Integrated optimization of sequential processes: General analysis and application to public transport

Planning in public transportation is traditionally done a sequential process: After the network design process, lines and their frequencies are planned. When these fixed, timetable determined based on timetable, vehicle crew schedules optimized. each step, passenger routes adapted to model behavior of passengers as realistically possible. It has been mentioned many publications that such process sub-optimal, integrated approaches, mainly heuristics, under consideration. Sequential planning not only common but also other applied problems, among others supply chain management, or organizing hospitals efficiently. The contribution this paper hence two-fold: one hand, we develop an integer programming formulation for three stages line planning, (periodic) timetabling, scheduling which includes optimization routes. This gives us exact rewriting approach problem. We discuss properties apply it experimentally data sets from LinTim library. On small examples, get optimal objective function value can be compared with outcome process. propose mathematical general processes used build formulations. For comparing counterparts analyze price sequentiality, i.e., ratio between solution obtained by solution. experiment different possibilities partial integration subset problems again illustrate our results using case transportation. may useful processes.