The Chairperson of the Department of Business Administration at TSU wants to for

ID: 465052 • Letter: T

Question

The Chairperson of the Department of Business Administration at TSU wants to forecast the number of students who will enroll in Operations Management next semester in order to determine how many sections to schedule. The chair has accumulated the following data on enrollment for the past 8 semesters: Students Enrolled Semester in OM 1 270 2 310 3 250 4 290 5 370 6 410 7 400 8 450 a) Compute an exponentially smoothed forecast for semester 9 (next semester) with = 0.30. Use 270 as the forecast for the 1st semester.

Explanation / Answer

Formula for first-order exponential smoothing is given as follows:

Ft = .Dt-1 + (1 – ). Ft-1

where, Ft = Forecast for next period.

Dt-1 = Actual demand (here actual student enrollment) in the previous period.

Ft-1 = Forecast in the previous period.

= Smoothing coefficient.

Given: = 0.3; Forecast for 1st semester = 270 students.

Table:

Semester

Students Enrolled in OM

Forecast, Ft = .Dt-1 + (1 – ). Ft-1

270

310

F2 = 0.3 x 270 + (1 – 0.3) x 270 = 270

250

F3 = 0.3 x 310 + (1 – 0.3) x 270 = 282

290

F4 = 0.3 x 250 + (1 – 0.3) x 282 = 272.4

370

F5 = 0.3 x 290 + (1 – 0.3) x 272.4 = 277.68

410

F6 = 0.3 x 370 + (1 – 0.3) x 277.68 = 305.376

400

F7 = 0.3 x 410 + (1 – 0.3) x 305.376 = 336.7632

450

F8 = 0.3 x 400 + (1 – 0.3) x 336.7632 = 355.7342

F9 = 0.3 x 450 + (1 – 0.3) x 355.7342 = 384.01 = 384 (approx.)

Therefore, exponentially smoothed forecast for semester 9 (next semester) = 384 students.