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Example 5.10a

Example 5.10a. Project Scheduling Models. Background Information. Tom Lingley knows that if the room construction activities continue to take as long as listed in the table below, the entire project will take a 20 working days to complete. Background Information – continued.

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Example 5.10a

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  1. Example 5.10a Project Scheduling Models

  2. Background Information • Tom Lingley knows that if the room construction activities continue to take as long as listed in the table below, the entire project will take a 20 working days to complete.

  3. Background Information – continued • Unfortunately, he is under pressure to finish it in the 15 working days. • He estimates that each activity could be crashed by a certain amount at a certain cost. • Specifically, he estimates the cost per day of activity time reduction and the maximum possible days of reduction for each activity in the table on the next slide. • For example, activity A’s duration could be reduced from 4 days to 3 days at cost $150, or it could be reduced from 4 days to 2 days at cost $300.

  4. Background Information – continued • How can Tom meet the 15-day deadline at minimal cost?

  5. Modifying the Model – continued • The overall solution is very similar to the model without crashing, so we will discuss only the required changes. • The modified model appears on the next slide. The following changes are required. • Reduction variables. We need changing cells for the amounts of crashing. Enter any initial values for these in the Reductions range.

  6. Modifying the Model – continued • Inequalities. The left side of the inequalities in the range G18:I28 are the same as before, but on the right side we need to account for the crashing. Do this by entering the formula=VLOOKUP(E18,LTable2,2)+(VLOOKUP(D18,LTable1,3)-VLOOKUP(D18,LTable1,6)) in cell I18 and copying it down. Note how we expanded the LTable1 definition so that we could capture the activity time reductions with the last VLOOKUP function. • Deadline. The project time cell, B30, is calculated as before. However, it is no longer the target cell; it is now the left side of the deadline constraint. • Total cost. Calculate the total crashing cost in cell B32 with the formula =SUMPRODUCT(Reductions,UnitCosts).

  7. Using Solver • The Solver dialog box is straightforward, so we do not show it here. • We want to minimize the total cost subject to inequalities, the deadline constraint, and the upper bounds on the reductions. • The changing cell ranges are the Reductions and EventTimes ranges. • We again ask for a sensitivity report so that we can identify the positive shadow prices and hence the critical path.

  8. Solution • The solution on the next slide indicates the critical path has not changed – it still consists of activities A, B, D, E, H, and J. • However, by spending $580, Tom can reduce the activity times for activities A, D, H, and J enough to meet the 15-day deadline. • Note the power of the Solver model. By including both the Reductions and EventTimes ranges as changing cells, the model simultaneously adjusts the reductions and then calculates the project time until the deadline is met at minimal cost.

  9. Sensitivity Analysis • This chapter is already long enough, so we will not pursue any sensitivity analysis. • But a natural sensitivity analysis is to find a project cost/project time trade-off. • To do so, we would use SolverTable, with the Deadline cell as the single input cell, and keep track of the total crashing cost. • This trade-off information should be very useful in many real-world project analyses.

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