Ronny Aboudi

Tabu Search for General Zero-One Integer Programs Using the Pivot and Complement Heuristic

Tabu search techniques have been applied to a wide class of optimization problems. Tabu search is a meta procedure that requires a subroutine to find local optima. In most examples of tabu search the subroutine used is problem specific. However, in order to apply tabu search successfully to general 0-1 integer programs, the subroutine must be general. The pivot and complement heuristic is a procedure that frequently finds feasible solutions for general 0-1 integer programs. In this paper we implement several elements of strategies proposed by tabu search method that result in general heuristics for 0-1 integer programs that could be included in an integer programming code. These heuristics employ the ZOOM/XMP implementation of the pivot and complement heuristic as a subroutine. Computational results indicate that these heuristics provide good bounds for many problems. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

A Synthesis of Tactical Fleet Planning Models for the Car Rental Industry

Daily tactical planning of the vehicle fleet is critical for a car rental business. In this decision-making process planners have to address the conflicting concerns of field management, namely, assuring adequate vehicle availability to satisfy customer demand while maintaining a high degree of utilization for each car in the fleet; this is achieved by the appropriate fleet deployment among car rental locations. This work was inspired by a series of problems encountered by the decision-makers of a major US car rental company. We first present the formulation of the tactical fleet planning model. Based on its structure, we decompose the model into a fleet deployment model and a transportation model. We develop optimal conditions for both subproblems and then we present a heuristic to reduce the gap from optimality for the complete model. We further present the application of the entire solution methodology via a case analysis for the State of Florida. Finally, we develop three extensions to the fleet deployment model to capture the cost of unsatisfied demand and fleet surplus, the service level, and a general price-demand function. We provide optimal closed-form conditions for all the extensions.

A mathematical programming model for the development of petroleum fields and transport systems

Abstract This paper describes the accomplishment of an operations research project concerning the development of petroleum fields and transport systems. All phases of the project are reported — the first contact with the client, the discussions that lead to the formulation of a mathematical programming model, the choice of solution techniques, and the computer implementation of a user-friendly system to be used by planners as a means of decision support.

Second-Degree Stochastic Dominance Decisions and Random Initial Wealth with Applications to the Economics of Insurance

It is known that if random prospect Y stochastically dominates prospect X by the second degree, then all risk-averse agents prefer to hold Y and some random initial wealth Z rather than X and the same initial wealth Z, if Z is statistically independent of both X and Y. We give more general conditions for the invariance of the stochastic dominance ordering to initial wealth to hold: that X be more positively dependent on Z than Y is, and that either X and Z or Y and Z be positively dependent. Applications to the choice of an insurance deductible and of insurance coverage are given.

Some facets for an assignment problem with side constraints

This paper presents a class of facet-defining inequalities for an assignment problem with the additional constraints that specified variables are required to be equal to each other. In a special case, the complete polyhedral description is given.

A facet generation and relaxation technique applied to an assignment problem with side constraints

Abstract We consider a solution method for combinatorial optimization problems based on a combination of Lagrangean relaxation and constraint generation techniques. The procedure is applied to a constrained assignment problem, where subsets of variables are specified, and variables belonging to the same subset must have the same value. The model can be applied to solve constrained job assignment or classroom assignment problems. The procedure we suggest requires only the solution of classical assignment subproblems. An illustrative numerical example is given.

A note on the Pivot and Complement heuristic for 0-1 programming problems

When solving large scale integer and mixed integer programming problems it is very important to find good feasible integer solutions at an early stage in the solution process. The Pivot and Complement heuristic is a procedure which very often generates good solutions at a relatively low computational cost. In this paper we demonstrate that repeated use of the Pivot and Complement heuristic with an additional objective function constraint, often gives a better solution than the one obtained in the first trial. We present some results obtained on a number of practical large scale problems of project sequencing type.

Second degree Pareto dominance

We present and discuss a binary relation aimed at the study of the re-distribution of income. We characterize, in a number of ways, the set of income allocations that can be reached from an initial allocation through a sequence of pair-wise equalizing transfers, where the sequence contains no flow of income from any donor to anyone else who ends up strictly richer than this donor himself ends up at the outcome of the entire sequence.

Transfer principles and relative inequality aversion a majorization approach

Abstract This paper characterizes two preorders over vectors, representing here income distributions, which, for the case of an order-preserving additive welfare function W =∑ 1 n u ( x i ), correspond to the increasing concave functions u which are more concave than u ( x )=ln x and than u ( x )=−1/ x , respectively. We provide a characterization of those W functions that is quite distinct from the one recently provided by Fleurbaey and Michel, Mathematical Social Sciences , 2001. The two sets of results are shown to be complementary.

Designing a Basic Income System; a Mathematical Programming Approach

There is an irreductible conflict between, on the one hand, the desire to allocate income in society in an equitable way and, on the other, the desire to alleviate poverty. The conflict materializes itself in the problem of designing a basic income (or negative income tax) system which requires formulating a workable compromise. This paper approaches the problem through solving a mathematical program whose utility-based objective function explicitly embodies both considerations. The solution describes a simple basic income system and its comparative statics indicate how the specification of the objective function leads to a more, or less, pro-poor solution.