Intersections of Corner Polyhedra

The aim of this paper is to present some results concerning the intersection of a generalized form of corner polyhedra and its relation to the integer polyhedron for the general linear integer programming problem. In particular a theorem proved earlier concerning such intersections for low dimensional problems will be proved here as a special case of theorems for higher dimensions

Optimizing a Decision-Maker's Preferences with a Minimum Amount of Information

The aim here is to obtain the minimum amount of information required from a decision maker in order to find his best alternative in a given problem

A Group Cut for the Traveling Salesman Problem

Held and Karp have shown how the good minimum spanning tree algorithm may be used in solving the Traveling Salesman problem by means of a generalized linear program involving l-trees. The size and structure of their dual problem are introduced. From this analysis a group cut is produced and methods by which this may resolve any duality gap are presented

A Job Shop Assignment Problem with Queuing Costs

Consider an assignment problem in which jobs are to be assigned to machines in such a way as to minimize the total cost of manufacture. In addition, there is, for each job, a queuing cost which is proportional to the time spent before completion. Each job takes a unit length of time to be completed once work is started on it by a machine. It will be shown that this problem may be formulated as a linear program whose optimal solution will be integral

Conditional Utility Independence and its Application to Time Streams

The evaluation of time streams is traditionally performed by some form of discounting and even the more sophisticated approaches require some form of independence assumptions between consequences in adjacent periods. Frequently a decision maker's preferences for consequences in a given period will depend on the particular outcome in the previous and/or following period. This paper gives a simple functional form which enables such preferences to be explicitly included in a utility function for time streams

On a Network Algorithm of Butrimenko

This paper considers an algorithm suggested by A. Butrimenko for a network communications problem. It is shown here that the algorithm converges, and to the optimal solution, when started from a particular initial solution

A Decision Analysis of Objectives for a Forest Pest Problem

The forests of Eastern Canada are subject to periodic outbreaks of a pest which devastates the trees causing major disruption to the logging industry. This paper gives details of a study to find a criterion by which management policy alternatives could be evaluated in conjunction with a simulation model of the forest. It describes the manner in which the important decision factors, or attributes, were determined and how a value function and a utility function were assessed over these attributes, taking into account the long time horizon involved of 50-100 years

Improved Bounds for Integer Programs: A Supergroup Approach

Recent work by Fisher and Shapiro has used Gomory's group theoretic methods together with Lagrange multipliers to obtain bounds for the optimal value of integer programs. Here it is shown how an extension of the associated abelian group to a supergroup can improve the bound without the artificiality of adding a cut. It is proved that there exists a finite group for which the dual ascent procedure of Fisher and Shapiro converges to the optimal integer solution. Constructive methods are given for finding this group. A worked example is included

Bounds for Generalized Integer Programs

Generalized linear programming problems have been well solved by column generation and dual ascent procedures. The same problems with the variables restricted to be integer have only been solved when all the coefficients are known explicitly. This paper finds lower bounds for the optimal value of such programs requiring only the implicit definition of the activities