Antonio Sforza

Solving a fuel delivery problem by heuristic and exact approaches

Abstract In this paper we study the case of a company that delivers different types of fuel to a set of fuel pumps. The company has one warehouse and supplies the pumps by a fleet of trucks with several tanks of differing capacities. The company’s aim is to satisfy the orders using the available resources (trucks and drivers) with the minimum total travel cost for delivery. The problem has been formulated as a Set Partitioning model, solved by a Branch-and-Price algorithm. A fast combinatorial heuristic was adopted both to find a good feasible solution very quickly and to provide an initial set of columns for the Branch-and-Price algorithm. Computational results are reported. The exact approach shows low computation time for the real instances provided by the company.

A metaheuristic for a two echelon location-routing problem

In this paper we consider the design problem of a two-echelon freight distribution system. The aim is to define the structure of a system optimizing the location and the number of two different kinds of facilities, the size of two different vehicle fleets and the related routes on each echelon. The problem has been modeled as a two-echelon location-routing problem (2E-LRP). A tabu-search heuristic efficiently combining the composing subproblems is presented. Results on small, medium and large size instances are reported.

An effective heuristic for large-scale capacitated facility location problems

The Capacitated Facility Location Problem (CFLP) consists of locating a set of facilities with capacity constraints to satisfy the demands of a set of clients at the minimum cost. In this paper we propose a simple and effective heuristic for large-scale instances of CFLP. The heuristic is based on a Lagrangean relaxation which is used to select a subset of “promising” variables forming the core problem and on a Branch-and-Cut algorithm that solves the core problem. Computational results on very large scale instances (up to 4 million variables) are reported.

A Cut and Branch Approach for the Capacitated p-Median Problem Based on Fenchel Cutting Planes

The capacitated p-median problem (CPMP) consists of finding p nodes (the median nodes) minimizing the total distance to the other nodes of the graph, with the constraint that the total demand of the nodes assigned to each median does not exceed its given capacity. In this paper we propose a cutting plane algorithm, based on Fenchel cuts, which allows us to considerably reduce the integrality gap of hard CPMP instances. The formulation strengthened with Fenchel cuts is solved by a commercial MIP solver. Computational results show that this approach is effective in solving hard instances or considerably reducing their integrality gap.

A penalty function heuristic for the resource constrained shortest path problem

Abstract The resource constrained shortest path problem (RCSP) consists of finding the shortest path between two nodes of an assigned network, with the constraint that traversing an arc of the network implies the consumption of certain limited resources. In this paper we propose a new heuristic for the solution of the RCSP problem in medium and large scale networks. It is based on the extension to the discrete case of the penalty function heuristic approach for the fast e -approximate solution of difficult large-scale continuous linear programming problems. Computational experience on test instances has shown that the proposed penalty function heuristic (PFH) is very effective in the solution of medium and large scale RCSP instances. For all the tests reported it provides very good upper bounds (in many cases the optimal solution) in less than 26 iterations, where each iteration requires only the computation of a shortest path.

A Steiner arborescence model for the feeder reconfiguration in electric distribution networks

In this paper we address the problem of finding the radial configuration of an electric distribution network that minimizes the total losses due to the Joule effect. We propose an interpretation of the feeder reconfiguration problem as a Steiner arborescence problem, formulated through a model with a separable quadratic objective function. The problem is then solved by a mixed-integer quadratic programming solver. Computational experience on test networks is reported, showing the effectiveness of the formulation.

Resource Constrained Shortest Path Problems in Path Planning for Fleet Management

In the management and control of a vehicle fleet on a road network, the problem arises of finding the best route in relation to the mission of the fleet and to the typology of freight or users. Sometimes the route has to be adapted not only to current traffic conditions, but also to the physical, geometric and functional attributes of the roads, related to their urban location and environmental characteristics.This problem is approached here through an extension of the classic Shortest Path problem, named Resource Constrained Shortest Path problem (RCSP), where the resources are related to the road link attributes, assumed as relevant to the specific planning problem. A classification scheme of these attributes is first proposed and RCSP is described and reviewed. Next, a General Resource Constrained Shortest Path problem (GRCSP) is defined, which can be found in all cases where it is necessary to plan, statically or dynamically, the path of a vehicle and to respect a set of constraints expressed in terms of parameters and indices associated with the roads on the network. For this general problem a model has been formulated and a Branch and Cut solution approach is proposed. Computational results obtained on test and real networks during the experimentation of a fleet with low emission vehicles are also given.

A decomposition approach for a very large scale optimal diversity management problem

Abstract.This paper focuses on the solution of the optimal diversity management problem formulated as a p-Median problem. The problem is solved for very large scale real instances arising in the car industry and defined on a graph with several tens of thousands of nodes and with several millions of arcs. The particularity is that the graph can consist of several non connected components. This property is used to decompose the problem into a series of p-Median subproblems of a smaller dimension. We use a greedy heuristic and a Lagrangian heuristic for each subproblem. The solution of the whole problem is obtained by solving a suitable assignment problem using a Branch-and-Bound algorithm.

Logical reduction tests for the p‐problem

Preprocessing plays a crucial role in solving combinatorial optimization problems. Itcan be realized through reduction tests which allow one to determine in advance the valuesthat a set of variables will take in the optimal solution, thus reducing the size of an instance.Reduction tests can be summarily classified in two main families: those based on reducedcosts and those based on logical implications. The first rely on reduced costs of the LinearProgramming problem associated to continuous relaxation. The second are based on thespecial features of the problem and on combinatorial techniques. In this paper, some effectivereduction tests for the p‐median problem are proposed, showing their impact on the size ofthe instances and on model formulation. Finally, some work perspectives to embed reductiontests into solution algorithms for the p‐median problem are pointed out.

An exact dynamic programming algorithm for large-scale unconstrained two-dimensional guillotine cutting problems

Abstract In the unconstrained two-dimensional cutting problems (U2DCP) small rectangular objects have to be extracted from a large rectangular sheet, with no limits on the number of small objects. The exact U2DCP solving approaches present in literature show some limits in tackling very large size instances, due to the high memory requirements. In this work we propose five improvements, three original and two derived from the literature, in order to overcome these limits and to reduce the computational burden of the knapsack function based U2DCP solving approaches. These improvements, based on proofed theoretical results, allow to reduce the search space and to avoid redundant solutions without loss of the feasible ones. The presented improvements, together with several computational refinements, are integrated in a new dynamic programming algorithm, which modifies the one by Russo et al. (2013 [16] ). The proposed algorithm has been experienced on test instances present in literature and compared with the best U2DCP solving approaches. The obtained results show that it significantly outperforms them and it determines the optimal solution of unsolved very large size instances.