Consider the following project with time measured in weeks and costs in dollars. The minimum time can be achieved at maximum cost by obtaining additional resources. Activity Predecessors A None B C, E A D G A F C D G A None 1 B, D - IMO Normal Minimum Normal Maximum Time Time Cost Cost 8 4 4800 5400 7 4 3900 4500 7 2 5100 6600 4 2 1200 2400 9 3 3600 4800 9 3 3300 6000 7 3 2700 3900 6 5 2200 3000 5 4 4300 4900 Assume the time for an activity can be reduced by any amount from its normal time to its minimum time and the cost to do so is proportional. For example, to reduced activity A from 8 weeks to 4 weeks costs an additional 5400-4800 600 total, or 600/4 = 150 per week reduction. Thus, the cost to complete activity A in 6 weeks would be 4800+ 2(150) = 5100. (a) Suppose you would like to reduced the total project cost as much as possible but the project duration can be no more than 20 weeks. Formulate a linear program- ming model to answer this question. Solve the model you created using Matlab or other software. What is the dollar cost of your solution? the duration? Suggestion: introduce another variable representing the number of weeks activity k is reduced from its normal duration. (b) Suppose you would like to reduced the total project time as much as possible but spend no more than $35,000 total. Formulate a linear programming model to an- swer this question. Solve the model you created using Matlab or other software. What is the dollar cost of your solution? the duration? Consider the following project with time measured in weeks and costs in dollars. The minimum time can be achieved at maximum cost by obtaining additional resources. Activity Predecessors A None B C, E A D G A F C D G A None 1 B, D - IMO Normal Minimum Normal Maximum Time Time Cost Cost 8 4 4800 5400 7 4 3900 4500 7 2 5100 6600 4 2 1200 2400 9 3 3600 4800 9 3 3300 6000 7 3 2700 3900 6 5 2200 3000 5 4 4300 4900 Assume the time for an activity can be reduced by any amount from its normal time to its minimum time and the cost to do so is proportional. For example, to reduced activity A from 8 weeks to 4 weeks costs an additional 5400-4800 600 total, or 600/4 = 150 per week reduction. Thus, the cost to complete activity A in 6 weeks would be 4800+ 2(150) = 5100. (a) Suppose you would like to reduced the total project cost as much as possible but the project duration can be no more than 20 weeks. Formulate a linear program- ming model to answer this question. Solve the model you created using Matlab or other software. What is the dollar cost of your solution? the duration? Suggestion: introduce another variable representing the number of weeks activity k is reduced from its normal duration. (b) Suppose you would like to reduced the total project time as much as possible but spend no more than $35,000 total. Formulate a linear programming model to an- swer this question. Solve the model you created using Matlab or other software. What is the dollar cost of your solution? the duration
