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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