:  Moving Average forecast and n=3 for the period 5 = average of 20, 30, 20

Weighted Moving Average forecast for the period 5 = (20*0.4)+(30*0.3)+(20*0.3)

naive forecast for period 5 = Actual data of period 4 = 20,

Hence, the statement "When the business environment is more dynamic, we tend to choose smaller smoothing constant value" is not true

1	B	C	D	E	F
2	Period	Ai	Weight	Moving Average forecast and n=3	Weighted Moving Average forecast
3	1	10
4	2	20	0.3
5	3	30	0.3
6	4	20	0.4
	5			23.33	23

2)

Absolute error = Abs(Actual - Forecast)

Square of error = error^2

Absolute percentage of error = (Absolute error/actual)*100

MAD, MAPE, MSE all are here average value,

Here, the statement "
MSE tends to exaggerate the error of the worst-performing data point , therefore, it is useless" is not true, other options are matching here.

1	B	C	D	E	F	G
2	Period	Ai	Fi	Absolute error	square of error	Absolute percentage of error
3	1	175	177	2	4	1.14%
4	2	168	180	12	144	7.14%
5	3	177	168	9	81	5.08%
6	4	175	170	5	25	2.86%
7	5	180	184	4	16	2.22%
8	6	242	233	9	81	3.72%
9	7	338	335	3	9	0.89%
10	8	117	110	7	49	5.98%
11				MAD	MSE	MAPE
12				6.375	51.125	3.63%

3)

Exponential forecast for period 2 = (Actual for period 1*0.8)+(forecast for period 1*0.2)

Here, F6=189.58 is not true, other options are matching clearly.

1	B	C	D
2	Period	Ai	Exponential forecast
3	1	120	100
4	2	130	116
5	3	100	127.2
6	4	150	105.44
7	5	170	141.088
8			164.2176

4)

here, the statement "The forecasting for December 2022 is 114.88" is not true,

other options are true, and On average, the monthly demand in June is about 108% of the grand average monthly demand. is also true as for June =(117.33-108.44)/108.44= 0.08 or it is 108% higher.

1	B	C	D	E	F	G	H
2	Month		2019	2020	2021	Average	Seasonal Index
3	1		114	105	98	105.67	0.97
4	2		95	98	97	96.67	0.89
5	3		118	116	108	114.00	1.05
6	4		119	107	97	107.67	0.99
7	5		110	114	98	107.33	0.99
8	6		115	120	117	117.33	1.08
9	7		110	105	118	111.00	1.02
10	8		97	97	105	99.67	0.92
11	9		119	120	108	115.67	1.07
12	10		97	119	113	109.67	1.01
13	11		104	114	101	106.33	0.98
14	12		100	118	113	110.33	1.02
15		Global average	108.44