Geometric Approaches to Bus Scheduling in Northern Ontario

Abstract

Aims: To study the current bus network of Ontario Northland from geometric point of view. Identify the best locations for the bus depots, considering different scenarios and number of depots. Provide insight into the best ways to open a new depot, relocate one or more of the existing depots or close a depot. Provide alternative schedule and compare it to the current schedule being used by Ontario Northland Passenger Division. Study design: We develop a mathematical model of the bus network using the discrete k-center and k-median formalisms and study the model numerically. Place and Duration of Study: Department of Computer Science and Mathematics, Nipissing University, between April and August 2012. Methodology: We study the road network, represented by 11 main locations using the discrete k-center and discrete k-median approach for k = 1, 2, 3. The distances in the model are the actual road distances along the bus network, rather than distances on the map. We develop an ad-hoc algorithmic approach, given the small size of the problem and obtain numerical characteristics of the suitability of each site, pair of sites, and triple of sites as depot locations. Results: We present the suitability and modified suitability numbers for each site as depot, for the top 25 pairs of sites, and for the top 25 triples of sites. Further, we present the top pairs and triples under the assumption that one of the current depots in North Bay and Sudbury is kept and the other is moved, or that a third depot is added to the two existing ones. Based on these results, we present a sample schedule, based on depots in North Bay and Matheson - the best pair of depots according to our analysis. We compare it to the current schedule used by ONTC and note that it realizes substantial time savings over the longer routes, e.g. over 2 hours saving on a 13-hour route between Toronto and Timmins. It has to be noted that all connection times are either the same or better, given that the proposed schedule has the same number of trips as the current one. Conclusion: The current location of the two bus depots operated by Ontario Northland in North Bay and Sudbury is non-optimal. The optimal location for two or three bus depots necessarily includes a northern location, farther north from the current two. Just based on the relocation of the depots or by opening a third bus depot north of the existing two, substantial savings in travel time can be obtained, without increasing the overall number of trips and thus the resources needed. We suggest that the research can be extended to include inventory and workforce considerations. A software tool that can be integrated into Ontario Northland’s enterprise operation system should be written, incorporating the results of this study as well as those possible additions/extensions suggested above.