ANÁLISIS E INTERPRETACIÓN DE RESULTADOS

Although the concept of Flex-Route transit service as an innovative transit service has been around since the late seventies, its implementation has not been widespread. Until very recently, the implementation of route deviation service by transit agencies was limited to rural and small urban areas due to the complexity of scheduling such a service in densely populated urban and suburban areas. Thus, the research on Flex-Route scheduling is scarce in the literature and most of the proposed scheduling heuristics are alterations of the algorithms used for scheduling DRT services.

In a Flex-Route transit system, service is provided at fixed times and locations (fixed stops), while also providing an on-demand service to customers off the fixed route. Thus, scheduling and dispatching Flex-Route transit can pose a significant challenge due to demand at fixed-stops, the requests for deviations, and the dynamics of bus schedule

adherence. This challenge has led to many proposed heuristics for scheduling Flex-Route transit.

Quadrifoglio, Dessouky, and Palmer (2007) developed a similar insertion algorithm to schedule the MAST system discussed earlier, while Zhao and Dessouky (2008) studied the optimal service capacity through a stochastic approach. Crainic, Malucelli, and Nonato (2001) described the MAST concept and incorporated it in a more general network setting while also providing a mathematical formulation. Other works can be found in Cortés and Jayakrishnan (2002), Horn (2002a, b), and Aldaihani and Dessouky (2003), which primarily focus on the operational control and scheduling of such systems.

Dessouky and Aldaihani (2003) proposed a hybrid service delivery method that integrates demand-responsive transit service and fixed route transit to satisfy a set of demand-responsive trips. In the service, DRT passengers use both DRT and FRT services to make their trips. The service has a set of (M) paratransit vehicles with known capacity that are used to pick up DRT passengers from their origins or from the fixed bus stops and drop them off at their final destinations or at the fixed bus stops. On the other hand, the fixed bus route system includes a set of (R) fixed bus routes. Each fixed bus route has a number of buses that travel through it, a set of bus stops and a time schedule. Passengers that are strictly served by the DRT vehicles are referred to as door-to-door requests while those passengers that transfer to a fixed route bus line are referred to as hybrid requests. While in dial-a-ride service the objective is primarily to determine the vehicles’ schedule, in a hybrid system the vehicles’ schedule as well as the delivery path for each request needs to be determined. The heuristic procedure determines the on- demand vehicle schedule and the best candidate path for each request.

The scheduling heuristic has four distinct stages: the insertion procedure; the improvement procedure; the re-sequencing step; and the re-assigning step. In the insertion procedure, the candidate path with the shortest on-demand vehicle travel distance is selected for the hybrid requests. This may not be a good rule in terms of minimizing the passenger trip time since the path with the shortest on-demand vehicle travel distance may connect to a fixed route bus line that will require waiting at the bus stop and have a long travel time on the bus. So in the next step the improvement

procedure searches for other candidate paths of each hybrid request that can reduce the passenger trip time.

In the re-sequencing step, a search technique is used in order to find an improved requests sequence, which leads to shorter vehicle distance in every vehicle while holding the request to vehicle assignment fixed. This leads to an improved schedule by moving individual predecessor (pickup point) and/or successor (delivery point) forward and/or backward in their corresponding route. Three conditions need to be satisfied while moving the pickup and delivery pair in order to have a feasible schedule. The first one is the precedence constraint where the pickup point of any request must be visited before the delivery point of the same request. The second is the on-demand vehicle capacity constraint. The third one is the pickup time window (and the delivery time window for the first leg of the hybrid requests). Finally, the re-assigning step tries to find which request should be removed from its current vehicle schedule, and where it should be inserted.

It is worth mentioning that the above-mentioned studies focused primarily on the static type of the Flex-Route problem, where requests are known in advance and routing schedules to meet those requests were built without allowing for additional real-time requests. As such, there is a dearth of research of scheduling flexible service in a real- time environment, where last-minute or real-time requests for service could originate after the static schedule has been built.

This research focuses on several design and scheduling variables, and their effects on the quality and cost of Flex-Route service. Specifically, the effects of relaxing the departure time constraints at the fixed stops of the service, and those of the slack time length were a major focus of this study. In this research, the real-time part of the problem and its impact on the static schedules were investigated through a sensitivity analysis of the variables mentioned above.