Four workers are available to perform tasks 1-4. However, worker 1 can\'t do tas

Question

Four workers are available to perform tasks 1-4. However, worker 1 can't do tasks 2, 3, or 4. Also, worker 2 can't do tasks 3 or 4 and worker 3 can't do tasks 1, 3, or 4. Worker 4 can do any task. Each worker can do at most one task, and each task should be performed at most once. Draw the network for the maximum flow problem that can be used to determine whether all tasks can be assigned to a suitable worker. (Please specify the source and sink nodes, arc directions and arc capacities) Formulate this problem as a linear program. Clearly define all variables and constraints a) b) the model using Ford-Fulkerson algorithm C all the iterations) d) Use the final iteration of Ford-Fulkerson algorithm to find a minimum cut for this network and verify the strong duality (i.e, maximum flowtotal capacity of the minimum cut).

Explanation / Answer

10.In project management resource-limited scheduling is a method for developing the shortest schedule for completing the project when resources are limited.This method is put into use when resources are limited . By using resource levelling approach of resource-limited scheduling project can be kept on schedule by adjusting the start and finished dates of independent activities as per the availability of resources. The goal is to match the demand with supply.

11. Here total number of workers available over a period of 10 days is 40 so per day 4 workers are available. Task 2 requires 1 worker for completion in 3 days and task 3 requires 3 workers for 3 days. We will employ 4 workers for 3 days for completion of task 2 and 3. Next we will 4 workers for 4 days for completion of task 1 which requires 2 workers for 4 days for completion and task 4 which requires 2 workers for completion in 4 days .Next we will employ 4 workers for 3 days for completion of task 5 which requires 1 worker for 3 days for completion and task 6 which requires 3 workers for completion in 3 days.

12. Here total number of work days required are 40 . These are calculated as follows:

Task 1 requires 2 workers for 4 days so total work days required are 8

Task 2 requires 1 worker for 3 days so total work days required are 3

Task 3 requires 3 workers for 3 days so total work days required are 9

Task 4 requires 2 workers for 4 days so total work days required are 8

Task 5 requires 1 worker for 3 days so total work days required are 3

Task 6 requires 3 workers for 3 days so total work days required are 9

Now if we add all work days total work days required for completing all tasks are 40 . We are allowed to use 3 workers at any point of time so we need 40/3 = 13.33 days to complete all the activities so new date for project completion will 14th. In tabular form it can be represented as follows :

worker1 task3 task3 task3 task6 task6 task6 task1 task1 task1 task1 task4 task4 task4 task4 worker2 task3 task3 task3 task6 task6 task6 task1 task1 task1 task1 task4 task4 task4 task4 worker3 task3 task3 task3 task6 task6 task6 task2 task2 task2 task5 task5 task5 Day 1 2 3 4 5 6 7 8 9 10 11 12 13

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