Groot, R.

train train units model stock number train unit circulation problem ef ficient circulation composition stock circulation problem solution station trip t transition carriage constraint capacity graph demand transition graphs passenger elimination railway train length transition graph fi xed costs kroon process transportation approach ficient length model 2 objective alkmaar paper fi xed stock circulation result integer train unit types function den helder solution approach figure instance value schrijver fi rst trip latter groot type “3” elimination phase line 3000 type j example programming model 1 uncoupled al fieri groot single-deck train units morning peak hours departure variable shunting science ns reizigers type “4” passenger trains management timetable fi rst network shunting movements helder account nijmegen business interval