An algorithm is given which finds all optimal solutions, for a given set of criteria, to political redistricting problems. Using "population units" as indivisible elements, the first phase generates all feasible districts, where feasibility indicates contiguity, compactness and limited...

There is given a finite set I and a family of subsets of I. We consider the problem of determining a minimum cardinality subfamily that is a partition of I. A branch-and-bound algorithm is presented. The bounds are obtained by determining chain decompositions of directed acyclic graphs. The...

Dynamic programming algorithms are developed for optimal capital allocation subject to budget constraints. We extend the work of Weingartner [Weingartner, H. M. 1966. Capital budgeting of interrelated projects: Survey and synthesis. Management Sci. 12(7, March) 485-516.] and Weingartner and Ness...

Redistricting, the redrawing of congressional district boundaries within the states, may occur every 10 years on the basis of the population census. Many redistricting plans are designed with partisan politics in mind, resulting in disputes and forcing judges to intervene. We address this...

In the course of the deliberations of the 1977 Lanchester Prize Committee, Alan J. Goldman brought to our attention an error in the proof of Lemma 1 of our paper (Cornuejols, G., M. L. Fisher, G. L. Nemhauser. 1977. Location of bank accounts to optimize float: an analytic study of exact and...

An algorithm, based on finding a shortest route in a finite directed network, is given for the assembly line balancing problem. Arc lengths are such that it is sufficient to find any path from the origin to destination node containing a minimal number of arcs. Computational results are presented...

A model is developed for planning the intake of employees as a function of time in the face of varying demand for service. The problem is complicated by resignations which, in part, depend on the intake. The model is solved by dynamic programming using a form of successive approximations to...

The number of days required to clear a check drawn on a bank in city j depends on the city i in which the check is cashed. Thus, to maximize its available funds, a company that pays bills to numerous clients in various locations may find it advantageous to maintain accounts in several...