Journal of Advanced Transportation / 2018 / Article / Alg 1

Research Article

Ridesharing Problem with Flexible Pickup and Delivery Locations for App-Based Transportation Service: Mathematical Modeling and Decomposition Methods

Algorithm 1

An optimal solution approach for solving subproblem .
Step 1. Initialize:
(1) , , as the accumulated traveling cost of vehicle at space-time vertex ;
(2) and , , to record the previous visiting node and time of each space-time
vertex within the routing path of vehicle , respectively;
(3) to record the space-time arcs within the least cost routing path of vehicle ;
Step 2. Do for each vehicle
Step 2.1. Set , ;
Step 2.2. Do for each space-time arc ;
If , then update , and the previous node and time of space-time vertex
as and ;
Step 2.3. Select ;
Step 2.4. If :
(1) Update the feasible solution of as ;
(2) Track back from space-time vertex to the dummy origin vertex via the
values of and , and then record all the relative space-time arcs in set ;
Step 3. Return set , then the relaxed solution of can be obtained as:
Step 4. Return the relaxed solution of .

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