A Note on the Ichoua et al (2003) Travel Time Model.

In this paper we exploit some properties of the travel time model proposed by Ichoua et al (2003), on which most of the current time-dependent vehicle routing literature relies. Firstly, we prove that any continuous piecewise lin- ear travel time model can be generated by an appropriate Ichoua et al (2003) 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 if the continuous piecewise linear travel time model satis- es the FIFO property, which allows 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

Recovering feasibility in real-time conflict-free vehicle routing

Conflict-Free Vehicle Routing Problems (CF-VRPs) arise in manufacturing, transportation and logistics facilities where Automated Guided Vehicles (AGVs) are utilized to move loads. Unlike \textit{Vehicle Routing Problems} arising in distribution management, CF-VRPs explicitly consider the limited capacity of the arcs of the guide path network to avoid collisions among vehicles. AGV applications have two peculiar features. First, the uncertainty affecting both travel times and machine ready times may result in vehicle delays or anticipations with respect to the fleet nominal plan. Second, the relatively high vehicle speed (in the order of one or two meters per second) requires vehicle plans to be revised in a very short amount of time (usually few milliseconds) in order to avoid collisions. In this paper we present fast exact algorithms to recover plan feasibility in real-time. In particular, we identify two corrective actions that can be implemented in real-time and formulate the problem as a linear program with the aim to optimize four common performance measures (total vehicle delay, total weighted delay, maximum route duration and total lateness). Moreover, we develop tailored algorithms which, tested on randomly generated instances of various sizes, prove to be three orders of magnitude faster than using off-the-shelf solvers

Probabilistic Model and Solution Algorithm for the Electricity Retailers in the Italian Market

The paper considers the problem of maximizing the profits of a retailer operating in the Italian electricity market. The problem consists in selecting the contracts portfolio and in defining the bidding strategy in the wholesales market while respecting the technical and regulatory constraints. A novel solution method based on a enhanced discovery of the search domain in the simulated annealing technique has been developed for its solution and a set of realistic test problems have been generated for its validation. The experimental results show that our method outperforms the standard simulated annealing by an improvement gap of 20,48% in average

On path ranking in time-dependent graphs

In this paper we study a property of time-dependent graphs, dubbed "path ranking invariance''. Broadly speaking, a time-dependent graph is "path ranking invariant'' if the ordering of its paths (w.r.t. travel time) is independent of the start time. In this paper we show that, if a graph is path ranking invariant, the solution of a large class of time-dependent vehicle routing problems can be obtained by solving suitably defined (and simpler) time-independent routing problems. We also show how this property can be checked by solving a linear program. If the check fails, the solution of the linear program can be used to determine a tight lower bound. In order to assess the value of these insights, the lower bounds have been embedded into an enumerative scheme. Computational results on the time-dependent versions of the extit{Travelling Salesman Problem} and the extit{Rural Postman Problem} show that the new findings allow to outperform state-of-the-art algorithms

On path ranking in time-dependent graphs

In this paper we study a property of time-dependent graphs, dubbed path ranking invariance. Broadly speaking, a time-dependent graph is path ranking invariant if the ordering of its paths (w.r.t. travel time) is independent of the start time. In this paper we show that, if a graph is path ranking invariant, the solution of a large class of time-dependent vehicle routing problems can be obtained by solving suitably defined (and simpler) time-independent routing problems. We also show how this property can be checked by solving a linear program. If the check fails, the solution of the linear program can be used to determine a tight lower bound. In order to assess the value of these insights, the lower bounds have been embedded into an enumerative scheme. Computational results on the time-dependent versions of the \textit{Travelling Salesman Problem} and the \textit{Rural Postman Problem} show that the new findings allow to outperform state-of-the-art algorithms.Comment: 28 pages, 2 figure

An exact solution to the TLP problem in a NC Machine

This paper considers a job sequencing problem for a single numerical controlled machining center. It is assumed that all the considered jobs must be processed on a single machine provided with a tool magazine with C positions, that no job requires more than C tools to be completely machined and that the tools may be loaded and unloaded from the tool magazine only when the machining operations for each job are completed. The decisional problem is referred to as the tool loading problem (TLP) and it determines the jobs machining sequence as well as the tools to load in the machine tool magazine before the machining operations on each job may start. In industrial cases where the tool switching time is both significant relative to job processing time and proportional to the number of tool switches, the performance criterion is the minimization of the number of tool switches. This paper demonstrates that the TLP is a symmetric sequencing problem. The authors enrich a branch-and-bound algorithm proposed in literature for the TLP with the new symmetric formulation. Computational experiments show the significant improvement obtained by the novel symmetric formulation of the TLP

The multi-period pp-center problem with time-dependent travel times

This paper deals with an extension of the $p$-center problem, in which arc traversal times vary over time, and facilities are mobile units that can be relocated multiple times during the planning horizon. We investigate the relationship between this problem and its single-period counterpart. We also derive some properties and a special case. The insight gained with this analysis is then used to devise a two-stage heuristic. Computational results on instances based on the Paris (France) road graph indicate that the algorithm is capable of determining good-quality solutions in a reasonable execution time

Robust Batch Process Scheduling in Pharmaceutical Industries: A Case Study

none4openT Adamo, G Ghiani, AD Grieco, E GuerrieroAdamo, T; Ghiani, G; Grieco, Ad; Guerriero,

A solution for a real-time stochastic capacitated vehicle routing problem with time windows

Real-time distribution planning presents major difficulties when applied to large problems. Commonly, this planning is associated to the capacitated vehicle routing problem with time windows (CVRPTW), deeply studied in the literature. In this paper we propose an optimization system developed to be integrated with an existing Enterprise Resource Planning (ERP) without causing major disruption to the current distribution process of a company. The proposed system includes: a route optimization module, a module implementing the communications within and to the outside of the system, a non-relational database to provide local storage of information relevant to the optimization procedure, and a cartographic subsystem. The proposed architecture is able to deal with dynamic problems included in the specification of the project, namely: arrival of new orders while already optimizing as well as locking and closing of routes by the system administrator. A back-office graphical interface was also implemented and some results are presented