Alfieri, A.

train train units problem number solution model stock value train unit circulation column constraint instance integer ef ficient circulation interval composition length stock circulation problem station trip t approach driver algorithm transition result carriage railway objective scheduling capacity graph paper process function ns reizigers research transition graphs demand passenger elimination programming solution approach depot order train length fi rst transition graph fi xed costs generation satis fied kroon phase table transportation 2- iap ficient example model 2 section alkmaar fi xed gaps instance piece stock circulation series train unit types objective function value di fferent lengths / european journal den helder figure timetable core instance integer solution schrijver column generation cpu time lemma fi rst trip