HW1+Solution

# HW1+Solution - IOE543Winter2010 Homework1Solution...

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IOE 543 Winter 2010 Homework 1 Solution 2.1 (a) Optimal sequence: 2 >1 >3 >4 The objective value is 333 (d) Both generic rules give the same sequence 2 >1 >3 >4. Since the objective function is of the form ∑ w C , rule (ii) is more suitable for the problem 2.2 (a) The optimal sequence is 1 >2 >3 >4 or 2 >1 >3 >4 The objective value is 6 (d) Rule (iii) is the most suitable for the problem 2.3 (a) All the optimal sequences are: 1 >3 >2 >4 1 >3 >4 >2 2 >3 >1 >4 2 >3 >4 >1 2 >4 >3 >1 2 >4 >1 >3 3 >4 >2 >1 3 >4 >1 >2 The objective value is 2 (b) Assume we are trying to divide the jobs into two sets. Set 1 includes the jobs that will meet their due dates, and Set 2 includes the jobs that will not meet their due dates. First arrange all the jobs in increasing order of their due dates, in our case {1 >2 >3 >4}. Scan jobs from the one with the earliest due dates. If one job can meet their deadline, add it to Set 1. Continue until you meet job k that if you include it in Set 1, it would be complete late. In our case, k=2. Currently Set 1 has job

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