In the crashing model in Example 15.3, we assumed that the cost per day crashed is constant. This is often unrealistic. For example, it might cost $300 to decrease the duration of an activity from 10 days to 9 days, but it might cost $450 to reduce it from 9 days to 8 days. One possible way to model this is to assume that the crashing cost, c(d), for reducing the duration by d days is a quadratic: c(d) = cd2 for some constant c > 0. This function produces the “increasing cost per day” behavior frequently seen. To try it out in Example 15.3, suppose the crashing cost for activity H, wiring offices, exhibits this quadratic behavior, with c = 300. Then, for example, the cost of reducing the duration of activity H from 12 days to 9 days is c(3) = 300(3)2 = $2700. Modify the Project Crashing Linear.xlsx model to accommodate this quadratic function, and then optimize to meet a deadline of 54 days. (You can still assume that activity H can be crashed by a maximum of 4 days.) Now you must use GRG Nonlinear Solver.
Example 15.3
MEETING A DEADLINE FOR THE LAN PROJECT
From the CPM calculations in Example 15.1, the insurance company knows that if the LAN activities continue to take as long as listed in Table 15.2, the entire project will take 62 working days to complete. However, the project manager is under pressure to finish the job in 56 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, as shown in Table 15.5. For example, activity A’s duration could be reduced from 10 days to 9 days at cost $600, or it could be reduced from 10 days to 8 days at cost $1200. (It is even possible to have a fractional reduction, such as from 10 days to 8.5 days at cost $900.) On the other hand, note that three of the activities cannot be crashed at all, probably due to technical considerations. How can the deadline be met at minimum cost?
Objective To use a Solver model to decide how much to crash each activity so that the deadline is met at minimum cost
Example 15.1
CREATING AN OFFICE LAN
An insurance company has decided to construct a local area network (LAN) in one of its large offices so that its employees can share printers, files, and other conveniences. The project consists of 15 activities, labeled A through O, as listed in Table 15.2. This table indicates the immediate predecessors and immediate successors of each activity, along with each activity’s expected duration. (At this point these durations are assumed known.) Note that activity A is the only activity that can start right away, and activity O is the last activity to be completed. This table implies the AON network in Figure 15.2. The company wants to know how long the project will take to complete, and it also wants to know which activities are on the critical path.
Objective To develop a spreadsheet model of the LAN project so that we can calculate the time required to complete the project and identify the critical activities.