MERCER ETM 645 - Integer Problems – Heuristics and Local Improvement Algorithms

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ETM 645-8 (Spring '14)Lesson: Integer Problems – Heuristics and Local Improvement AlgorithmsObjectives:1. Define and understand benefits of heuristics or in-exact methods.2. Review heuristics for the Knapsack problem, Scheduling problems, and TSP.3. Describe local improvement algorithms.4. Review examples of local improvement algorithms.Assignment:1. Read journal article “Minimizing Lmax for large-scale, job-shop scheduling problems”.Homework:1. Use the cutting plane algorithm to solve the following IP:Max z = 14x1 + 18x2st -x1 + 3x2 <= 6 7x1 + x2 <= 35 X1, x2 >= 0; x1, x2 are integers.The optimal tableau for this IP’s linear programming relaxation is given below.z x1 x2 s1 s2 rhs1 0 0 56/11 2 8/11 126 0 0 1 7/22 1/22 3 1/2 0 1 0 - 1/22 3/22 4 1/2 2. See next page.Homework:2. Develop a heuristic for the following problem:Using the following precedence diagram and job data, determine the days on which each job should be performed and the minimum number of workers in order to complete the project within five 8-hour days. Jobs must be completed on the day the job is started. Note there is no limit to the number of workers who can be assigned to a job and the time to perform the job is a linear function of the number of workers assigned. For instance, if 4 workers are assigned to a job that takes 8 hours, the job will be completed in 2 hours.jobprocessingtime1 122 73 94 145 166 87 98 79 1610 141234567


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MERCER ETM 645 - Integer Problems – Heuristics and Local Improvement Algorithms

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