In the LAN crashing model in Example 15.3, suppose that activity D is now an immediate successor to activity C, that is, activity D cannot begin until activity C is finished. Everything else stays the same. (However, note that activity B is no longer an immediate predecessor of activity D, and activity G is no longer an immediate successor of activity C.) Modify both the Project Crashing.xlsx and Product Crashing Linear.xlsx files and run the appropriate Solver on each of them to meet a deadline of 58 days. Do you get the same schedule from each of them? (The idea is that the linear model, if set up correctly, should find the optimal solution easily, but Evolutionary Solver might have some trouble getting the exact optimal solution.)
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.