I am trying to create a mixed integer model that has as an objective to schedule routes for a single vehicle within its timeline. Let me try to elaborate.
Let's say we have a single vehicle vrp and 6 customers and these customers have time windows. In order to facilitate the problem, let's say that with a certain algorithm we created the routes, taking into consideration the time windows and capacity constraints and post process, we need to reschedule these routes within the vehicle's working hours, in order find the best fit (start as soon as possible). So if the vehicle's working hours are 05:00 - 23:00, the first route should start as closely to 05:00 as possible, the second should start after the expected return of the first, and the third should start after the expected return of the second. The start of the first route must be after the vehicle's start working hours and the end of the last route must be before the vehicle's end working hours. Customer's time windows must be taken into consideration.
So a possible timeline would be:
Customer's Time windows 1st route: [6-12, 6-12, 6-22] load time: 05:00 ETA: 10:15 2nd route: [6-12, 12-18,12-18] load time: 10:30 ETA: 14:30 3rd route: [12-18, 6-22,6-22] load time: 15:00 ETA: 18:00
Is there a known math model that schedules time windowed routes (but doesn't create them).
Thank you in advance.
It kind of sounds like a job shop scheduling problem that each route is a job that needs to be done and each job has a several amount of tasks (customers) and we have one machine (the vehicle). Can the tasks of a job have time windows in job shop scheduling?