A construction contractor has undertaken a job with 7 major tasks. Some of the tasks can begin at any time, but others have predecessors that must be completed first. The following table shows these predecessor task numbers, together with the minimum and maximum time (in days) allowed for each task, and the total cost that would be associated with accomplishing each task in its minimum and maximum times (more time usually saves expense) Min time Max time Min cost Max cost Predecessor tasks 6. 12 1600 1000 None 8. 16 2400 1800 None 3 16 24 2900 2000 2 4 14 20 1900 1300 1,2 5 4 16 3800 2000 3 6 12 16 2900 2200 3 7 2 12 1300 800 4 The contractor seeks a way to complete all work in 40 days at least total cost, assuming that the cost of each task is linearly interpolated from times between the minimum and maximum. 1. Formulate an algebraic linear programming model of this time/cost planning problem using the decision variables (j = 1,...,7) s; : start time of taks j (in days) t; : days to complete task j.
A construction contractor has undertaken a job with 7 major tasks. Some of the tasks can begin at any time, but others have predecessors that must be completed first. The following table shows these predecessor task numbers, together with the minimum and maximum time (in days) allowed for each task, and the total cost that would be associated with accomplishing each task in its minimum and maximum times (more time usually saves expense) Min time Max time Min cost Max cost Predecessor tasks 6. 12 1600 1000 None 8. 16 2400 1800 None 3 16 24 2900 2000 2 4 14 20 1900 1300 1,2 5 4 16 3800 2000 3 6 12 16 2900 2200 3 7 2 12 1300 800 4 The contractor seeks a way to complete all work in 40 days at least total cost, assuming that the cost of each task is linearly interpolated from times between the minimum and maximum. 1. Formulate an algebraic linear programming model of this time/cost planning problem using the decision variables (j = 1,...,7) s; : start time of taks j (in days) t; : days to complete task j.
Chapter1: Making Economics Decisions
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Transcribed Image Text:A construction contractor has undertaken a job with 7 major tasks. Some of the tasks can begin at
any time, but others have predecessors that must be completed first. The following table shows these
predecessor task numbers, together with the minimum and maximum time (in days) allowed for each task,
and the total cost that would be associated with accomplishing each task in its minimum and maximum
times (more time usually saves expense)
Min time Max time Min cost Max cost Predecessor
tasks
None
1000
1800
12
1600
2
8
16
2400
None
16
24
2900
1900
2000
2
14
20
1300
1,2
4
16
16
3800
2000
3
12
2900
2200
3
7
2
12
1300
800
The contractor seeks a way to complete all work in 40 days at least total cost, assuming that the cost of
each task is linearly interpolated from times between the minimum and maximum.
1. Formulate an algebraic linear programming model of this time/cost planning problem using the
decision variables (j = 1,...,7)
sj : start time of taks j (in days)
t; : days to complete task j.
Your model should have an objective function summing interpolated cost and main constraints to
enforce precedence relationships and the time limit.
2. Enter and solve your model in GAMS. Your GAMS model should be algebraic.
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