Gianfranco Guastaroba

A survey on two-echelon routing problems

The delivery of freight from its origin to its destination is often managed through one or more intermediate facilities where storing, merging and consolidation activities are performed. This type of distribution systems is commonly called multi-echelon, where each echelon refers to one level of the distribution network. Multi-echelon distribution systems are often considered by public administrations when implementing their transportation and traffic planning strategies as well as by private companies in their distribution networks. City logistics and multi-modal transportation systems are the most cited examples of multi-echelon distribution systems. Two-echelon distribution systems are a special case of multi-echelon systems where the distribution network comprises two levels. This latter type of distribution systems has inspired an ever growing body of literature in the last few years. This paper provides an overview of two-echelon distribution systems where routes are present at both levels. We consider three classes of problems: the two-echelon location routing problem, the two-echelon vehicle routing problem, and the truck and trailer routing problem. For each class we provide an introduction and survey the foremost related papers that have appeared in the operations research literature.

Kernel Search: An application to the index tracking problem

In this paper we study the problem of replicating the performances of a stock market index, i.e. the so-called index tracking problem, and the problem of out-performing a market index, i.e. the so-called enhanced index tracking problem. We introduce mixed-integer linear programming (MILP) formulations for these two problems. Furthermore, we present a heuristic framework called Kernel Search. We analyze and evaluate the behavior of several implementations of the Kernel Search framework to the solution of the index tracking problem. We show the effectiveness and efficiency of the framework comparing the performances of these heuristics with those of a general-purpose solver. The computational experiments are carried out using benchmark and newly created instances.

On the effectiveness of scenario generation techniques in single-period portfolio optimization

In single-period portfolio selection problems the expected value of both the risk measure and the portfolio return have to be estimated. Historical data realizations, used as equally probable scenarios, are frequently used to this aim. Several other parametric and non-parametric methods can be applied. When dealing with scenario generation techniques practitioners are mainly concerned on how reliable and effective such methods are when embedded into portfolio selection models. In this paper we survey different techniques to generate scenarios for the rates of return. We also compare the techniques by providing in-sample and out-of-sample analysis of the portfolios obtained by using these techniques to generate the rates of return. Evidence on the computational burden required by the different techniques is also provided. As reference model we use the Worst Conditional Expectation model with transaction costs. Extensive computational results based on different historical data sets from London Stock Exchange Market (FTSE) are presented and some interesting financial conclusions are drawn.

A heuristic for BILP problems: The Single Source Capacitated Facility Location Problem

In the Single Source Capacitated Facility Location Problem (SSCFLP) each customer has to be assigned to one facility that supplies its whole demand. The total demand of customers assigned to each facility cannot exceed its capacity. An opening cost is associated with each facility, and is paid if at least one customer is assigned to it. The objective is to minimize the total cost of opening the facilities and supply all the customers. In this paper we extend the Kernel Search heuristic framework to general Binary Integer Linear Programming (BILP) problems, and apply it to the SSCFLP. The heuristic is based on the solution to optimality of a sequence of subproblems, where each subproblem is restricted to a subset of the decision variables. The subsets of decision variables are constructed starting from the optimal values of the linear relaxation. Variants based on variable fixing are proposed to improve the efficiency of the Kernel Search framework. The algorithms are tested on benchmark instances and new very large-scale test problems. Computational results demonstrate the effectiveness of the approach. The Kernel Search algorithm outperforms the best heuristics for the SSCFLP available in the literature. It found the optimal solution for 165 out of the 170 instances with a proven optimum. The error achieved in the remaining instances is negligible. Moreover, it achieved, on 100 new very large-scale instances, an average gap equal to 0.64% computed with respect to a lower bound or the optimum, when available. The variants based on variable fixing improved the efficiency of the algorithm with minor deteriorations of the solution quality.

Linear Programming Models based on Omega Ratio for the Enhanced Index Tracking Problem

Modern performance measures differ from the classical ones since they assess the performance against a benchmark and usually account for asymmetry in return distributions. The Omega ratio is one of these measures. Until recently, limited research has addressed the optimization of the Omega ratio since it has been thought to be computationally intractable. The Enhanced Index Tracking Problem (EITP) is the problem of selecting a portfolio of securities able to outperform a market index while bearing a limited additional risk. In this paper, we propose two novel mathematical formulations for the EITP based on the Omega ratio. The first formulation applies a standard definition of the Omega ratio where it is computed with respect to a given value, whereas the second formulation considers the Omega ratio with respect to a random target. We show how each formulation, nonlinear in nature, can be transformed into a Linear Programming model. We further extend the models to include real features, such as a cardinality constraint and buy-in thresholds on the investments, obtaining Mixed Integer Linear Programming problems. Computational results conducted on a large set of benchmark instances show that the portfolios selected by the model assuming a standard definition of the Omega ratio are consistently outperformed, in terms of out-of-sample performance, by those obtained solving the model that considers a random target. Furthermore, in most of the instances the portfolios optimized with the latter model mimic very closely the behavior of the benchmark over the out-of-sample period, while yielding, sometimes, significantly larger returns.

Kernel search for the capacitated facility location problem

The Capacitated Facility Location Problem (CFLP) is among the most studied problems in the OR literature. Each customer demand has to be supplied by one or more facilities. Each facility cannot supply more than a given amount of product. The goal is to minimize the total cost to open the facilities and to serve all the customers. The problem is

An ILP-refined tabu search for the Directed Profitable Rural Postman Problem

\mathcal{NP}

A Tabu Search heuristic procedure in Markov chain bootstrapping

-hard. The Kernel Search is a heuristic framework based on the idea of identifying subsets of variables and in solving a sequence of MILP problems, each problem restricted to one of the identified subsets of variables. In this paper we enhance the Kernel Search and apply it to the solution of the CFLP. The heuristic is tested on a very large set of benchmark instances and the computational results confirm the effectiveness of the Kernel Search framework. The optimal solution has been found for all the instances whose optimal solution is known. Most of the best known solutions have been improved for those instances whose optimal solution is still unknown.

Modeling the Pre Auction Stage The Truckload Case

In transportation services, the costs are highly dependent on the opportunity to serve neighboring customers. In this paper we study the problem faced by a shipper that has to serve a set of customers with one internal vehicle and to outsource the service of some of them. The problem is to identify the set of customers to outsource with the goal of minimizing the sum of the traveling costs (routing costs) and the costs associated with the outsourced customers (penalty costs). As the problem can be expressed as the maximization of the difference between a profit gained from the served customers and the traveling cost, we call this problem the Directed Profitable Rural Postman Problem (DPRPP). We propose an ILP-refined tabu search algorithm that combines a tabu search scheme with an Integer Linear Programming (ILP) model. Computational experiments carried out on several sets of instances show the good performance of the proposed solution procedure.

Intermediate Facilities in Freight Transportation Planning: A Survey

Markov chain theory is proving to be a powerful approach to bootstrap finite states processes, especially where time dependence is non linear. In this work we extend such approach to bootstrap discrete time continuous-valued processes. To this purpose we solve a minimization problem to partition the state space of a continuous-valued process into a finite number of intervals or unions of intervals (i.e. its states) and identify the time lags which provide “memory” to the process. A distance is used as objective function to stimulate the clustering of the states having similar transition probabilities. The problem of the exploding number of alternative partitions in the solution space (which grows with the number of states and the order of the Markov chain) is addressed through a Tabu Search algorithm. The method is applied to bootstrap the series of the German and Spanish electricity prices. The analysis of the results confirms the good consistency properties of the method we propose.