Volume 39 Issue 3
Jun.  2021
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CHEN Kejia, FANG Yunfei, LUO Jiayi. A Programming Model for the Flexible Multi-depot Heterogeneous Dial-a-ride Problems[J]. Journal of Transport Information and Safety, 2021, 39(3): 103-110. doi: 10.3963/j.jssn.1674-4861.2021.03.013
Citation: CHEN Kejia, FANG Yunfei, LUO Jiayi. A Programming Model for the Flexible Multi-depot Heterogeneous Dial-a-ride Problems[J]. Journal of Transport Information and Safety, 2021, 39(3): 103-110. doi: 10.3963/j.jssn.1674-4861.2021.03.013

A Programming Model for the Flexible Multi-depot Heterogeneous Dial-a-ride Problems

doi: 10.3963/j.jssn.1674-4861.2021.03.013
  • Received Date: 2020-07-18
  • A mathematical model of mixed-integer non-linear programming is firstly constructed to solve a new dial-a-ride problem(DARP), the multi-depot heterogeneous dial-a-ride problem with flexible depots(MDHDARP-FD), as well as minimize the total driving cost.Due to the complexity of the proposed model, some strategies of linearizing constraints, aggregating variables, and strengthening inequalities are performed to reformulate the non-linear model.During linearizing constraints, non-linear constraints are rewritten as equivalent linear constraints.Aggregating variables, decision variables with the same properties, are aggregated to reduce the number of variables, with strengthened inequalities and valid inequalities introduced to strengthen the model.As a result, a new linear programming model with a small solution space is obtained and can be tractable.Then the dial-a-ride problem is simulated by combining different vehicles and passengers'demands.Simulation results show that compared with the traditional dial-a-ride problems, the model can obtain a group of optimal vehicle routes respecting the complex constraints and reduce the total driving cost, vehicle driving time, and solution time.The total driving cost can be reduced by 1.51%to 6.69%for different DARPs on an average, verifying that the total driving cost of dial-a-ride problems can be reduced with the introduced flexible depots.

     

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