Marta Mesquita

Set partitioning/covering-based approaches for the integrated vehicle and crew scheduling problem

In the integrated vehicle and crew scheduling problem (VCSP) one has to simultaneously assign vehicles to timetabled trips and drivers to vehicles. In this paper, the VCSP is described by an integer linear programming formulation combining a multicommodity network flow model with a set partitioning/covering model. We propose an algorithm that starts with a pre-processing phase to define the set of tasks and to obtain an initial set of duties. In a second phase, we solve the linear programming relaxation of the models using a column generation scheme. Whenever the resulting solution is not integer, branch-and-bound techniques are used over the set of feasible crew duties generated while solving the linear programming relaxation in order to obtain a feasible solution for the VCSP. We show that, under some conditions, just one subset of the decision variables is required to be integer. Computational experience, with randomly generated data publicly available for benchmarking on the WEB is reported, and the results show the effectiveness of our approach concerning both, the quality of the solutions and the CPU time needed to obtain them. Moreover, the approach can be applied to large instances.

Multiple Depot Vehicle Scheduling Problem: A New Heuristic Based on Quasi-Assignment Algorithms

This work is concerned with the multiple depot vehicle scheduling problem where one has to group timetabled trips into chains and, at the same time, assign those chains to depots in order to minimize fleet size costs and dead-heading time. A new mathematical programming formulation is presented for such problem which is known to be NP-hard (Bertossi et al, 1987). Lagrangean relaxation is used, with the corresponding relaxed problem being decomposed into: a semi-assignment problem; a multiple depot vehicle scheduling problem without the requirement that each vehicle must return to the source depot. This last problem is solved by an adaptation of the quasi-assignment algorithm for the multiple depot vehicle scheduling problem (Branco,1989), which takes into account the depots capacities. Computational experience is reported for problems randomly generated according to real life data.

Exact Algorithms for the Multi-Depot Vehicle Scheduling Problem Based on Multicommodity Network Flow Type Formulations

We compare the linear programming relaxation of different mathematical formulations for the multi-depot vehicle scheduling problem. As a result of this theoretical analysis, we select for development a tree search procedure based on a multicommodity network flow formulation that involves two different types of decision variables: one type is used to describe the connections between trips, in order to obtain the vehicle blocks, while the other type is related to the assignment of trips to depots. We also develop a branch and bound algorithm based on the linear relaxation of a more compact multicommodity network flow formulation, in the sense that it contains just one type of variable and fewer constraints than the previous model. Computational experience is presented to compare the two algorithms.

A new model for the integrated vehicle-crew-rostering problem and a computational study on rosters

Operational planning within public transit companies has been extensively tackled but still remains a challenging area for operations research models and techniques. This phase of the planning process comprises vehicle-scheduling, crew-scheduling and rostering problems. In this paper, a new integer mathematical formulation to describe the integrated vehicle-crew-rostering problem is presented. The method proposed to obtain feasible solutions for this binary non-linear multi-objective optimization problem is a sequential algorithm considered within a preemptive goal programming framework that gives a higher priority to the integrated vehicle-crew-scheduling goal and a lower priority to the driver rostering goals. A heuristic approach is developed where the decision maker can choose from different vehicle-crew schedules and rosters, while respecting as much as possible management’s interests and drivers’ preferences. An application to real data of a Portuguese bus company shows the influence of vehicle-crew-scheduling optimization on rostering solutions.

A decomposition approach for the integrated vehicle-crew-roster problem with days-off pattern

The integrated vehicle-crew-roster problem with days-off pattern aims to simultaneously determine minimum cost vehicle and daily crew schedules that cover all timetabled trips and a minimum cost roster covering all daily crew duties according to a pre-defined days-off pattern. This problem is formulated as a new integer linear programming model and is solved by a heuristic approach based on Benders decomposition that iterates between the solution of an integrated vehicle-crew scheduling problem and the solution of a rostering problem. Computational experience with data from two bus companies in Portugal and data from benchmark vehicle scheduling instances shows the ability of the approach for producing a variety of solutions within reasonable computing times as well as the advantages of integrating the three problems.

Issues on Dynamic Cognitive Map modelling of purse-seine fishing skippers behavior

This paper focus on obtaining a qualitative dynamic model based on real world data taken from a real world qualitative system: the day to day behavior of purse seine fishing fleet skippers. The model is based on a dynamic cognitive mapping approach (rule based fuzzy cognitive maps - RB-FCM) where several developments had to be made in order to obtain a workable system. Most changes were due to timing issues, which are essential in the study of system dynamics but have traditionally been avoided in most dynamic cognitive maps modelling approaches.

A decompose-and-fix heuristic based on multi-commodity flow models for driver rostering with days-off pattern

Facing severe budgetary constraints, public transport companies are forced to efficiently manage staff, one of the most expensive resources.

An Integrated Vehicle-Crew-Roster Problem with Days-Off Pattern

The integrated vehicle-crew-roster problem with days-off pattern aims to simultaneously determine minimum cost sets of vehicle and daily crew schedules that cover all timetabled trips and a minimum cost roster covering all daily crew duties according to a pre-defined days-off pattern. This problem is modeled as a mixed binary linear programming problem. A heuristic approach with embedded column generation and branch-and-bound techniques within a Benders decomposition is proposed. The new methodology was tested on real instances and the computational results are promising.

TSP with Multiple Time-Windows and Selective Cities

We address a special TSP in which the set of cities is partitioned into two subsets: mandatory cities and selective cities. All mandatory cities should be visited once within one of the corresponding predefined multiple time windows. A subset of the selective cities, whose cardinality depends on the tour completion time, should be visited within one of the associated multiple time windows. The objective is to plan a tour, not exceeding a predefined number of days, that minimizes a linear combination of the total traveled distance as well as the total waiting time. We present a mixed integer linear programming (MILP) model for the problem and propose a heuristic approach to solve it. Computational experiments address two real world problems that arise in different practical contexts.