January 2001, Volume 52, Issue 1, Pages 48 - 54

Case-Oriented Paper

An improved solution methodology for the arsenal exchange model (AEM) JD Weir1, JT Moore1 & MG Stoecker2 1Air Force Institute of Technology USA     2Spectral Systems, Inc., Dayton, OH, USA     Correspondence to: JT Moore, Department of Operational Sciences, AFIT/ENS, 2950 P St, Wright-Patterson AFB OH 45433-7765. E-mail: james.moore@afit.af.mil

Keywords

goal programming;   linear programming;   integer programming;   military

Abstract

We develop an iterative approach for solving a linear programming problem with prioritized goals. We tailor our approach to preemptive goal programming problems and take advantage of the fact that at optimality, most constraints are not binding. To overcome the problems posed by redundant constraints, our procedure ensures redundant constraints are not present in the problems we solve. We apply our approach to the arsenal exchange model (AEM). AEM allocates weapons to targets using linear programs (LPs) formulated by the model. Our methodology solves a subproblem using a specific subset of the constraints generated by AEM. Violated constraints are added to the original subproblem and redundant constraints are not included in any of the subproblems. Our methodology was used to solve five test cases. In four of the five test cases, our methodology produced an optimal integer solution. In all five test cases, solution quality was maintained or improved.

Received October 1999; Accepted July 2000

^© Macmillan Publishers Ltd 2001