Integrated multi-choice goal programming and multi-segment goal programming for supplier selection considering imperfect-quality and price-quantity discounts in a multiple sourcing environment

Supplier selection (SS) is a multi-criteria and multi-objective problem, in which multi-segment (e.g. imperfect-quality discount (IQD) and price-quantity discount (PQD)) and multi-aspiration level problems may be significantly important; however, little attention had been given to dealing with both of them simultaneously in the past. This study proposes a model for integrating multi-choice goal programming and multi-segment goal programming to solve the above-mentioned problems by providing the following main contributions: (1) it allows decision-makers to set multiple aspiration levels on the right-hand side of each goal to suit real-world situations, (2) the PQD and IQD conditions are considered in the proposed model simultaneously and (3) the proposed model can solve a SS problem with n suppliers where each supplier offers m IQD with r PQD intervals, where only n⌈lnm×rln2⌉$n\lceil {\frac{{\ln {\rm }m \times r}}{{\ln {\rm }2}}} \rceil$ extra binary variables are required. The usefulness of the proposed model is explained using a real case. The results indicate that the proposed model not only can deal with a SS problem with multi-segment and multi-aspiration levels, but also can help the decision-maker to find the appropriate order quantities for each supplier by considering cost, quality and delivery.