Question

This activity has the purpose of assessing the students knowledge how to make a time series forecast using quantitative models.

1. The following data represents the average “delivery speed” to fulfill customer’s orders in a hypothetical organization. In period 10, changes were made on the fulfillment process, as a result of an improvement Six Sigma initiative.

Period	1	2	3	4	5	6	7	8	9	10
Delivery Speed (Days)	5	6	8	4	6	7	6	6	7	8
Period	11	12	13	14	15	16	17	18	19	20
Delivery Speed (Days)	6	4	5	6	5	4	8	4	7	4

2.Explain if the change made in Period 10 was sound. 3. What is your forecast of delivery-speed in Period 21. You have to choose a model (consider at least three models and using the MAD explain which is the best.)

Answer 1

The nature of the plot suggests that there is no significant reduction in the number of days after period 10 in that after period 16, the number of days has again increased. So, the countermeasure taken seems ineffective.

The time series does not have a significant trend thought some seasonality may be present. So, we will apply the following three methods.

• Naive method
• Moving average (4 periods)
• Exponential smoothing (with an optimized smoothing constant)

Naive method

t	At	Ft = At-1	|At - Ft|
1	5
2	6	5	1
3	8	6	2
4	4	8	4
5	6	4	2
6	7	6	1
7	6	7	1
8	6	6	0
9	7	6	1
10	8	7	1
11	6	8	2
12	4	6	2
13	5	4	1
14	6	5	1
15	5	6	1
16	4	5	1
17	8	4	4
18	4	8	4
19	7	4	3
20	4	7	3
		MAD =	1.84

Moving Average

t	At	Ft = (At-1+At-2+At-3+At-4)/4	|At - Ft|
1	5
2	6
3	8
4	4
5	6	5.75	0.25
6	7	6.00	1.00
7	6	6.25	0.25
8	6	5.75	0.25
9	7	6.25	0.75
10	8	6.50	1.50
11	6	6.75	0.75
12	4	6.75	2.75
13	5	6.25	1.25
14	6	5.75	0.25
15	5	5.25	0.25
16	4	5.00	1.00
17	8	5.00	3.00
18	4	5.75	1.75
19	7	5.25	1.75
20	4	5.75	1.75
		MAD =	1.15625

Exponential smooting

a =	0.106
t	At	Ft = a*At-1 + (1 - a)*Ft-1	|At - Ft|
1	5	5.00
2	6	5.00
3	8	5.11	2.89
4	4	5.41	1.41
5	6	5.26	0.74
6	7	5.34	1.66
7	6	5.52	0.48
8	6	5.57	0.43
9	7	5.61	1.39
10	8	5.76	2.24
11	6	6.00	0.00
12	4	6.00	2.00
13	5	5.79	0.79
14	6	5.70	0.30
15	5	5.73	0.73
16	4	5.66	1.66
17	8	5.48	2.52
18	4	5.75	1.75
19	7	5.56	1.44
20	4	5.72	1.72
		MAD =	1.34

From the MAD values, the Moving average forecast seems more accurate and hence we will choose this model to forecast for period 21.

Forecast = F₂₁ = 5.75 (MA(4))