Alternative optimization strategies for large-scale production-allocation problems

Many optimization problems arising in practice are so complicated that the current tools for optimization do not supply a single, clean answer. We are forced to apply a variety of optimization methods on approximate models, so that we also obtain a variety of approximate solutions. Using a production-allocation problem in Philips Electronics Industries as a vehicle for communication, we generate several near-optimal solutions via decomposition, piece-wise linear programming, and mixed-integer programming. Next, we show that multi-criteria analysis could be used to select one of the resulting allocation patterns for implementation in practice. Thus, instead of a problem with a continuum of alternatives, we eventually consider a finite number of alternatives under several conflicting performance criteria. The study particularly illustrates the significance of mathematical modelling in the power game between globally operating product divisions and locally operating national organizations.