On the weighting of the mean-absolute-deviation cost minimization model

Research Online is the open access institutional repository for the University of Wollongong. For further information contact the UOW (2013). On the weighting of the mean-absolute-deviation cost minimization model. Abstract The mean-absolute-deviation cost minimization model, which aims to minimize sum of the mean value and the absolute deviation (AD) of the total cost multiplied by a given non-negative weighting, is one of a number of typical robust optimization models. This paper first uses a straightforward example to show that the solution obtained by this model with some weightings is not actually an optimal decision. This example also illustrates that the mean-absolute-deviation cost minimization model cannot be regarded as the conventional weighted transformation of the relevant multiobjective minimization model aiming to simultaneously minimize the mean value and AD. This paper further proves that the optimal solution obtained by the mean-absolute-deviation cost minimization model with the weighting not exceeding 0.5 will not be absolutely dominated by any other solution. This tight upper bound provides a useful guideline for practical applications. (2013). On the weighting of the mean-absolute-deviation cost minimization model. Abstract The mean-absolute-deviation cost minimization model, which aims to minimize sum of the mean value and the absolute deviation of the total cost multiplied by a given non-negative weighting, is one of the typical robust optimization models. This paper first uses a straightforward example to show that the solution obtained by this model with some weightings is actual not an optimal decision. This example also illustrates that the mean-absolute-deviation cost minimization model cannot be regarded as the conventional weighted transformation of the relevant multiobjective minimization model aiming to simultaneously minimize the mean value and absolute deviation. This paper further proves that the optimal solution obtained by the mean-absolute-deviation cost minimization model with the weighting not exceeding 0.5 will not be absolutely dominated by any other solution. This tight upper bound provides a useful guideline for practical applications.