Modify the multiple project-scheduling model in Example 15.4 so that each project has its own due date. These due dates are listed in the file P15_13.xlsx. Assume no revenue is earned unless a project is completed by its due date. Assuming that the objective is still to maximize total revenue, when should each project be started?
EXAMPLE 15.4 SCHEDULING PROJECTS AT TIMBURTON
Timburton Construction has 10 projects that it can (if desired) complete within the next 10 months. Each project earns a certain revenue when it is completed, but only if it is completed within the next 10 months. Otherwise, the project earns no revenue. The number of workers needed each month, the number of months needed to complete each project, and the revenue earned from each completed project are listed in Table 15.7. We assume that after the company begins working on a project, it must work on the project during consecutive months until the project is completed. Timburton has 220 workers available each month. How can it maximize the revenue earned during the next 10 months? Objective To find starting times for the projects so that total revenue is maximized and worker utilization each month is no greater than worker availability.
WHERE DO THE NUMBERS COME FROM?
The setup here is a simplified version of what might happen in a real company. In reality, each project would probably be composed of well-defined tasks, each of which would require workers (and maybe other resources) over some duration. As for the revenues, the all-or-nothing nature we are assuming here might be built into contracts for the project, where the company is paid by a client only if it completes the client’s project by a certain deadline. Of course, these deadlines could differ across projects. This generalization could easily be incorporated into our model.