Decision Variables and Constraints for Golf Hole Construction

This document discusses the decision variables and constraints for the construction of golf holes. It covers the objective function of maximizing the enjoyment index and various constraints such as size, cost, and par. The document also provides the mathematical representation of the constraints and objective function for different models.

Part 1: Action plan
1. Decision variables
The decision variable of the number of golf holes that are to be constructed for each type
of golf hole. If we let the number of the golf holes be represented by y.
Then
y1=Straight par 5
y2=Dogleg par 5
y3=Straight par 4
y4 =Dogleg par 4
y5=long par 3
y6=Short par 3
2. Objective function
The objective of the linear programming is to maximise the total enjoyment index of the
project.
3. Constraints
These are the conditions that the linear program have to adhere to they include;
Straight par 5>= 1
Dogleg par 5 >= 1
Straight par 4>= 2
Dogleg par 4 >= 2
Long par 3 >= 1
Short par 3 >= 1
Par 5 <= 4
Par 4 <= 14
Par 3 <= 4
Total Size <= 42
Total Size >= 36
Total Cost <= $20,000,000
Total Par <= 72
Total Par >= 70
Number of holes= 18

Another constraint of the project is the clubhouse to be constructed by the firm. This is
represented by t. where;
t1=standard clubhouse
t2=Exclusive clubhouse
4. Mathematical representation of the constraints and the objective function
Standard model
Max ; 2 y1 +1.5 y2+1.5 y3 +2 y4 +1.75 y5 +2.25 y6
s . t
5 y1+ 5 y2 +4 y3 +4 y4 +3 y5+ 3 y6 ≤ 72
5 y1+5 y2 +4 y3 +4 y4 +3 y5+3 y6 ≥ 70
y1 + y2+ y3+ y4 + y5 + y6=18
3 y1+ 3.5 y2+2 y3 +2.5 y4 +1 y5+0.75 y6+2t1 ≤ 42
3 y1+ 3.5 y2+2 y3 +2.5 y4 +1 y5+0.75 y6+ 2t1 ≥ 36
1000000 y1+1500000 y2 +750000 y3+ 900000 y4 +600000 y5+ 650000 y6 +3500000 t1 ≤ 20000000
y1 ≥ 1
y2 ≥1
y3 ≥2
y4 ≥ 2
y5 ≥1
y6 ≥1
y1 + y2 ≤ 4
y3 + y4 ≤ 14
y5 + y6 ≤ 4
Exclusive model
Max ; 2 y1 +1.5 y2+1.5 y3 +2 y4 +1.75 y5 +2.25 y6+4t2
s . t

5 y1+ 5 y2 +4 y3 +4 y4 +3 y5+ 3 y6 ≤ 72
5 y1+5 y2 +4 y3 +4 y4 +3 y5+3 y6 ≥ 70
y1 + y2+ y3+ y4 + y5 + y6=18
3 y1+ 3.5 y2+2 y3 +2.5 y4 +1 y5+0.75 y6+ 4 t2 ≤ 42
3 y1+ 3.5 y2+2 y3 +2.5 y4 +1 y5+0.75 y6+ 4 t2 ≥ 36
1000000 y1+1500000 y2 +750000 y3+ 900000 y4 +600000 y5+650000 y6 + 6000000t1 ≤ 20000000
y1 ≥ 1
y2 ≥1
y3 ≥2
y4 ≥ 2
y5 ≥1
y6 ≥1
y1 + y2 ≤ 4
y3 + y4 ≤ 14
y5 + y6 ≤ 4
Exclusive model option 1
Max ; 2 y1 +1.5 y2+1.5 y3 +2 y4 +1.75 y5 +2.25 y6+3t2
s . t
5 y1+ 5 y2 +4 y3 +4 y4 +3 y5+ 3 y6 ≤ 72
5 y1+5 y2 +4 y3 +4 y4 +3 y5+3 y6 ≥ 70
y1 + y2+ y3+ y4 + y5 + y6=18
3 y1+ 3.5 y2+2 y3 +2.5 y4 +1 y5+0.75 y6+ 3t2 ≤ 42
3 y1+ 3.5 y2+2 y3 +2.5 y4 +1 y5+0.75 y6+ 3t2 ≥ 36
1000000 y1+1500000 y2 +750000 y3+ 900000 y4 +600000 y5+650000 y6 + 4500000 t1 ≤20000000
y1 ≥ 1
y2 ≥1

