The multi-depot VRP with vehicle interchanges

In real-world logistic operations there are a lot of situations that can be exploited to get better operational strategies. It is important to study these new alternatives, because they can represent significant cost reductions to the companies working with physical distribution. This thesis defines the Multi-Depot Vehicle Routing Problem with Vehicle Interchanges (MDVRPVI). In this problem, both vehicle capacities and duration limits on the routes of the drivers are imposed. To favor a better utilization of the available capacities and working times, it is allowed to combine pairs of routes at predefined interchange locations. The objective of this thesis is to analyze and solve the Multi-Depot Vehicle Routing Problem adding the possibility to interchange vehicles at predefined points. With this strategy, it is possible to reduce the total costs and the number of used routes with respect to the classical approach: The Multi-Depot Vehicle Routing Problem (MDVRP). It should be noted that the MDVRP is more challenging and sophisticated than the single-depot Vehicle Routing Problem (VRP). Besides, most exact algorithms for solving the classical VRP are difficult to adapt in order to solve the MDVRP (Montoya-Torres et al., 2015). From the complexity point of view, the MDVRPVI is NP-Hard, since it is an extension of the classical problem, which is already NP-Hard. We present a tight bound on the costs savings that can be attained allowing interchanges. Three integer programming formulations are proposed based on the classical vehicle-flow formulations of the MDVRP. One of these formulations was solved with a branch-and-bound algorithm, and the other two formulations, with branch-and-cut algorithms. Due to its great symmetry, the first formulation is only able to solve small instances. To increase the dimension of the instances used, we proposed two additional formulations that require one or more families of constraints of exponential size. In order to solve these formulations, we had to design and implement specific branch-and-cut algorithms. For these algorithms we implemented specific separation methods for constraints that had not previously been used in other routing problems. The computational experience performed evidences the routing savings compared with the solutions obtained with the classical approach and allows to compare the efficacy of the three solution methods proposed.En les operacions logístiques del món real es donen situacions que poden ser explotades per obtenir millors estratègies operacionals. És molt important estudiar aquestes noves alternatives, perquè poden representar una reducció significativa de costos per a les companyies que treballen en distribució de mercaderies. En aquesta tesi es defineix el Problema d'Enrutament de Vehicles amb Múltiples Dipòsits i Intercanvi de Vehicles (MDVRPVI). En aquest problema, es consideren tant la capacitat dels vehicles com els límits de duració de les rutes dels conductors. Per tal de millorar la utilització de les capacitats i temps de treball disponibles, es permet combinar parelles de rutes en punts d'intercanvi predefinits. L'objectiu d'aquesta tesi és analitzar i resoldre el problema d'Enrutament de Vehicles amb Múltiples Dipòsits, on es permet l'intercanvi de vehicles. Amb aquesta estratègia, és possible reduir els costos totals i el nombre de les rutes utilitzades respecte l'enfocament clàssic: el problema d'Enrutament de Vehicles amb Múltiples Dipòsits (MDVRP). Cal assenyalar que el MDRVP és més desafiant i sofisticat que el problema d'Enrutament de Vehicles d'un únic dipòsit (VRP). A més, molts algoritmes exactes per resoldre el VRP clàssic son complicats d'adaptar per resoldre el MDVRP (Montoya-Torres et al., 2015). Des del punt de vista de la complexitat, el MDRVPVI és NP-Dur, perquè és una extensió del problema clàssic, que també ho és. Presentem una cota ajustada de l'estalvi en els costos de distribució que es pot obtenir permetent els intercanvis. Es proposen tres formulacions de programació sencera basades en la formulació clàssica “vehicle-flow” del MDVRP. La primera formulació, degut a la seva grandària i la seva simetria, només permet resoldre instàncies molt petites. Per augmentar la dimensió de les instàncies abordables, es proposen dues formulacions addicionals que requereixen una o vàries famílies de restriccions de mida exponencial. Per això, per tal de resoldre el problema amb aquestes formulacions, ha calgut dissenyar i implementar sengles algorismes de tipus branch-and-cut. En aquests algorismes s'han implementat mètodes de separació específics per a les restriccions que no s'havien utilitzat prèviament en altres problemes de rutes. L’experiència computacional realitzada evidencia els estalvis obtinguts comparació amb les solucions corresponents l'enfocament clàssic. També es compara l’eficàcia dels tres mètodes propostes a l'hora de resoldre el problema.Postprint (published version

