This paper studies a variant of the unit-demand Capacitated Vehicle Routing Problem, namely the Balanced Vehicle Routing Problem, where each route is required to visit a maximum and a minimum number of customers. A po...
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This paper studies a variant of the unit-demand Capacitated Vehicle Routing Problem, namely the Balanced Vehicle Routing Problem, where each route is required to visit a maximum and a minimum number of customers. A polyhedral analysis for the problem is presented, including the dimension of the associated polyhedron, description of several families of facet-inducing inequalities and the relationship between these inequalities. The inequalities are used in a branch-and-cut algorithm, which is shown to computationally outperform the best approach known in the literature for the solution of this problem. (C) 2018 Elsevier B.V. All rights reserved.
Multi-compartment vehicle routing problems arise in a variety of problem settings in which different product types have to be transported separated from each other. In this paper, a problem variant which occurs in the...
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Multi-compartment vehicle routing problems arise in a variety of problem settings in which different product types have to be transported separated from each other. In this paper, a problem variant which occurs in the context of glass waste recycling is considered. In this problem, a set of locations exists, each of which offering a number of containers for the collection of different types of glass waste (e.g. colorless, green, brown glass). In order to pick up the contents from the containers, a fleet of homogeneous disposal vehicles is available. Individually for each disposal vehicle, the capacity can be discretely separated into a limited number of compartments to which different glass waste types are assigned. The objective of the problem is to minimize the total distance to be travelled by the disposal vehicles. For solving this problem to optimality, a branch-and-cut algorithm has been developed and implemented. Extensive numerical experiments have been conducted in order to evaluate the algorithm and to gain insights into the problem structure. The corresponding results show that the algorithm is able to solve instances with up to 50 locations to optimality and that it reduces the computing time by 87% compared to instances from the literature. Additional experiments give managerial insights into the use of different variants of compartments with flexible sizes.
The problem of maintenance scheduling and staffing at an aircraft heavy maintenance service company is studied. The objective is to establish an integrated aircraft maintenance schedule and maintenance technicians'...
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ISBN:
(纸本)9781450361033
The problem of maintenance scheduling and staffing at an aircraft heavy maintenance service company is studied. The objective is to establish an integrated aircraft maintenance schedule and maintenance technicians' rosters to fulfil different maintenance requests while minimizing the overall tardiness cost and labor cost. Upon receiving the maintenance requests, the hangar planner has to determine if the maintenance company is capable to serve the aircraft within the planning period, then allocate the parking stands and staying time of each aircraft in the hangar for the subsequent maintenance operations. Due to the complexity of the combinatorial problem, the commercial solver using branch-and-bound algorithm is incapable to tackle with the medium-sized instance within reasonable time. To enhance the computational efficiency, a framework of branch-and-cut algorithm is proposed in this paper, aiming to decompose the original model and tighten the lower bound of the original problem by the effective cuts. The concept of combinatorial benders' decomposition algorithm is adopted in the development of algorithm.
The Team Orienteering Problem aims at maximizing the total amount of profit collected by a fleet of vehicles while not exceeding a predefined travel time limit on each vehicle. In the last years, several exact methods...
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The Team Orienteering Problem aims at maximizing the total amount of profit collected by a fleet of vehicles while not exceeding a predefined travel time limit on each vehicle. In the last years, several exact methods based on different mathematical formulations were proposed. In this paper, we present a new two-index formulation with a polynomial number of variables and constraints. This compact formulation, reinforced by connectivity constraints, was solved by means of a branch-and-cut algorithm. The total number of instances solved to optimality is 327 of 387 benchmark instances, 26 more than any previous method. Moreover, 24 not previously solved instances were closed to optimality.
In this paper, we propose a branch-and-cut algorithm for solving a nonconvex quadratically constrained quadratic programming (QCQP) problem with a nonempty bounded feasible domain. The problem is first transformed int...
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In this paper, we propose a branch-and-cut algorithm for solving a nonconvex quadratically constrained quadratic programming (QCQP) problem with a nonempty bounded feasible domain. The problem is first transformed into a linear conic programming problem, and then approximated by semidefinite programming problems over different intervals. In order to improve the lower bounds, polar cuts, generated from corresponding cut-generation problems, are embedded in a branch-and-cut algorithm to yield a globally epsilon(r)-epsilon(z)-optimal solution (with respect to feasibility and optimality, respectively) in a finite number of iterations. To enhance the computational speed, an adaptive branch-and-cut rule is adopted. Numerical experiments indicate that the number of explored nodes required for solving QCQP problems can be significantly reduced by employing the proposed polar cuts.
