Journal of Advanced Transportation / 2018 / Article / Alg 3

Research Article

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

Algorithm 3

Reassigning procedure for modifying and to and .
Step 1. Initialize:
 (1) to record the pickup and delivery space-time vertexes of the passengers in ;
 (2) to record the passengers that are picked up by vehicle ;
 (3) The feasible solution and ;
Step 2. Do for each vehicle
  If :
 Step 2.1. Update list by adding passengers under the vehicle
 capacity limit ;
 Step 2.2. Do from the first vertex to the last one :
  Step 2.2.1. If , then turn to the space-time vertex , ();
  Step 2.2.2. Otherwise, turn to the space-time vertex ();
  Step 2.2.3. If ():
    If the set of passengers to be delivered at space-time vertex is not empty,
    i.e., , then update and ,
    and execute step 2.1 otherwise;
  Step 2.2.4. Otherwise, if , then update ;
  Step 2.2.5. Update , repeat Step 2.2.1 and 2.2.2 to locate the next space-time vertex for
  continuing reassigning process;
 Step 2.3. Update , and as , ( and ) and
 ( and ), respectively;
 Step 2.4. If , terminate the iteration; otherwise, update and continue the iteration;
Step 3. Return the feasible solution and .

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