Eliminating Permanently Dominated Opportunities in Multiple-Criteria and Multiple-Constraint Level Linear Programming

Given a problem of multiple-criteria and multiple-constraint level (MC2) linear programming, we can use the MC2-simplex method to effectively identify a set of potential solutions. These potential solutions maximize the MC2 problem under some possible changes of resource availability levels and criterion coefficients. An opportunity that is not selected in any potential solutions is called a permanently dominated opportunity. This paper proposes techniques to recognize and eliminate permanently dominated opportunities from further consideration in the process of solving the given MC2 problem. The elimination technique for multiple-criteria (MC) linear programming is also discussed.