Question

3. [13 marks] A company is interested in forecasting demand for a product. They have reason to believe that the demand is not affected by any seasonal changes and that it does not increase or decrease systematically over time. They have data for the last 9 periods (below).

Period	1	2	3	4	5	6	7	8	9
Demand	230	210	220	250	300	280	240	230	200

In each part of this question, show your work: show the equation you use, how you plug in, and your final answer. Please do not round any answers. Hint: see lecture 22 example 3.

a) [3 marks] Use a 4-period moving average to forecast demand for period 10.

b) [3 marks] Use a 3-period weighted moving average to forecast demand for period 10 using weights of 0.6, 0.3, and 0.1, respectively. Show your work.

c) [3 marks] Suppose the forecast for period 9 was 235 units. Use exponential smoothing with a smoothing constant of 0.6 to forecast demand for period 10.

d) [4 marks] Suppose the actual demand in period 10 was 211 units. Which of your forecasting methods from parts a through c performed best, and why? Please provide a table similar to the one shown on slide 48 of lecture 22, and make your conclusion based on your table.

Answer 1

Answer:-

Given That:-

A company is interested in forecasting demand for a product. They have reason to believe that the demand is not affected by any seasonal changes and that it does not increase or decrease systematically over time.

solution:-

period	demand
1	230
2	210
3	220
4	250
5	300
6	280
7	240
8	230
9	200

a) [3 marks] Use a 4-period moving average to forecast demand for period 10.

Forecast using 4 - period moving average

F5 = (230+210+220+250)/4

F5 = 227.5

F6 = (210+220+250+300)/4

F6 = 245

F7 = (220+250+300+280)/4

F7 = 262.5

F8 = (250+300+280+240)/4

F8 = 267.5

F9 = (300+280+240+230)/4

F9 = 262.5

F10 = (280+240+230+200)/4

F10 = 237.5

b) [3 marks] Use a 3-period weighted moving average to forecast demand for period 10 using weights of 0.6, 0.3, and 0.1, respectively. Show your work.

Forecast using 3 - period weighted moving average

The most recent observation receives the most weight (0.6) a weight of 0.3 to second most observation and a weight of 0.1 to the third most observation.

Forecast for week 4 = 0.1(230) + 0.3(210) + 0.6(220) = 218

Forecast for week 5 = 0.1(210) + 0.3(220) + 0.6(250) = 237

Forecast for week 6 = 0.1(220) + 0.3(250) + 0.6(300) = 277

Forecast for week 7 = 0.1(250) + 0.3(300) + 0.6(280) = 283

Forecast for week 8 = 0.1(300) + 0.3(280) + 0.6(240) = 258

Forecast for week 9 = 0.1(280) + 0.3(240) + 0.6(230) = 238

Forecast for week 10 = 0.1(240) + 0.3(230) + 0.6(200) = 213

c) [3 marks] Suppose the forecast for period 9 was 235 units. Use exponential smoothing with a smoothing constant of 0.6 to forecast demand for period 10.

Suppose forecast for period 9 was 235 units.

Forecast using exponential smoothing with a smoothing constant of 0.6

given

= 0.6(200) + 0.4(235)

= 214

d) [4 marks] Suppose the actual demand in period 10 was 211 units. Which of your forecasting methods from parts a through c performed best, and why? Please provide a table similar to the one shown on slide 48 of lecture 22, and make your conclusion based on your table.

Method	Forecasted Demand
Moving Average	238
Weighted moving Average	213
Exponential smoothing	214

Actual Demand   = 211

Weighted moving average is best among these three cases for this data. Becasue, it gives more weightage to the latest available data and then reducing the weightage for subsequent data.

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