Operations Research

Federgruen, Awi

doi: 10.1287/opre.28.3.794pmid: N/A

This paper considers undiscounted two-person, zero-sum sequential games with finite state and action spaces. Under conditions that guarantee the existence of stationary optimal strategies, we present two successive approximation methods for finding the optimal gain rate, a solution to the optimality equation, and for any ϵ > 0, ϵ-optimal policies for both players.

Widhelm, William B.

doi: 10.1287/opre.28.3.822pmid: N/A

Recent limited computational results have indicated that the normed Generalized Lagrangian Multiplier (GLM) search performs better than the standard non-normed procedure equivalent to the Dantzig-Wolfe (D-W) approach. Previous arguments for the superiority of the normed procedure were based on multiplier-space considerations where the normed approach yields a more geometrically centered cut. In this note, the payoff-space geometry is investigated. Here, the normed procedure weights the search in accordance with the closeness of the constraint values to the requirements vector whereas the D-W approach ignores this information.

Glover, Fred; Mulvey, John M.

doi: 10.1287/opre.28.3.829pmid: N/A

We show how to formulate a 0-1 integer programming problem as a “mixed integer” generalized network and as a discrete “0-U” pure network problem. Special integer programming structures allow convenient simplifications. The usefulness of these formulations is in providing new relaxations for integer programming that can take advantage of recent advances in the development of efficient computer programs for network problems. We cite three practical applications in which these ideas have led to marked improvement in solution efficiency.

Ward, J. E.; Wendell, R. E.

doi: 10.1287/opre.28.3.836pmid: N/A

We propose a new norm, called the one-infinity norm, for characterizing distance in facility location problems. This new norm, which is a hybrid version of the rectilinear and Tchebycheff norms, not only gives a good characterization of distance (as compared, for example, to results by Love and Morris) but also has two alternate interpretations of travel. Furthermore, it yields linear programming formulations of location problems.

White, D. J.

doi: 10.1287/opre.28.3.844pmid: N/A

Moskowitz developed a useful algorithm for finding admissible decision functions by viewing the expected utility vectors over a finite number of states as the sum of component vectors and developing a recurrence approach. This paper generalizes the results to sum set situations and corrects Moskowitz's proof.