A new normalized goal programming model for multi-objective problems: A case of supplier selection and order allocation

This paper models the problem of supplier selection as a multi-objective optimization problem (MOOP) where minimization of price, rejects and lead-time are considered as three objectives. The paper considers two different cases: (1) the crisp MOOP in which the goals of objectives are predetermined; and (2) the fuzzy MOOP in which the weights of objectives are predetermined. In both cases, the aim is to achieve some levels of consistency among different objectives. To do so, a normalized goal programming approach is developed and tested for both cases. In order to compare the effectiveness of the proposed method, a comparative analysis is presented which includes weighted goal programming, compromise programming, TOPSIS, weighted objectives, min–max goal programming and weighted max–min models. An illustrative example reveals that our proposed model is able to achieve the desirable consistency among all objectives.