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Group consensus is an important method for making business decisions. In this paper, the consensus process is defined as a dynamic and interactive group decision process, which is coordinated by a moderator who helps the experts to gradually move their opinions closer to each other. This paper describes the importance of group consensus and the need to minimize the cost of this process. Furthermore, this paper describes the costs associated with decision making using group consensus and then describes three methods of reaching consensus assuming quadratic costs for a single-criterion decision problem. The first method finds the group opinion (consensus) that yields the minimum cost of reaching throughout the group. The second method finds the opinion with the minimum cost of the consensus provided that all experts must be within a given distance of the group opinion. The last method finds the maximum number of experts that can fit within the consensus, given a specified budget constraint. Index Terms--Distributed decision making, group decision making, multiple experts.

For a simple finite graph G = (V, E) of order n, the optimal linear-arrangement problem seeks a vertex labeling f: V [right arrow] {1, 2, ..., n} for which the expression [[summation of].sub.({u,v})[member of]E]|f(u) - f(v)| is minimized. In this brief, we examine the following notion. Given some F G, is there a spanning tree of G having an optimal labeling that is also optimal for G? We specify some graph classes, which always exhibit these critical spanning trees and demonstrate how to construct them. Index Terms--Critical subgraph, graph theory, linear arrangement.

THE IDEA OF DIETING AS AN OPERATIONS RESEARCH PROBLEM CAME TO ME WHILE TEACHING A LECTURE ON BOTTLENECKS. AT THE TIME I WAS IN MY MID-THIRTIES AND CLASSIFIED IN THE […]

This paper presents both approximate and exact merged knapsack cover inequalities, a class of cutting planes for knapsack and multiple knapsack integer programs. These inequalities combine the information from knapsack constraints and cover inequalities. Approximate merged knapsack cover inequalities can be generated through a O (n log ⁡ n) algorithm, where n is the number of variables. This class of inequalities can be strengthened to an exact version with a pseudo-polynomial time algorithm. Computational experiments demonstrate an average improvement of approximately 8 % in solution time and 5 % in the number of ticks from CPLEX when approximate merged knapsack cover inequalities are implemented as preprocessing cuts to solve some benchmark multiple knapsack problems. Furthermore, exact merged knapsack cover inequalities improve the solution time and number of ticks of some random multiple knapsack instances by 15 % and 5 % , respectively. [ABSTRACT FROM AUTHOR]

TODD EASTON [*] MARY C. KING [+] EASTON T. and KING M. C. (2000) Differences in wage levels among metropolitan areas: less-educated workers in the United States, Reg. Studies 34, [...]

The simplex method, created by George Dantzig, optimally solves a linear program by pivoting. Dantzig's pivots move from a basic feasible solution to a different basic feasible solution by exchanging exactly one basic variable with a nonbasic variable. This paper introduces the double pivot simplex method, which can transition between basic feasible solutions using two variables instead of one. Double pivots are performed by identifying the optimal basis in a two variable linear program using a new method called the slope algorithm. The slope algorithm is fast and allows an iteration of DPSM to have the same theoretical running time as an iteration of the simplex method. Computational experiments demonstrate that DPSM decreases the average number of pivots by approximately 41% on a small set of benchmark instances. [ABSTRACT FROM AUTHOR]

Baseball is an incredibly complex game in which the manager makes numerous difficult decisions. This paper describes a stochastic integer program that determines the best defensive starting positions to minimize the expected batting average of a particular player. To test this optimal defense against other standard Major League Baseball®defenses, a simulation is created. A computational study demonstrates how the optimal defense can be used to decrease Derek Jeter’s batting average in a statistically significant manner. [ABSTRACT FROM PUBLISHER]