Forecasting & Smoothing Methods

 

Solved Problem #1: see text book

 

Solved Problem #2: see textbook (manual example using seasonal relatives)

 

Solved Problem #3: see textbook

 

Solved Problem #4: see textbook (you do not have to do this problem manually, use the template and notice how the template answers differ slightly from the seasonal relatives provided in the manual example)

 

To avoid manually entering the data into the templates it can be copied and pasted from Data Sets on the Lesson Page. Use “copy, paste special, values” to transfer the data to the template.

 

#1: A commercial bakery has recorded sales (in dozens) for three products, as shown below.

 

		Day		Blueberry	Cinnamon		Cupcakes
				Muffins	buns
		1		30	18		45
		2		34	17		26
		3		32	19		27
		4		34	19		23
		5		35	22		22
		6		30	23		48
		7		34	23		29
		8		36	25		20
		9		29	24		14
		10		31	26		18
		11		35	27		47
		12		31	28		26
		13		37	29		27
		14		34	31		24
		15		33	33		22
a.  Determine the Naïve forecast for day 16.

b.   What does the use of sales data rather than demand data imply?

 

#2: National Scan, Inc., sells radio frequency inventory tags. Monthly sales ($000) for a seven-month period were as follows:

 

Month	Sales
Feb	19
Mar	18
Apr	15
May	20
Jun	18
Jul	22
Aug	20

 

1. Plot the monthly data.

1. Forecast September sales volume in thousands of dollars using the following methods: Show your answers in the space provided.

 

1.       Naïve

 

2.       Five-month moving average

3.       Weighted moving average using .60 for August, .30 for July, and .10 for June

4.       Exponential smoothing with a smoothing constant of .20

5.       Linear trend equation.

 

#3: A cosmetics manufacturer’s marketing department has developed a linear trend equation that can be used to predict annual sales of its popular Hand & Foot Cream.

 

F_t  =80+15t where

 

F _t= annual sales (000 bottles)

 

t   = 0corresponds to1990

 

1. Indicate how much the sales are increasing or decreasing?

1. Predict sales for the year 2006 using the equation? This is a manual problem!

 

#4: Freight car loadings over a 12-year period at a busy port are as follows: The units are in thousands of tons.

 

Year	Loadings
1	220
2	245
3	280
4	275
5	300
6	310
7	350
8	360
9	400
10	380
11	420
12	450
13	460
14	475
15	500
16	510
17	525
18	541

 

1. Determine the linear trend equation for the freight car loadings.

1. What is the slope? Interpret it.

 

c.	Use the trend equation to predict the freight loadings for years 20 and 21.
d.	The manager intends to install new equipment when the loadings exceeds 800 (thousand tons) per
	year. Assuming the current trend continues the loading volume will reach that level in
	approximately what year? This is a manual problem!

 

 

#5: A manager of a store that sells and installs spas wants to prepare a forecast for January, February and March of next year. Her forecasts are a combination of trend and seasonality.

 

The linear trend equation is

 

F_t  =70+5t where

 

t =0 corresponds to June of last year

 

The seasonal relatives are 1.10 for January, 1.02 for February, and .95 for March.

 

1. What demand should she predict for January, February and March of next year? This is a manual problem! If you need some hints on this problem, refer to solved problem #2 in the textbook.

 

#6: Obtain estimates of daily relatives for the number of customers at a restaurant for the evening meal given the past 4 weeks of historical data. Day 1 is day 1 of week 1, day 8 is day 1 of week 2, etc.

 

Day	Served
1	80
2	75
3	78
4	95
5	130
6	136
7	40
8	82
9	77
10	80
11	94
12	125
13	135
14	42
15	84
16	77
17	83
18	96
19	135
20	140
21	37
22	87
23	82
24	98
25	103
26	144
27	144
28	48

 

 

a.  Construct a graph that will enable you to visualize the daily variation in meals served.

b.       What are the daily adjusted seasonal relatives?

c.        Plot the adjusted seasonal relatives on a graph for each day of the week?

 

1. Determine the forecast for meals to be served for the next 7 days.

1. Plot historical demand with forecast on the same graph.

 

#7: A farming cooperative manager wants to estimate quarterly relatives for grain shipments, based on the 5 years of data shown below (quantities are in metric tons). You will have to enter this data into the template manually.

 

		QUARTER
Year	1	2	3	4
1	200	250	210	340
2	210	252	212	360
3	215	260	220	358
4	225	272	233	372
5	232	284	240	381

 

 

a.       Calculate the quarterly adjusted seasonal relatives.

 

b.       Use the adjusted seasonal relative to determine what percentage shipments in quarter 4 are greater than shipments quarter 3.