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 .