Index tracking with fixed and variable transaction costs

Index tracking is a form of passive portfolio (fund) management that attempts to mirror the performance of a specific index and generate returns that are equal to those of the index, but without purchasing all of the stocks that make up the index. We present two mixed-integer linear programming formulations of this problem. In particular we explicitly consider both fixed and variable transaction costs. Computational results are presented for data sets drawn from major world markets.     

Linear Operators that Preserve Commuting Pairs of Nonnegative Real Matrices

A pair of n×n matrices (A, B) is called a commuting pair if AB=BA. We characterize the linear operators that preserve the set of commuting pairs of matrices over a subsemiring of nonnegative real numbers.     

Linear operators strongly preserving digraphs whose maximum cycle length

We characterize those linear operators L such that for all digraphsD,L(D) has maximal cycle length L if an only if D has maximum cycle length L. We do this for L =0 and L = 1, the cases L ≤2 having been done previously.     

Metaheuristics with disposal facility positioning for the waste collection VRP with time windows

This paper improves heuristic algorithms presented in Benjamin and Beasley (Comput Oper Res 37(12):2270–2280, 2010) for solving the waste collection vehicle routing problem with time windows, particularly the real life waste collection benchmark problems from Kim et al. (Comput Oper Res 33(12):3624–3642, 2006). These consist of ten test problems, involving up to 2,092 customers and 19 waste disposal facilities. The main difference between this paper and Benjamin and Beasley (Comput Oper Res 37(12):2270–2280, 2010) is that here we use a disposal facility positioning (DFP) procedure to evaluate routes for our algorithms. Since the problem involves multiple disposal facilities, the objective of DFP is to choose the best disposal facilities to go on the vehicle route. Computational results indicate that our algorithms with DFP produce substantially better quality routes than previous approaches in the literature.     

O.R. Education — A Survey of Young O.R. Workers

This paper presents the results of a survey into O.R. education that was conducted with the help of those attending the Young O.R. Conference (YOR II) held at Nottingham University in March 1982. The results of a workshop debate held at the conference into the direction of O.R. education are also discussed.The conclusions drawn are that O.R. education in this country appears to be quite successful but that it is failing to deal satisfactorily with a number of issues. These issues relate to keeping up-to-date with changes in computer technology and their impact upon O.R. workers; the teaching of methodology to deal with ill-defined problems; preparation for the political and working environment of organizations; and the fostering of desirable personal characteristics.     

Algorithms for Unconstrained Two-Dimensional Guillotine Cutting

In this paper we consider the unconstrained, two-dimensional, guillotine cutting problem. This is the problem that occurs in the cutting of a number of rectangular pieces from a single large rectangle, so as to maximize the value of the pieces cut, where any cuts that are made are restricted to be guillotine cuts.We consider both the staged version of the problem (where the cutting is performed in a number of distinct stages) and the general (non-staged) version of the problem.A number of algorithms, both heuristic and optimal, based upon dynamic programming are presented. Computational results are given for large problems.     

Linear transformations on matrices: The invariance of commuting pairs of matrices

Let L be a linear transformation on the set of all n×n matrices over an algebraically closed field of characteristic 0. It is shown that if AB=BA implies L(A)L(B)=L(B)L(A) and if either L is nonsingular or the implication in the hypothesis can also be reversed, then L is a sum of a scalar multiple of a similarity transformation and a linear functional times the identity transformation.     

Boolean-rank-preserving operators and Boolean-rank-1 spaces

We study the extent to which certain theorems on linear operators on field-valued matrices carry over to linear operators on Boolean matrices. We obtain analogues and near analogues of several such theorems. One of these leads us to consider linear spaces of m × n Boolean matrices whose nonzero members all have Boolean rank 1. We obtain a structure theorem for such spaces that enables us to determine the maximum Boolean dimension of such spaces and their maximum cardinality.