Abstract A new “rich” variation on the multi-objective vehicle routing problem (VRP), called the ... more Abstract A new “rich” variation on the multi-objective vehicle routing problem (VRP), called the multi-tiered vehicle routing problem with global cross-docking (MTVRPGC), is introduced in this paper. With respect to previously studied VRPs, the MVRPTGC includes the following novel features: (i) segregation of facilities into different tiers that distinguish them in terms of different processing and storage capabilities, (ii) cross-docking at a pre-specified subset of facilities in the network (a feature referred to as global cross-docking), and (iii) the possibility of spill-over into subsequent planning periods of demand for facility visitation. The problem originated from a real-life application concerning the collection and delivery of pathology specimens in the transportation network of a pathology health-care service provider. Other industrial applications may, however, benefit from this type of VRP, such as mail sorting. A mixed integer linear programming (MILP) model for this VRP is proposed, and tested computationally in respect of sixteen small hypothetical test instances. A multi-objective ant colony optimization (MACO) algorithm for solving larger real-world instances of the MTVRPGC is also proposed. The solutions returned by the MACO algorithm are compared with those achieved by the MILP in respect to the sixteen instances and also compared to actual collection and delivery routes of a real pathology healthcare service provider operating in South Africa and it is found that adopting the routes suggested by the algorithm results in substantial improvements of all the objectives pursued relative to the status quo.
International Transactions in Operational Research, 2021
The school bus routing problem (SBRP) involves interrelated decisions such as selecting the bus s... more The school bus routing problem (SBRP) involves interrelated decisions such as selecting the bus stops, allocating the students to the selected bus stops, and designing the routes for transporting the students to the school taking into account the bus capacity constraint, with the objective of minimizing the cost of the routes. This paper addresses the SBRP when the reaction of students to the selection of bus stops is taken into account, that is, when students are allowed to choose the selected bus stop that best suits them. A bilevel optimization model with multiple followers is formulated, and its transformation into a single‐level mixed integer linear programming (MILP) model is proposed. A simple and effective metaheuristic algorithm is also developed to solve the problem. This algorithm involves solving four MILP problems at the beginning, which can be used to obtain tight upper bounds of the optimal solution. Extensive computational experiments on SBRP benchmark instances from...
EURO Journal on Transportation and Logistics, Sep 1, 2015
ABSTRACT In this tutorial, we give an overview of two fundamental problems arising in the optimiz... more ABSTRACT In this tutorial, we give an overview of two fundamental problems arising in the optimization of a railway system: the train timetabling problem (TTP), in its non-periodic version, and the train platforming problem (TPP). We consider for both problems the planning stage, i.e. we face them from a tactical point of view. These problems correspond to two main phases that are usually optimized in close sequence by the railway infrastructure manager. First, in the TTP phase, a schedule of the trains in a railway network is determined. A schedule consists of the arrival and departure times of each train at each (visited) station. Second, in the TPP phase, one needs to determine a stopping platform and a routing for each train inside each (visited) station, according to the schedule found in the TTP phase. Due to the complexity of the two problems, an integrated approach is generally hopeless for real-world instances. Hence, the two phases are considered separately and optimized in sequence. Although there exist several versions for both problems, depending on the infrastructure manager and train operators requirements, we do not aim at presenting all of them, but rather at introducing the reader to the topic using small examples. We present models and solution approaches for the two problems in a didactic way and always refer the reader to the corresponding papers for technical details.
ABSTRACT Several variants of generalized minimum spanning tree problems (GMSTPs) have been introd... more ABSTRACT Several variants of generalized minimum spanning tree problems (GMSTPs) have been introduced in the literature in different papers by a number of authors. Roughly speaking, all these variants are generalizations of the classical minimum spanning tree on an undirected graph G=(V,E) in which the node set V is partitioned into a given set of clusters, and the minimum tree has to ‘span’ those clusters instead of simple nodes. In particular, in this paper we are concerned with two specific variants, the most classical one in which exactly one node in each cluster has to be visited (E-GMSTP), and the less studied problem in which at least one node in each cluster has to be reached (L-GMSTP). This paper presents several effective techniques to improve on the branch-and-cut approaches for E-GMSTP and L-GMSTP proposed by C. Feremans, M. Labbé and G. Laporte [Networks 43, No. 2, 71–86 (2004; Zbl 1069.68114)] and by C. Feremans [“Generalized spanning trees and extensions”, Ph.D. thesis, Univ. Libre Bruxelles, Brussels (2001)], respectively. In particular, we improved on the performances through: (i) new effective heuristic algorithms, (ii) updated branching strategies, and (iii) the use of general-purpose Chvátal-Gomory cuts. Finally, a generalization of both problems requiring some clusters to be visited exactly once and the remaining clusters at least once is presented.
Corrections that should be made to the paper by Ingargiola and Korsh (Ingargiola, G. P., J. F. Ko... more Corrections that should be made to the paper by Ingargiola and Korsh (Ingargiola, G. P., J. F. Korsh. 1977. A general algorithm for one-dimensional knapsack problems. Opns. Res. 25 752–759.) on a general algorithm for one-dimensional knapsack problems.
It is common to report optimality gap values in the computational results section of papers relat... more It is common to report optimality gap values in the computational results section of papers related to the solution of optimization problems. Several years of refereeing experience have taught us that these gaps are often improperly defined or incorrectly computed. In this note, we offer some comments on this topic.
