Cristiano Arbex Valle

Heuristic and exact algorithms for a min-max selective vehicle routing problem

In this work, we investigate a vehicle routing problem where not all clients need to be visited and the goal is to minimize the longest vehicle route. We propose two exact solution approaches for solving the problem: a Branch-and-cut (BC) algorithm and a Local Branching (LB) method that uses BC as its inner solver. Our computational experience indicates that, in practice, the problem is difficult to solve, mainly when the number of vehicles grows. In addition to the exact methods, we present a heuristic that relies on GRASP and on the resolution of a restricted integer program based on a set covering reformulation for the problem. The heuristic was capable of significantly improving the best solutions provided by BC and LB, in one tenth of the times taken by them to achieve their best upper bounds.

Exact algorithms for a selective Vehicle Routing Problem where the longest route is minimized

Abstract In this paper, we study a non-capacitated Vehicle Routing Problem (VRP) where not necessarily all clients need to be visited and the goal is to minimize the length of the longest vehicle route. An Integer Programming Formulation, a Branch-and-cut (BC) method and a Local Branching (LB) framework that uses BC as the inner solver are presented. Sharper upper bounds are obtained by LB, when the same time limit was imposed on the execution times of both approaches. Our results also suggest that the min-max nature of the objective function combined with the fact that not all vertices need to be visited make such problem very difficult to solve.

Optimally solving the joint order batching and picker routing problem

In this work we investigate the problem of order batching and picker routing in storage areas. These are labour and capital intensive problems, often responsible for a substantial share of warehouse operating costs. In particular, we consider the case of online grocery shopping in which orders may be composed of dozens of items.

Market neutral portfolios

In this paper we consider the problem of constructing a market neutral portfolio. This is a portfolio of financial assets that (ideally) exhibits performance independent from that of an underlying market as represented by a benchmark index. We formulate this problem as a mixed-integer nonlinear program, minimising the absolute value of the correlation between portfolio return and index return. Our model is a flexible one that incorporates decisions as to both long and short positions in assets. Computational results, obtained using the software package Minotaur, are given for constructing market neutral portfolios for eleven different problem instances derived from universes defined by S&P international equity indices. We also compare our approach against an alternative approach based on minimising the absolute value of regression slope (the zero-beta approach).

Modelling and Solving the Joint Order Batching and Picker Routing Problem in Inventories

In this work we investigate the problem of order batching and picker routing in inventories. These are labour and capital intensive problems, often responsible for a substantial share of warehouse operating costs. In particular, we consider the case of online grocery shopping in which orders may be composed of dozens of items. To the best of our knowledge, no exact algorithms have been proposed for this problem. We therefore introduce three integer programming formulations for the joint problem of batching and routing, one of them involving exponentially many constraints to enforce connectivity requirements and two compact formulations based on network flows. For the former we implement a branch-and-cut algorithm which separates connectivity constraints. We built a test instance generator, partially based on publicly-available real world data, in order to compare empirically the three formulations.

An optimisation approach to constructing an exchange-traded fund

In this paper we consider the problem of deciding the portfolio of assets that should underlie an exchange-traded fund (ETF). We formulate this problem as a mixed-integer nonlinear program. We consider ETFs which have positive leverage with respect to their benchmark index and ETFs which have negative leverage (inverse, short, ETFs). Our formulation is a flexible one that incorporates decisions as to both long and short positions in assets, as well as including rebalancing and transaction cost. Computational results are given for problems, derived from universes defined by S&P international equity indices, involving up to 1,200 assets.

Factor neutral portfolios

In this paper, we consider the problem of constructing a factor neutral portfolio (FNP). This is a portfolio of financial assets that exhibits performance independent from a number of underlying factors. We formulate this problem as a mixed-integer linear program, minimising the time-averaged absolute value factor contribution to portfolio return. In this paper, we investigate both ordinary (least-squares, mean) regression and quantile regression, specifically median regression, to estimate factor coefficients. Computational results are given for constructing FNPs using stocks drawn from the Standard and Poor’s 500 index.

Exact solution approaches for the Multi-period Degree Constrained Minimum Spanning Tree Problem

Abstract The Multi-period Degree Constrained Minimum Spanning Tree Problem (MP-DCMSTP) is defined in terms of a finite discretized planning horizon, an edge weighted undirected graph G, degree bounds and latest installation dates assigned to the vertices of G. Since vertices must be connected to a root node no later than their latest installation dates and edges’ weights are non-increasing over time, the problem asks for optimally choosing and scheduling edges’ installation over the planning horizon, enforcing connectivity of the solution at each time period, so that in the end of the planning horizon, a degree constrained spanning tree of G is found. We show that the decision version of a combinatorial relaxation for the problem, that of finding a Multi-period Minimum Spanning Tree Problem (MP-MSTP), is NP-Complete. We propose a new integer programming formulation for MP-DCMSTP that is at least as good as the multi-commodity flow formulation in the literature. We also introduce some new valid inequalities which allowed our strengthened formulation to produce the strongest known bounds to date. Two MP-DCMSTP exact algorithms exploring the strengthened formulation are introduced here. One of them, RCBC, is a hybrid method involving two phases, the first being a Lagrangian Relax-and-cut method that works as a pre-processor procedure to the second phase, a Branch-and-cut algorithm. The other approach, SRCBC, uses RCBC to solve a sequence of smaller MP-DCMSTP instances generated from the original one in the hope of solving the latter faster. Our computational results indicate that SRCBC solved more instances to proven optimality, generally in one fourth of the time taken by RCBC to solve similar instances. For those instances left unsolved by both, SRCBC also provided much better feasible solutions within the same CPU time limit.

Novel approaches for portfolio construction using second order stochastic dominance

In the last decade, a few models of portfolio construction have been proposed which apply second order stochastic dominance (SSD) as a choice criterion. SSD approach requires the use of a reference distribution which acts as a benchmark. The return distribution of the computed portfolio dominates the benchmark by the SSD criterion. The benchmark distribution naturally plays an important role since different benchmarks lead to very different portfolio solutions. In this paper we describe a novel concept of reshaping the benchmark distribution with a view to obtaining portfolio solutions which have enhanced return distributions. The return distribution of the constructed portfolio is considered enhanced if the left tail is improved, the downside risk is reduced and the standard deviation remains within a specified range. We extend this approach from long only to long-short strategies which are used by many hedge fund and quant fund practitioners. We present computational results which illustrate (1) how this approach leads to superior portfolio performance (2) how significantly better performance is achieved for portfolios that include shorting of assets.