Quadratic assignment problem mathematical modelling for process planning

Abstract

Increased global competition and frequent unpredictable market changes are current challenges facing manufacturing enterprises. Part design and engineering specifications changes trigger frequent and costly changes in process plans, which often require changes in their manufacturing system. Process planning is a key support function that should be further developed to cope with these challenges. A sequential hybrid approach at the macro-level has been exploited. At the heart of the proposed method, a new mathematical model based on the popular Quadratic Assignment Problem (QAP) is solved, where sub-operations are assigned positions and clustered to represent operations in one-dimensional space. A linearisation of the quadratic model is performed and, hence, solved for optimality. The proposed model cures the conceptual flaws in the classical solutions of the Traveling Salesperson Problem (TSP). It also overcomes the complexity of the sub-tour elimination constraints and, for the first time, mathematically formulates precedence constraints, which is a cornerstone of the process planning problem. The developed methods, their limitations and merits are conceptually and computationally analysed, compared and validated against other models in the literature using detailed industrial case studies. General algebraic modeling system language, its SBB mixed-integer non-linear programming (MINLP) solver and CPLEX solvers are used. The presented innovative new concepts and novel formulations represent significant contributions to knowledge in the field of process planning. Their effectiveness and applicability are validated in different domains of applications, namely metal cutting, inspection and assembly.