y3 ≥2
y4 ≥ 2
y5 ≥1
y6 ≥1
y1 + y2 ≤ 4
y3 + y4 ≤ 14
y5 + y6 ≤ 4
Exclusive model option 2
Max ; 2 y1 +1.5 y2+1.5 y3 +2 y4 +1.75 y5 +2.25 y6+4t2
s . t
5 y1+ 5 y2 +4 y3 +4 y4 +3 y5+ 3 y6 ≤ 72
5 y1+5 y2 +4 y3 +4 y4 +3 y5+3 y6 ≥ 70
y1 + y2+ y3+ y4 + y5 + y6=18
3 y1+ 3.5 y2+2 y3 +2.5 y4 +1 y5+0.75 y6+ 4 t2 ≤ 42
3 y1+ 3.5 y2+2 y3 +2.5 y4 +1 y5+0.75 y6+ 4 t2 ≥ 36
1000000 y1+1500000 y2 +750000 y3+ 900000 y4 +600000 y5+650000 y6 +5200000 t1 ≤ 20000000
y1 ≥ 1
y2 ≥1
y3 ≥2
y4 ≥ 2
y5 ≥1
y6 ≥1
y1 + y2 ≤ 4
y3 + y4 ≤ 14
y5 + y6 ≤ 4
Exclusive model option 3

Max ; 2 y1 +1.5 y2+1.5 y3 +2 y4 +1.75 y5 +2.25 y6+4t2
s . t
5 y1+ 5 y2 +4 y3 +4 y4 +3 y5+ 3 y6 ≤ 72
5 y1+5 y2 +4 y3 +4 y4 +3 y5+3 y6 ≥ 70
y1 + y2+ y3+ y4 + y5 + y6=18
3 y1+ 3.5 y2+2 y3 +2.5 y4 +1 y5+0.75 y6+ 4 t2 ≤ 42
3 y1+ 3.5 y2+2 y3 +2.5 y4 +1 y5+0.75 y6+ 4 t2 ≥ 36
1000000 y1+1500000 y2 +750000 y3+ 900000 y4 +600000 y5+650000 y6 + 6000000t1 ≤ 22000000
y1 ≥ 1
y2 ≥1
y3 ≥2
y4 ≥ 2
y5 ≥1
y6 ≥1
y1 + y2 ≤ 4
y3 + y4 ≤ 14
y5 + y6 ≤ 4
Alternate model
Max ; 2 y1 +1.5 y2+1.5 y3 +2 y4 +1.75 y5 +2.25 y6+2 t1
s . t
5 y1+ 5 y2 +4 y3 +4 y4 +3 y5+ 3 y6 ≤ 72
5 y1+5 y2 +4 y3 +4 y4 +3 y5+3 y6 ≥ 70
y1 + y2+ y3+ y4 + y5 + y6=18
3 y1+ 3.5 y2+2 y3 +2.5 y4 +1 y5+0.75 y6+ 3t1 ≤ 42
3 y1+ 3.5 y2+2 y3 +2.5 y4 +1 y5+0.75 y6+3t1 ≥ 36
1000000 y1+1500000 y2 +750000 y3+ 900000 y4 +600000 y5+650000 y6 + 4000000 t1 ≤20000000
y1 ≥ 1

y2 ≥1
y3 ≥2
y4 ≥ 2
y5 ≥1
y6 ≥1
y1 + y2 ≤ 4
y3 + y4 ≤ 14
y5 + y6 ≤ 4