Linear approach for solving a piecewise linear vendor selection problem of quantity discounts using lexicographic method

The multi-objective problem pertaining to vendor selection becomes complicated with the inclusion of a discount pricing schedule due to its nature of piecewise linearity. To overcome the difficulty of solving such a piecewise linear multi-objective problem, a linear approach is described in this paper. The use of the lexicographic method enables the decision-maker to establish the limit for defective components and late deliveries as constraints in the model. Demand can be exactly met considering the defective components present in the supply. Applying this approach to a manufacturing firm has proved its practicality. Also, the proposed methodology can be effectively used in JIT/Lean supply environments by fixing the number of vendors .