Optimum assignment of trains to platforms under partial schedule compliance

The paper develops a linear mixed integer programming formulation for allocating platforms optimally to trains arriving at a busy multi-platform station. The formulation does not assume that all trains arrive as per schedule, in fact it assumes that the exact arrival times of trains are known shortly (an hour or so) before the actual arrivals of the trains. Such variation in arrival times often necessitates delaying of trains (on the entry tracks) due to non-availability of platforms; these delays may also cause queuing up of trains on the tracks. While determining the optimum allocation the formulation takes into account the inconvenience caused due to (i) delay, (ii) allocation of non-preferred platforms (some platforms may be preferred for some trains - as is the case in India), and (iii) last minute reassignment of platforms. The constraints ensure that all physical and safety related restrictions are satisfied. Various problems developed from the schedule of arrivals at a busy station in India are also solved and the results analyzed.