An alternate approach to solving the job scheduling problem presented in Problem 3.17 is one that seeks to minimize total project costs. This assumes that the costs for each job are also known in advance, Furthermore, it may be possible to accelerate some or all of the construction activities by allocating more resources to those jobs.
Consider the costs indicated for each of the construction activities presented in the table below. The description of each job is the same as in Problem 3.17 with the base costs for each job indicated. An alternate completion time and cost is also included in the table. For example, the installation of the ceiling superstructure, which normally takes four days at a total cost of $2,100, can be completed in two days if you are willing to increase that cost to $3,600.
Job | Base Cost | Base Duration | Crash Cost | Crash Duration |
1 | $2,500 | 9 | $3,100 | 6 |
2 | $2,700 | 7 | $3,200 | 5 |
3 | $1,800 | 5 | $2,600 | 3 |
4 | $1,400 | 3 | $1,700 | 2 |
5 | $4,200 | 6 | $6,300 | 3 |
6 | $3,200 | 7 | $5,600 | 4 |
7 | $2,100 | 4 | $3,600 | 2 |
8 | $4,200 | 9 | $8,300 | 5 |
9 | $2,300 | 7 | $4,600 | 4 |
10 | $4,200 | 5 | $4,900 | 4 |
11 | $3,800 | 8 | $5,200 | 5 |
12 | $4,000 | 11 | $6,400 | 7 |
Your contract also has a penalty clause that if the project is not finished in 20 days, you must pay a penalty computed using the following formula:
Penalty = 6.38 (number of days over 20)2
Formulate a. linear program that determines the scheduled starting time for each job so as to minimize total project cost, including penalty that might be owed.
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