A new exact algorithm to solve the multi-trip vehicle routing problem with time windows and limited duration

Abstract

International audienceThis article tackles the multi-trip vehicle routing problem with time windows and limited duration. A trip is a timed route such that a succession of trips can be assigned to one vehicle. We provide an exact two-phase algorithm to solve it. The first phase enumerates possible ordered lists of clients which match the maximum trip duration criterion. The second phase uses a Branch and Price scheme to generate and choose a best set of trips so that all customers are visited. We propose a set covering formulation as the column generation master problem, where columns (variables) represent trips. The sub-problem selects appropriate timing for trips and has a pseudo-polynomial complexity. Computational results on Solomon's benchmarks are presented. The computational times obtained with our new algorithm are much lower than the ones recently obtained in the only two studies published on this problem to date

A memetic algorithm for the patient transportation problem

“…Thus, Azi et al [2] developed a two-phase exact algorithm for the MTVRPTW with a single vehicle in which all non-dominated feasible routes are enumerated in the first phase, and some routes are then selected and scheduled to form a solution. A number of authors recently extended the framework to the problem with multiple vehicles [3,30,20]. For meta-heuristics, however, only Battarra et al [6] have presented an adaptive guidance approach for solving the problem with the objective of minimizing the number of required vehicles.…”

“…Parameter μ is the minimum size of the population, and λ decides when to invoke survivor selection. For the preliminary test, we choose 10 instances with different numbers of requests: 4 holiday instances (instances 5, 10, 15, 20) and 6 non-holiday instances (instances 5,10,15,20,25,30). Four different values are tested for each parameter, giving us 16 pairs of parameter combinations.…”

A branch-and-cut algorithm for a realistic dial-a-ride problem

“…We adopt a set of domination rules similar to those in Hernandez et al (2013) to eliminate dominated labels. If trips r and r 0 lead to the same node, then r dominates r 0 if and only if q r 6 q r 0 ; o min r 6 o min r 0 ; o max r P o max r 0 ; h r 6 h r 0 ; d r 6 d r 0 ; A r 6 A r 0 ; B r P B r 0 ; V j r ¼ V j r 0 ð8j ¼ 1; .…”

“…For more detailed information about these resources, please see Hernandez et al (2013). Resources q r ; o min r and o max r are relative to the relaxed capacity constraints and the minimum assistant requirement constraints.…”

“…In this way, any feasible trip of Model II under original time window constraints is also feasible for Model I under the relaxed time window constraints. We adopt a label-setting algorithm similar to that proposed by Hernandez et al (2013) for the multi-trips VRP with time windows and limited duration (MTVRPTW-LD). Let L r ¼ ðq r ; o min r ; o max r ; d r ; A r ; h r ; B r ; V 1 r ; Á Á Á ; V 2n r Þ be a label representing a partial trip r associated with node i where.…”