Methodology for an orderly quadratic assignment problem

An assignment arrangement problem (AAP), in which an arrangement represents a geometric straight line joining two pre-defined points (for facility and location), is introduced. This problem is a special class of QAP, and is different from all existing QAP's, as it requires a pre-established order between all assignments included in addition to a multi-objective function involved. It is shown that this un-conventional problem cannot be solved using current conventional exchange heuristic procedures. A new pairwise exchange is developed and programmed for solution and evaluation. The AAP and the solution procedure introduced are flexible and may be applicable to other problems which fit the general QAP formulation.