Training Major Bill Bligh Director of the Army War Colleges

Training

Major Bill Bligh, Director of the Army War College’s new six-month attaché training program, is concerned about how the 20 officers taking the course spend their time while in his charge. Major Bligh recognizes that there are 168 hours per week and thinks his students have been using them rather inefficiently.

Bligh lets:

X1 = number of hours of sleep needed per week

X2 = number of personal hours

X3 = number of hours of class and studying

X4 = number of hours of social time off base

He thinks that students should study 30 hours a week to have time to absorb the material. This is his most important goal. Bligh feels that students need at most 7 hours of sleep per night on average and that this goal is number 2. He believes that goal number 3 is to provide at least 20 hours per week of social time.

Formulate this goal programming problem

Solve with the software (lindo or excel) of your choice.

Solution

Total hours x= 168 hours è 7days

X = 1 week = 168 hours = 7 days + 7 nights

X1 = number of hours of sleep needed per week

Based on goal number 2 students need at most 7 hours of sleep per night on average

So,

X1=7*7 = 49 Hours per week

X3 = number of hours of class and studying

30 hours a week to have time to absorb the material

X3 = 30 hours per week

X4 = number of hours of social time off base

that goal number 3 is to provide at least 20 hours per week of social time.

X4 = 20 hours per week

X2 = number of personal hours

69

X1+X2+ X1+X2 = X

X=168

X1=49

X2=?

X3=30

X4=20

X2 = x-(X1+X2+X3)

X2 = 168-(49+30+20);

X2 = 168-99;

X2 = 99

MAX 2 X4 + S5

ST

X1 + S1 = 168

S1- 0.5 X1 - X2 - S2 = 0

2 X1 + S2 - 0.5 X2 - X3 - S3 = 0

2 X2 + S3 - 0.5 X3 - X4 - S4 = 0

2 X3 + S4 - 0.5 X4 - S5 = 0

END