A note on relaxed gravity models

Relaxed gravity models, that is, gravity models with upper and lower bounds on the marginal totals, often have solutions with the property that the upper or lower bounds are satisfied with equality for most marginal totals. In this paper modifications are presented for the relaxed gravity models, which overcome this unwanted model property. The paper contains illustrative examples with data from the county of O�stergo�tland, Sweden.

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

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

Gravity models with multiple objectives-- Theory and applications

The gravity model has been widely used to predict trip matrices in transportation planning, both as a descriptive and an optimizing model. In this paper we present multiobjective programming formulations of the gravity model. The models use the concept of entropy, both as a measure of interactivity in the system, and as a distance measure, for measuring the distance from a reference or target point suggested by the planner. We also present gravity model formulations which do not require consistent estimates for the demand and supply in the different sites. These relaxed multiobjective gravity models include objectives for the demands and supplies, where the distance from some a priori given values is measured in entropy terms. The use of the models is illustrated on 1975 census data from the county of Östergötland, Sweden.

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