Most ISOs in the US minimize the total bid cost and then settle the market based on locational marginal prices. Minimizing the total bid cost, however, may not lead to maximizing the social welfare. Studies indicate that for energy only, payment cost minimization (PCM) leads to reduced payments for a given set of bids, and the “hockey-stick” bidding a less likely to occur. Since co-optimization of energy with ancillary services leads to a more efficient allocation, it is important to solve PCM co-optimization while considering transmission capacity constraints for a comparison with other auction mechanisms. In this paper, PCM is formulated using price definition system-wide constraints. This problem formulation introduces difficulties such as nonlinearity, non-separability and complexity of convex hull. To overcome these difficulties, the nonlinear terms are linearized thereby allowing to be solved by using branch-and-cut. At the same time, the linearization is performed in a way that the “surrogate optimality condition” is satisfied thereby allowing the problem to be solved efficiently.