An improved solution methodology for the arsenal exchange model (AEM)
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An improved solution methodology for the arsenal exchange model (AEM) JD Weir1, JT Moore1* and MG Stoecker2 1
Air Force Institute of Technology USA and 2Spectral Systems, Inc., Dayton, OH, USA
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 speci®c 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 ®ve test cases. In four of the ®ve test cases, our methodology produced an optimal integer solution. In all ®ve test cases, solution quality was maintained or improved. Keywords: goal programming; linear programming; integer programming; military
Introduction Goal programming has a wide range of applications.1 Goal programs are particularly well suited to modelling planning problems. Examples of planning problems modelled with goal programming include production planning, manpower planning and military planning. In our research, we applied the concept of relaxation developed by Geoffrion2 and presented by Lasdon3 to develop a methodology for solving linear preemptive goal programming problems. We draw upon the work of Myers4 to guide constraint management and take our inspiration for managing the prioritized goals from Arthur and Ravindran.5 We use an application of our methodology to the arsenal exchange model (AEM) to explain and test our approach and demonstrate the ef®ciencies we gain when the methodology is applied and tailored to a speci®c model. The basic idea is to relax all but a speci®c set of constraints. We solve this relaxed problem. Then we check satisfaction of the relaxed constraints and the highest priority goals not yet considered. Based on this check, we modify the constraint set and iterate. The arsenal exchange model (AEM) is an aggregated, two-sided, strategic exchange model used primarily for strategic weapon system analysis, strategic nuclear policy and arms control analysis, and general strategic calcula-
*Correspondence: JT Moore, Department of Operational Sciences, AFIT=ENS, 2950 P St, Wright-Patterson AFB OH 45433-7765. E-mail: james.moore@a®t.af.mil
tions.6 It performs allocations of weapons to targets in an attempt to maximize prioritized goal achievement. Since only an integer number of weapons can be allocated to an integer number of targets, AEM formulates the problem as an integer programming (IP) problem. The
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