A number of projects must be carried out in a shop, and each project j must start and finish within a time window [rj, dj].
Once started, the project must run pj days without interruption. Only one project can be underway at any one time. Every month, the shop is shut down briefly to clean and maintain the equipment, and no project can be in process during this period.
The goal is to find a feasible schedule.
Formulate this problem and indicate how to solve it with logic-based Benders decomposition.
Hint: let each month's schedule be a sub problem. Note that logic-based Benders can provide a scheme for optimizing a master schedule (here, assignment of jobs to months) and daily schedules simultaneously. The monthly resource constraints take the form of a relaxation of the sub problem within the master problem.