The multi-depot VRP with vehicle interchanges

In real-world logistic operations there are a lot of situations that can be exploited to get better operational strategies. It is important to study these new alternatives, because they can represent significant cost reductions to the companies working with physical distribution. This thesis defines the Multi-Depot Vehicle Routing Problem with Vehicle Interchanges (MDVRPVI). In this problem, both vehicle capacities and duration limits on the routes of the drivers are imposed. To favor a better utilization of the available capacities and working times, it is allowed to combine pairs of routes at predefined interchange locations. The objective of this thesis is to analyze and solve the Multi-Depot Vehicle Routing Problem adding the possibility to interchange vehicles at predefined points. With this strategy, it is possible to reduce the total costs and the number of used routes with respect to the classical approach: The Multi-Depot Vehicle Routing Problem (MDVRP). It should be noted that the MDVRP is more challenging and sophisticated than the single-depot Vehicle Routing Problem (VRP). Besides, most exact algorithms for solving the classical VRP are difficult to adapt in order to solve the MDVRP (Montoya-Torres et al., 2015). From the complexity point of view, the MDVRPVI is NP-Hard, since it is an extension of the classical problem, which is already NP-Hard. We present a tight bound on the costs savings that can be attained allowing interchanges. Three integer programming formulations are proposed based on the classical vehicle-flow formulations of the MDVRP. One of these formulations was solved with a branch-and-bound algorithm, and the other two formulations, with branch-and-cut algorithms. Due to its great symmetry, the first formulation is only able to solve small instances. To increase the dimension of the instances used, we proposed two additional formulations that require one or more families of constraints of exponential size. In order to solve these formulations, we had to design and implement specific branch-and-cut algorithms. For these algorithms we implemented specific separation methods for constraints that had not previously been used in other routing problems. The computational experience performed evidences the routing savings compared with the solutions obtained with the classical approach and allows to compare the efficacy of the three solution methods proposed.En les operacions logístiques del món real es donen situacions que poden ser explotades per obtenir millors estratègies operacionals. És molt important estudiar aquestes noves alternatives, perquè poden representar una reducció significativa de costos per a les companyies que treballen en distribució de mercaderies. En aquesta tesi es defineix el Problema d'Enrutament de Vehicles amb Múltiples Dipòsits i Intercanvi de Vehicles (MDVRPVI). En aquest problema, es consideren tant la capacitat dels vehicles com els límits de duració de les rutes dels conductors. Per tal de millorar la utilització de les capacitats i temps de treball disponibles, es permet combinar parelles de rutes en punts d'intercanvi predefinits. L'objectiu d'aquesta tesi és analitzar i resoldre el problema d'Enrutament de Vehicles amb Múltiples Dipòsits, on es permet l'intercanvi de vehicles. Amb aquesta estratègia, és possible reduir els costos totals i el nombre de les rutes utilitzades respecte l'enfocament clàssic: el problema d'Enrutament de Vehicles amb Múltiples Dipòsits (MDVRP). Cal assenyalar que el MDRVP és més desafiant i sofisticat que el problema d'Enrutament de Vehicles d'un únic dipòsit (VRP). A més, molts algoritmes exactes per resoldre el VRP clàssic son complicats d'adaptar per resoldre el MDVRP (Montoya-Torres et al., 2015). Des del punt de vista de la complexitat, el MDRVPVI és NP-Dur, perquè és una extensió del problema clàssic, que també ho és. Presentem una cota ajustada de l'estalvi en els costos de distribució que es pot obtenir permetent els intercanvis. Es proposen tres formulacions de programació sencera basades en la formulació clàssica “vehicle-flow” del MDVRP. La primera formulació, degut a la seva grandària i la seva simetria, només permet resoldre instàncies molt petites. Per augmentar la dimensió de les instàncies abordables, es proposen dues formulacions addicionals que requereixen una o vàries famílies de restriccions de mida exponencial. Per això, per tal de resoldre el problema amb aquestes formulacions, ha calgut dissenyar i implementar sengles algorismes de tipus branch-and-cut. En aquests algorismes s'han implementat mètodes de separació específics per a les restriccions que no s'havien utilitzat prèviament en altres problemes de rutes. L’experiència computacional realitzada evidencia els estalvis obtinguts comparació amb les solucions corresponents l'enfocament clàssic. També es compara l’eficàcia dels tres mètodes propostes a l'hora de resoldre el problema