The problem of maintenance scheduling and staffing at an aircraft heavy maintenance service company is studied. The objective is to establish an integrated aircraft maintenance schedule and maintenance technicians'...
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The problem of maintenance scheduling and staffing at an aircraft heavy maintenance service company is studied. The objective is to establish an integrated aircraft maintenance schedule and maintenance technicians' rosters to fulfil different maintenance requests while minimizing the overall tardiness cost and labor cost. Upon receiving the maintenance requests, the hangar planner has to determine if the maintenance company is capable to serve the aircraft within the planning period, then allocate the parking stands and staying time of each aircraft in the hangar for the subsequent maintenance operations. Due to the complexity of the combinatorial problem, the commercial solver using branch-andbound algorithm is incapable to tackle with the medium-sized instance within reasonable time. To enhance the computational efficiency, a framework of branch-and-cut algorithm is proposed in this paper, aiming to decompose the original model and tighten the lower bound of the original problem by the effective cuts. The concept of combinatorial benders' decomposition algorithm is adopted in the development of algorithm.
In many supply chain scenarios in which short lifespan products are considered, production and transportation decisions must be made in a coordinated manner with no inventory stage. Hence, a solution to this problem c...
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In many supply chain scenarios in which short lifespan products are considered, production and transportation decisions must be made in a coordinated manner with no inventory stage. Hence, a solution to this problem conveys information about production starting times of each product lot at facility and delivery times of the lots to various customer-sites located in different geographic regions. In this paper, we study a variant of the problem that single product with limited shelf life is produced at single facility. Once produced, production lot is directly distributed to the customers with non-ignorable transportation time by single vehicle having limited capacity before the lifespan. Objective is to determine the minimum time required to produce and deliver all customer demands. To this end, we develop a branch-and-cut (B&C) algorithm using several valid inequalities adopted from the existing literature to improve lower bounds and applying a local search based on simulated annealing approach to improve upper bounds. On test problems available in the literature, we evaluate the performance of the B&C algorithm. Results show the promising performance of the B&C algorithm.
In this paper we study the profitable windy rural postman problem. This is an arc routing problem with profits defined on a windy graph in which there is a profit associated with some of the edges of the graph, consis...
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In this paper we study the profitable windy rural postman problem. This is an arc routing problem with profits defined on a windy graph in which there is a profit associated with some of the edges of the graph, consisting of finding a route maximizing the difference between the total profit collected and the total cost. This problem generalizes the rural postman problem and other well-known arc routing problems and has real-life applications, mainly in snow removal operations. We propose here a formulation for the problem and study its associated polyhedron. Several families of facet-inducing inequalities are described and used in the design of a branch-and-cut procedure. The algorithm has been tested on a large set of benchmark instances and compared with other existing algorithms. The results obtained show that the branch-and-cut algorithm is able to solve large-sized instances optimally in reasonable computing times. (C) 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS). All rights reserved.
Let G(V,E) be a connected undirected graph and assume that an edge e=i,j∈E may be priced differently, at the different spanning trees of G that contain it. A cost ce applying when e is leaf implying, i.e., when e bel...
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The Covering Salesman Problem (CSP) is a generalization of the Traveling Salesman Problem in which the tour is not required to visit all vertices, as long as all vertices are covered by the tour. The objective of CSP ...
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The Covering Salesman Problem (CSP) is a generalization of the Traveling Salesman Problem in which the tour is not required to visit all vertices, as long as all vertices are covered by the tour. The objective of CSP is to find a minimum length Hamiltonian cycle over a subset of vertices that covers an undirected graph. In this paper, valid inequalities from the generalized traveling salesman problem are applied to the CSP in addition to new valid inequalities that explore distinct aspects of the problem. A branch-and-cut framework assembles exact and heuristic separation routines for integer and fractional CSP solutions. Computational experiments show that the proposed framework outperformed methodologies from literature with respect to optimality gaps. Moreover, optimal solutions were proven for several previously unsolved instances.
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