Petrochemical companies have focused on mergers and acquisitions (M&A) as a strategic option; however, there are very few quantitative tools which can critically evaluate M&A. The objectives of M&A are rapid growth by increasing the external scale of a company and strengthening its cost competitiveness. In particular, many petrochemical mergers occur within a complex. This study presents, a novel mathematical model to select an optimal target company for the vertical merger in a petrochemical complex. The model is applied to the problem of one acquirer and five target companies within a complex. The results of the optimization studies are analyzed with regard to profit, synergy, variability, and cost efficiency of the merger. One target company is ultimately selected with a synergy of $264 million with $0.81 million of capital investment. The industrial case study demonstrates the viability of the given model for analyzing real M&A problems within a complex.