Cost Factor Focused Scheduling and Sequencing: A Neoteric Literature Review

The hastily emergent concern from researchers in the application of scheduling and sequencing has urged the necessity for analysis of the latest research growth to construct a new outline. This paper focuses on the literature on cost minimization as a primary aim in scheduling problems represented with less significance as a whole in the past literature reviews. The purpose of this paper is to have an intensive study to clarify the development of cost-based scheduling and sequencing (CSS) by reviewing the work published over several parameters for improving the understanding in this field. Various parameters, such as scheduling models, algorithms, industries, journals, publishers, publication year, authors, countries, constraints, objectives, uncertainties, computational time, and programming languages and optimization software packages are considered. In this research, the literature review of CSS is done for thirteen years (2010-2022). Although CSS research originated in manufacturing, it has been observed that CSS research publications also addressed case studies based on health, transportation, railway, airport, steel, textile, education, ship, petrochemical, inspection, and construction projects. A detailed evaluation of the literature is followed by significant information found in the study, literature analysis, gaps identification, constraints of work done, and opportunities in future research for the researchers and experts from the industries in CSS

An exact algorithm for a Vehicle-and-Driver Scheduling Problem

This article introduces a combinatorial optimization problem that consists of assigning tasks to machines and operators, and sequencing the tasks assigned to each one. Two configurations exist. Machines alternate configurations, while the operators must start and finish the process in the same configuration. Moreover, machines and operator have limited capacities, The sequencing of the tasks must guarantee that each one is performed by a machine and an operator at the same time, and it is determined in order to minimize an overall cost function. Two critical aspects of the problem are the need of synchronizing the machine and the operator performing each task, and the need of minimizing the changeovers, which are pairs of tasks done consecutively by the same machine but by different operators. The problem is modeled as a vehicle routing problem with two types of vehicles and with two depots. We propose a mixed integer programming formulation, and introduce valid inequalities to strengthen its linear programming relaxation. We describe separation routines for these inequalities and design a branch-and-cut algorithm for the problem. The algorithm is tested on a set of benchmark instances showing that it is able to solve to optimality instances with up to 50 customers. (C) 2016 Elsevier Ltd. All rights reserved

VDSP instances

These are the 69 instances used in the article: B. Domínguez-Martín, I. Rodríguez-Martín, J.J. Salazar-González, 2017. An exact algorithm for a Vehicle-and-Driver Scheduling Problem. Computers & Operations Research, vol. 81, pp.247-256. https://doi.org/10.1016/j.cor.2016.12.022. The instance name gives information about the number of nodes, the number of vehicles of each type available at the depots, and the class of the instance. For example, n16-1-1-1-1a.dat is an instance with 16 nodes, including the depots, one vehicle of each type at each depot, and the class of the instance is a. These data files have the same format as the classical CVRP instances from the literature, but some new parameters have been added. That is: The first line contains the name of the instance. The next lines contain: TYPE = ‘CVRP’ because the instances are CVRP instances adapted to our problem. DIMENSION = the number of nodes, including the depots EDGE_WEIGHT_TYPE = ‘EUC_2D’ because we use the Eucliden distance for all our instances. The next lines contains the capacity of the vehicles of type 1 (CAPACITY Y) and the capacity of the vehicles of type 2 (CAPACITY X). VEHICLES1 and VEHICLES 2 denotes the number of vehicles of type 2 available at first and second depot, respectively. DRIVERS1 and DRIVERS2 denotes the number of vehicle of type 1 available ar first and seconds depot, respectively. The lines after NODE_COORD_SECTION contain the following information: n x y where n=customer number (1 and the last number correspond to the depots), x=x coordinate, y=y coordinate. The lines after DEMAND_SECTION show the following information: n d where n=customer number (0 and the last number correspond to the depots), d=customer demand(0 for the depots and 1 for the customers) Finally, DEPOT_SECTION1 and DEPOT_SECTION2 indicate that the first and the last node represent the first and the second depot, respectively