Abstract A new “rich” variation on the multi-objective vehicle routing problem (VRP), called the ... more Abstract A new “rich” variation on the multi-objective vehicle routing problem (VRP), called the multi-tiered vehicle routing problem with global cross-docking (MTVRPGC), is introduced in this paper. With respect to previously studied VRPs, the MVRPTGC includes the following novel features: (i) segregation of facilities into different tiers that distinguish them in terms of different processing and storage capabilities, (ii) cross-docking at a pre-specified subset of facilities in the network (a feature referred to as global cross-docking), and (iii) the possibility of spill-over into subsequent planning periods of demand for facility visitation. The problem originated from a real-life application concerning the collection and delivery of pathology specimens in the transportation network of a pathology health-care service provider. Other industrial applications may, however, benefit from this type of VRP, such as mail sorting. A mixed integer linear programming (MILP) model for this VRP is proposed, and tested computationally in respect of sixteen small hypothetical test instances. A multi-objective ant colony optimization (MACO) algorithm for solving larger real-world instances of the MTVRPGC is also proposed. The solutions returned by the MACO algorithm are compared with those achieved by the MILP in respect to the sixteen instances and also compared to actual collection and delivery routes of a real pathology healthcare service provider operating in South Africa and it is found that adopting the routes suggested by the algorithm results in substantial improvements of all the objectives pursued relative to the status quo.
International Transactions in Operational Research, 2021
The school bus routing problem (SBRP) involves interrelated decisions such as selecting the bus s... more The school bus routing problem (SBRP) involves interrelated decisions such as selecting the bus stops, allocating the students to the selected bus stops, and designing the routes for transporting the students to the school taking into account the bus capacity constraint, with the objective of minimizing the cost of the routes. This paper addresses the SBRP when the reaction of students to the selection of bus stops is taken into account, that is, when students are allowed to choose the selected bus stop that best suits them. A bilevel optimization model with multiple followers is formulated, and its transformation into a single‐level mixed integer linear programming (MILP) model is proposed. A simple and effective metaheuristic algorithm is also developed to solve the problem. This algorithm involves solving four MILP problems at the beginning, which can be used to obtain tight upper bounds of the optimal solution. Extensive computational experiments on SBRP benchmark instances from...
EURO Journal on Transportation and Logistics, Sep 1, 2015
ABSTRACT In this tutorial, we give an overview of two fundamental problems arising in the optimiz... more ABSTRACT In this tutorial, we give an overview of two fundamental problems arising in the optimization of a railway system: the train timetabling problem (TTP), in its non-periodic version, and the train platforming problem (TPP). We consider for both problems the planning stage, i.e. we face them from a tactical point of view. These problems correspond to two main phases that are usually optimized in close sequence by the railway infrastructure manager. First, in the TTP phase, a schedule of the trains in a railway network is determined. A schedule consists of the arrival and departure times of each train at each (visited) station. Second, in the TPP phase, one needs to determine a stopping platform and a routing for each train inside each (visited) station, according to the schedule found in the TTP phase. Due to the complexity of the two problems, an integrated approach is generally hopeless for real-world instances. Hence, the two phases are considered separately and optimized in sequence. Although there exist several versions for both problems, depending on the infrastructure manager and train operators requirements, we do not aim at presenting all of them, but rather at introducing the reader to the topic using small examples. We present models and solution approaches for the two problems in a didactic way and always refer the reader to the corresponding papers for technical details.
ABSTRACT Several variants of generalized minimum spanning tree problems (GMSTPs) have been introd... more ABSTRACT Several variants of generalized minimum spanning tree problems (GMSTPs) have been introduced in the literature in different papers by a number of authors. Roughly speaking, all these variants are generalizations of the classical minimum spanning tree on an undirected graph G=(V,E) in which the node set V is partitioned into a given set of clusters, and the minimum tree has to ‘span’ those clusters instead of simple nodes. In particular, in this paper we are concerned with two specific variants, the most classical one in which exactly one node in each cluster has to be visited (E-GMSTP), and the less studied problem in which at least one node in each cluster has to be reached (L-GMSTP). This paper presents several effective techniques to improve on the branch-and-cut approaches for E-GMSTP and L-GMSTP proposed by C. Feremans, M. Labbé and G. Laporte [Networks 43, No. 2, 71–86 (2004; Zbl 1069.68114)] and by C. Feremans [“Generalized spanning trees and extensions”, Ph.D. thesis, Univ. Libre Bruxelles, Brussels (2001)], respectively. In particular, we improved on the performances through: (i) new effective heuristic algorithms, (ii) updated branching strategies, and (iii) the use of general-purpose Chvátal-Gomory cuts. Finally, a generalization of both problems requiring some clusters to be visited exactly once and the remaining clusters at least once is presented.
Corrections that should be made to the paper by Ingargiola and Korsh (Ingargiola, G. P., J. F. Ko... more Corrections that should be made to the paper by Ingargiola and Korsh (Ingargiola, G. P., J. F. Korsh. 1977. A general algorithm for one-dimensional knapsack problems. Opns. Res. 25 752–759.) on a general algorithm for one-dimensional knapsack problems.
It is common to report optimality gap values in the computational results section of papers relat... more It is common to report optimality gap values in the computational results section of papers related to the solution of optimization problems. Several years of refereeing experience have taught us that these gaps are often improperly defined or incorrectly computed. In this note, we offer some comments on this topic.
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