Paolo Dell'Olmo

New Algorithms for Examination Timetabling

In examination timetabling a given set of examinations must be assigned to as few time slots as possible so as to satisfy certain side constraints and so as to reduce penalties deriving from proximity constraints. In this paper, we present new algorithms for this problem and report the results of an extensive experimental study. All our algorithms are based on local search and are compared with other existing implementations in the literature.

On finding dissimilar Pareto-optimal paths

The aim of the present paper is to provide a methodology for finding a set of alternative paths between an origin and a destination site on which routing one or a set of dangerous goods. Finding a set of paths allows one to equally distribute the total risk among the population exposed. The concept of equity of risk is here related to the concept of determining spatially dissimilar paths. We divide our approach into two phases. In the first phase we find a set of Pareto-Optimal paths between an origin and a destination, by implementing a multicriteria shortest path algorithm. In the second one, for each path previously found, and by using a geographical information system, we construct a Buffer Zone approximating the impact area of a material being released after an accident. Based on these Buffer Zones, a dissimilarity index between every pair of paths can be derived in order to find the most spatially different routes. We then compare our method with an iterative penalty method and discuss computational results based both on a real application and on test problems.

Multi-objective management in freight logistics: Increasing capacity, service level and safety with optimization algorithms

In this chapter, we introduce freight distribution logistic, discussing some statistics about future trends in this area. Basically, it appears that, even though there has been a slight increase in the use of rail and water transportation modes, there is room to obtain a more efficient use of the road mode, mainly not to increase air pollution (fossil-fuel combustion represents about 80% of the factors that jeopardize air quality). In order to be able to reach an equilibrium among different transportation modes, the entire supply chain has to be studied to install the appropriate service capacity and to define effective operational procedures to optimize the system performance. 1.1 Freight Distribution Logistic The way the governments and the economic world are now looking at transportation problems in general and at distribution logistic in particular has changed from past years. Europe, in particular, has adopted the so-called European Sustainable Development Strategy (SDS) in the European Council held in Gothenburg in June 2001. That was the opportunity to set out a coherent approach to sustainable development renewed in June 2006 to reaffirm the aim of continuous improvement of quality of life and economic growth through the efficient use of resources, and promoting the ecological and the social innovation potentials of the economy. Recently, in December 2007, the European Council insisted on the need to give priority to implementation measures. Paragraph 56 of Commission Progress Report of 22 October 2007 reads “. . . The EU must continue to work to move towards more sustainable trans-

Scheduling models for air traffic control in terminal areas

We propose a job-shop scheduling model with sequence dependent set-up times and release dates to coordinate both inbound and outbound traffic flows on all the prefixed routes of an airport terminal area and all aircraft operations at the runway complex. The proposed model is suitable for representing several operational constraints (e.g., longitudinal and diagonal separations in specific airspace regions), and different runway configurations (e.g., crossing, parallel, with or without dependent approaches) in a uniform framework. The complexity and the highly dynamic nature of the problem call for heuristic approaches. We propose a fast dynamic local search heuristic algorithm for the job-shop model suitable for considering one of the different performance criteria and embedding aircraft position shifting control technique to limit the controllers/pilots’ workload. Finally, we describe in detail the experimental analysis of the proposed model and algorithm applied to two real case studies of Milan-Malpensa and Rome-Fiumicino airport terminal areas.

Minimizing total completion time subject to release dates and sequence‐dependentprocessing times

We consider the problem of scheduling jobs with release dates and sequence‐dependentprocessing times on a single machine to minimize the total completion time. We show thatthis problem is equivalent to the Cumulative Traveling Salesman Problem with additionaltime constraints. For this latter problem, we give a dynamic programming formulation fromwhich lower bounds are derived. Two heuristic algorithms are proposed. Performanceanalysis of both lower bounds and heuristics on randomly generated test problems are carriedout. Moreover, the application of the model and algorithms to the real problem of sequencinglanding aircraft in the terminal area of a congested airport is analyzed. Computational resultson realistic data sets show that heuristic solutions can be effective in practical contexts.

Novel Local-Search-Based Approaches to University Examination Timetabling

Examination timetabling assigns examinations to a given number of time slots so that there are no conflicts. A conflict occurs if a student has to take more than one examination at the same time, or when the number of students that must take an exam exceeds the capacity of the classroom assigned. The objective is to minimize penalties from proximity constraints. We present new algorithms based on local search and report on an extensive experimental study. We consider also a variant where the concern is to produce conflict-free timetables minimizing the number of time slots, regardless of how close exams appear in the schedule. The algorithms proposed also manage the trade-off between the two objective functions and produce the best results on several standard benchmark instances, compared to the best existing algorithms.

A new hierarchical architecture for Air Traffic Management: Optimisation of airway capacity in a Free Flight scenario

We describe a new two-level hierarchical architecture for air traffic management problems with corresponding mathematical models. The first level represents the air route network, and its solutions provide the air traffic flows on each arc of the network. This level interacts with the second one, which represents the single airway and its own air traffic flows. This latter model allows us to assign the optimal air traffic route to each aircraft and to optimise the airways capacity. Furthermore, for the airway optimisation model we have also carried out a computational analysis, providing both exact and heuristic solutions, for problem instances based on real data. These are obtained with the Cplex solver exploiting the mixed integer mathematical formulation and with a proposed heuristic algorithm for problems of larger size, respectively. The heuristic solutions obtained are within a maximum gap of 13% from the LP relaxation.

Scheduling multiprocessor tasks on a dynamic configuration of dedicated processors

In the classical scheduling theory, it is widely assumed that a task can be processed by only one processor at a time. With the rapid development of technology, this assumption is no longer valid. In this work we present a problem of scheduling tasks, each of which requires for its processing a set of processors simultaneously and which can be executed on several alternative sets of processors. Scheduling algorithms based on dynamic and linear programming are presented that construct minimum length non-preemptive and preemptive schedules, respectively. Results of computational experiments are also reported.

Flow Shop No-Wait Scheduling With Sequence Dependent Setup Times And Release Dates

We consider the problem of scheduling no-wait jobs, with release dates and sequence dependent setup times, on a flow shop to minimize the makespan. We show that this problem is equivalent to the asymmetric traveling salesman problem with additional visiting time constraints. For this latter problem we give a mathematical formulation and two lower bounds. Two heuristic algorithms for solving the scheduling problem are proposed. Performance analysis of both lower bounds and heuristics on randomly generated test problems are carried out.

A 13/12 approximation algorithm for bin packing with extendable bins

Abstract A set of items has to be assigned to a set of bins with size one. If necessary, the size of the bins can be extended. The objective is to minimize the total size, i.e., the sum of the sizes of the bins. The Longest Processing Time heuristic is applied to this NP-hard problem. For this approximation algorithm we prove a worst-case bound of 13 12 which is shown to be tight when the number of bins is even.