Transformation and restructuring of linear multiobjective programs: A fundamental method to resolve complex problems

It is difficult for a decision maker, confronted with a complex linear MCDM problem, to reach a final choice if he/she is presented with a large number of nondominated solutions. In general, the smaller the size of the nondominated set, the faster and easier the decision can be made. If the problem has only one nondominated solution, the solution will be chosen without hesitation. Using the concept of cone separation, the authors present fundamental theorems which guarantee a linear MCDM problem with a unique nondominated solution. As facilities for decision support, they investigate theorems and present methodologies for transforming and restructing decision problems in order to obtain a unique nondominated point. Transformation and restructuring are done through altering the four decision elements: alternatives, criteria, outcomes, and preference structures. The issue is studied in the scope of problem structures. Examples are given throughout to facilitate understanding.