VDSP instances

These are the 69 instances used in the article: B. Domínguez-Martín, I. Rodríguez-Martín, J.J. Salazar-González, 2017. An exact algorithm for a Vehicle-and-Driver Scheduling Problem. Computers & Operations Research, vol. 81, pp.247-256. https://doi.org/10.1016/j.cor.2016.12.022. The instance name gives information about the number of nodes, the number of vehicles of each type available at the depots, and the class of the instance. For example, n16-1-1-1-1a.dat is an instance with 16 nodes, including the depots, one vehicle of each type at each depot, and the class of the instance is a. These data files have the same format as the classical CVRP instances from the literature, but some new parameters have been added. That is: The first line contains the name of the instance. The next lines contain: TYPE = ‘CVRP’ because the instances are CVRP instances adapted to our problem. DIMENSION = the number of nodes, including the depots EDGE_WEIGHT_TYPE = ‘EUC_2D’ because we use the Eucliden distance for all our instances. The next lines contains the capacity of the vehicles of type 1 (CAPACITY Y) and the capacity of the vehicles of type 2 (CAPACITY X). VEHICLES1 and VEHICLES 2 denotes the number of vehicles of type 2 available at first and second depot, respectively. DRIVERS1 and DRIVERS2 denotes the number of vehicle of type 1 available ar first and seconds depot, respectively. The lines after NODE_COORD_SECTION contain the following information: n x y where n=customer number (1 and the last number correspond to the depots), x=x coordinate, y=y coordinate. The lines after DEMAND_SECTION show the following information: n d where n=customer number (0 and the last number correspond to the depots), d=customer demand(0 for the depots and 1 for the customers) Finally, DEPOT_SECTION1 and DEPOT_SECTION2 indicate that the first and the last node represent the first and the second depot, respectively

VDSP instances

These are the 69 instances used in the article: B. Domínguez-Martín, I. Rodríguez-Martín, J.J. Salazar-González, 2017. An exact algorithm for a Vehicle-and-Driver Scheduling Problem. Computers & Operations Research, vol. 81, pp.247-256. https://doi.org/10.1016/j.cor.2016.12.022. The instance name gives information about the number of nodes, the number of vehicles of each type available at the depots, and the class of the instance. For example, n16-1-1-1-1a.dat is an instance with 16 nodes, including the depots, one vehicle of each type at each depot, and the class of the instance is a. These data files have the same format as the classical CVRP instances from the literature, but some new parameters have been added. That is: The first line contains the name of the instance. The next lines contain: TYPE = ‘CVRP’ because the instances are CVRP instances adapted to our problem. DIMENSION = the number of nodes, including the depots EDGE_WEIGHT_TYPE = ‘EUC_2D’ because we use the Eucliden distance for all our instances. The next lines contains the capacity of the vehicles of type 1 (CAPACITY Y) and the capacity of the vehicles of type 2 (CAPACITY X). VEHICLES1 and VEHICLES 2 denotes the number of vehicles of type 2 available at first and second depot, respectively. DRIVERS1 and DRIVERS2 denotes the number of vehicle of type 1 available ar first and seconds depot, respectively. The lines after NODE_COORD_SECTION contain the following information: n x y where n=customer number (1 and the last number correspond to the depots), x=x coordinate, y=y coordinate. The lines after DEMAND_SECTION show the following information: n d where n=customer number (0 and the last number correspond to the depots), d=customer demand(0 for the depots and 1 for the customers) Finally, DEPOT_SECTION1 and DEPOT_SECTION2 indicate that the first and the last node represent the first and the second depot, respectively