Emanuela Guerriero

Rolling-horizon and fix-and-relax heuristics for the parallel machine lot-sizing and scheduling problem with sequence-dependent set-up costs

In this paper we develop new rolling-horizon and fix-and-relax heuristics for the identical parallel machine lot-sizing and scheduling problem with sequence-dependent set-up costs. Unlike previous papers, our procedures are based on a compact formulation relying on the hypotheses of identical machines. This feature makes our approach suitable for large-scale applications (with hundreds of machines) arising in the textile and fiberglass industries. Moreover, our procedures are shown to provide a feasible solution for any feasible instance. Comparisons with lower bounds provided by a truncated branch-and-bound show that the gap between the best heuristic solution and the lower bound never exceeds 3%.

Robust scheduling of parallel machines with sequence-dependent set-up costs

In this paper we propose a robust approach for solving the scheduling problem of parallel machines with sequence-dependent set-up costs. In the literature, several mathematical models and solution methods have been proposed to solve such scheduling problems, but most of which are based on the strong assumption that input data are known in a deterministic way. In this paper, a fuzzy mathematical programming model is formulated by taking into account the uncertainty in processing times to provide the optimal solution as a trade-off between total set-up cost and robustness in demand satisfaction. The proposed approach requires the solution of a non-linear mixed integer programming (NLMIP), that can be formulated as an equivalent mixed integer linear programming (MILP) model. The resulting MILP model in real applications could be intractable due to its NP-hardness. Therefore, we propose a solution method technique, based on the solution of an approximated model, whose dimension is remarkably reduced with respect to the original counterpart. Numerical experiments conducted on the basis of data taken from a real application show that the average deviation of the reduced model solution over the optimum is less than 1.5%.

Analysis and Branch-and-Cut Algorithm for the Time-Dependent Travelling Salesman Problem

Given a graph whose arc traversal times vary over time, the time-dependent travelling salesman problem (TDTSP) consists in finding a Hamiltonian tour of least total duration covering the vertices of the graph. The contribution of this paper is twofold. First, we describe a lower and upper bounding procedure that requires the solution of a simpler (yet NP-hard) asymmetric travelling salesman problem (ATSP). In addition, we prove that this ATSP solution is optimal for the TDTSP if all the arcs share a common congestion pattern. Second, we formulate the TDTSP as an integer linear programming model for which valid inequalities are devised. These inequalities are then embedded into a branch-and-cut algorithm that is able to solve instances with up to 40 vertices.

Fix and Relax Heuristic for a Stochastic Lot-Sizing Problem

This paper addresses a particular stochastic lot-sizing and scheduling problem. The evolution of the uncertain parameters is modelled by means of a scenario tree and the resulting model is a multistage stochastic mixed-integer program. We develop a heuristic approach that exploits the specific structure of the problem. The computational experiments carried out on a large set of instances have shown that the approach provides good quality solutions in a reasonable amount of time.

Parallel tabu search for a pickup and delivery problem under track contention

This article introduces the Pickup and Delivery Problem under Track Contention, a particular vehicle routing problem in which loads have to be transported between origin-destination pairs by means of vehicles travelling along a capacitated network. Two sequential heuristics and a parallel tabu search are proposed. Computational experiments show that the parallel tabu search is able to find much better solutions than the sequential procedures, although this comes at the expense of a higher computing time.

A Note on the Ichoua, Gendreau, and Potvin (2003) Travel Time Model

In this paper we exploit some properties of the travel time model proposed by Ichoua, Gendreau, and Potvin [Ichoua S, Gendreau M, Potvin J-Y (2003) Vehicle dispatching with time-dependent travel times. Eur. J. Oper. Res. 144:379--396], on which most of the current time-dependent vehicle-routing literature relies. First, we prove that any continuous piecewise-linear travel time model, satisfying the FIFO property, can be generated by an appropriate model. We also show that the model parameters can be obtained by solving a system of linear equations for each arc. Then such parameters are proved to be nonnegative, which allows us to interpret them as (dummy) speeds. Finally, we illustrate the procedure through a numerical example. As a by-product, we are able to link the travel time models of a road graph and the associated complete graph over which vehicle-routing problems are usually formulated.

Simultaneous personnel and vehicle shift scheduling in the waste management sector

Urban waste management is becoming an increasingly complex task, absorbing a huge amount of resources, and having a major environmental impact. The design of a waste management system consists in various activities, and one of these is related to the definition of shift schedules for both personnel and vehicles. This activity has a great incidence on the tactical and operational cost for companies. In this paper, we propose an integer programming model to find an optimal solution to the integrated problem. The aim is to determine optimal schedules at minimum cost. Moreover, we design a fast and effective heuristic to face large-size problems. Both approaches are tested on data from a real-world case in Southern Italy and compared to the current practice utilized by the company managing the service, showing that simultaneously solving these problems can lead to significant monetary savings.

MIP neighborhood synthesis through semantic feature extraction and automatic algorithm configuration

We propose an Automatic Neighborhood Design algorithm.The procedure relies on the extraction of semantic features from a MIP model.The algorithm is assessed on four well-known combinatorial optimization problems. The definition of a good neighborhood structure on the solution space is a key step when designing several types of heuristics for Mixed Integer Programming (MIP). Typically, in order to achieve efficiency in the search, the neighborhood structures need to be tailored not only to the specific problem but also to the peculiar distribution of the instances to be solved (reference instance population). Nowadays, this is done by human experts through a time-consuming process comprising: (a) problem analysis, (b) literature scouting and (c) experimentation. In this paper, we illustrate an Automatic Neighborhood Design algorithm that mimics steps (a) and (c). Firstly, the procedure extracts some semantic features from a MIP compact model. Secondly, these features are used to derive automatically some neighborhood design mechanisms. Finally, the proper mix of such mechanisms is sought through an automatic configuration phase performed on a training set representative of the reference instance population. When assessed on four well-known combinatorial optimization problems, our automatically-generated neighborhoods outperform state-of-the-art model-based neighborhoods with respect to both scalability and solution quality.

A lower bound for the quickest path problem

Abstract The point-to-point quickest path problem is a classical network optimization problem with numerous applications, including that of computing driving directions. In this paper, we define a lower bound on the time-to-target which is both accurate and fast to compute. We show the potential of this bound by embedding it into an A⁎ algorithm. Computational results on three large European metropolitan road networks, taken from the OpenStreetMap database, show that the new lower bound allows us to achieve an average reduction of 14.36%. This speed-up is valuable for a typical web application setting, where a server needs to answer a multitude of quickest path queries at the same time. Even greater computing time reductions (up to 28.06%) are obtained when computing paths in areas with moderate speeds, e.g. historical city centers.

Path and speed optimization for conflict-free pickup and delivery under time windows

This article introduces a variant of the conflict-free pickup and delivery problem with time windows in which speeds can be regulated. The problem arises in several areas of transportation and logistics including routing and scheduling of automated guided vehicles in port terminals and coordination of unmanned aerial vehicles in controlled airspace. A particular aspect of this problem is that at most one vehicle can traverse an arc of the transportation network at any time. The problem studied in this paper is to determine the vehicle paths and speeds on each arc of the path in such a way that no conflicts arise, the time windows are met, and the total energy consumption is minimized. A branch-and-bound algorithm is described in which a lower bound is obtained by solving a separable nonlinear problem in quadratic time. If the solution of the relaxation is not conflict free, a set of space-based and time-based branching constraints are generated to resolve the detected conflicts. Computational experiments ...