Journal of Advanced Transportation / 2018 / Article / Alg 4

Research Article

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

Algorithm 4

DP based implementing algorithm for constructing feasible solutions of and .
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 ;
(4) ,
to present the generalized vehicle traveling cost for each vehicle on each space-time arc;
Step 2. Do for each vehicle
Step 2.1 Set , ;
Step 2.2 Do for each space-time arc ;
If , then update , and ;
Step 2.3 Select ;
Step 2.4 Track back from space-time vertex to the dummy origin vertexes
via and , and then record all the relative space-time arcs in set ;
Step 3 Return set , then the feasible solution of and can be obtained as:
;
Step 4 Return the feasible solution and .

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