Summary: In any large organization, millions of dollars are spent on outsourcing. Most large organizations are outsourcing those activities that are either not cost efficient if done in-house or not core to their businesses. One of the most critical steps in outsourcing is vendor selection, which is a strategic decision. We model the vendor selection problem as a multi-objective optimization problem, where one or more buyers order multiple products from different vendors in a multiple sourcing network. Price, lead-time and rejects (quality) are explicitly considered as three conflicting criteria that have to be minimized simultaneously. A pricing model under quantity discounts is used to represent the purchasing cost. We present and compare several multi-objective optimization methods for solving the vendor selection problem. The methods include weighted objective, goal programming and compromise programming. The multicriteria models and the methods are illustrated using a realistic example. Value path approach is used to compare the results of different models.