Operations Management Principles Ip 2

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The objective of the report is to develop a forecast given the actual quantities for 23 periods (Refer Table I).

Table I ЁC Actual Quantities for Periods 1 to 23

Period Actual Quantity

1 429

2 222

3 276

4 167

5 266

6 305

7 430

8 415

9 388

10 368

11 220

12 457

13 267

14 277

15 242

16 590

17 147

18 566

19 267

20 361

21 338

22 351

23 217

The first step in the forecasting process is to choose a suitable forecasting technique. Since a forecast is required for the next period only, the techniques being considered are Moving average, Weighted Moving Average and Exponential Smoothing. (Stevenson, 2007, p.96) In order to make an appropriate choice the nature of the given data must be studied. For this a plot of the given data is drawn (Stevenson, 2007, p.96) and shown in Figure 1.

Figure 1 ЁC Plot of Actual Quantity

From the plot it is evident that the process is fairly stable, though there is significant variation about a central level. There is no consistent directional change. Nor does the quantity for any period seem to be dependent on the immediately preceding quantities. In this situation Weighted Moving Average and Exponential Smoothing techniques do not offer any advantage. In fact they may suffer the disadvantage of chasing the previous value. Hence the Moving Average technique is appropriate and will be adopted. (Stevenson, 2007, pp.72-6)

In order to ascertain the optimum number of periods the moving averages will be calculated using 3 periods, 4 periods and 5 periods. The final selection will be made based on suitable measures of error. Since for a 5 period moving average the calculation will begin from period 6, period 6 is chosen as the starting period for other calculations as well. For each period the forecasted quantity for period 24 is determined. The moving averages are tabulated in Table II.

Table II ЁC Results of Moving Average Calculations

Period Actual Quantity MA with 3 periods MA with 4 periods MA with 5 periods

1 429

2 222

3 276

4 167

5 266

6 305 236 233 272

7 430 246 254 247

8 415 334 292 289

9 388 383 354 317

10 368 411 385 361

11 220 390 400 381

12 457 325 348 364

13 267 348 358 370

14 277 315 328 340

15 242 334 305 318

16 590 262 311 293

17 147 370 344 367

18 566 326 314 305

19 267 434 386 364

20 361 327 393 362

21 338 398 335 386

22 351 322 383 336

23 217 350 329 377

24 302 317 307

The 3 period, 4 period and 5 period moving average gives a forecast for the 24th period of 302 units, 317 units and 307 units respectively. Given the fact that the actual data varies from 147 units to 590 units the forecasts are fairly close to each other.

The forecasts for the 24th period depend on the actual quantities of the last 3, 4 and 5 periods respectively for the 3 period, 4 period and 5 period moving average calculations. However the calculation of the other forecasted quantities enable the determination of the error for each of the three calculations. Two measures of error are being calculated. One is the Mean Absolute Deviation (MAD) and the other is the Mean Square Error (MSE). While adding the errors of individual periods it is essential to ensure that the positive errors of some periods are not offset by negative errors of other periods. MAD does this by taking the absolute value of the individual errors and the MSE does this by squaring the individual errors. The formulas for the exact calculations are shown below. (Stevenson, 2007, pp.90-1)

MAD = ÐŽÐ-|At ЁC Ft|/n where t = 1 to n

MSE = ÐŽÐ-(At ЁC Ft)2/(n ЁC 1) where t = 1 to n

At = actual quantity for period t

Ft = forecasted quantity for period t

n = number of periods

The calculations of MAD and MSE are shown in Table 3 and Table 4 respectively.

Table 3 ЁC Calculation of MAD

Period Actual Quantity |At ЁC Ft|

MA with

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