In this study, performance of a combined power and cogeneration plant is evaluated. The plant is basically the captive power plant (CPP) of Numaligarh Refinery Limited (NRL), located in Golaghat district of Assam, India. The plant consists of a gas turbine (GT) plant as topping and a steam turbine (ST) plant as bottoming cycle. In the CPP, there was also provision for extracting steam from the ST at two different points for process heating in the refinery. CPP operational data regarding pressure, temperature and mass flow rates were collected from the refinery. It was observed that although the performance related data (the GT and ST power outputs) were available but the air flow rate (AFR) of the GT plant was not known. Therefore, this study aimed first at estimating the unknown AFR using an inverse method for which a differential evolution (DE) based optimization algorithm was used. Next, it was attempted to estimate both the AFR and fuel flow rate (FFR) simultaneously assuming that suppose the FFR is also not known. The objective was to find out better combinations of FFR and AFR over the base case corresponding to the single parameter (only AFR) estimation. The performance of the CPP was evaluated with the estimated AFR corresponding to the base case and also with the one of best FFR/AFR combination out of 25 such combinations obtained from simultaneous estimation. For the base case, the overall energy and exergy efficiency of the CPP were found to be 15.39% and 15.37% respectively. However, if the process heating is also taken into consideration, then these efficiencies in cogeneration mode increase to 21.04% and 21.0%. But with the selected best FFR/AFR combination obtained from simultaneous estimation, the overall energy efficiencies of the combined and the cogeneration plant could be improved from 15.39% to 17.68% and from 21.04% to 24.16% respectively. This has also reduced the total plant irreversibility from 183.729 MW to 152.955 MW. It was found that the maximum exergy destruction occurs in the combustion chamber (58.62%) of the GT plant followed by the utility boiler (29.37%) and heat recovery steam generator (3.76%). The results confirmed lower efficiencies for the plant indicating opportunities for further performance improvement particularly in the GT plant. NRL must go for other performance diagnostic tests which might give some actionable recommendations for restoring the lost performance. In the conclusions, other possible causes of low performances are discussed and necessary recommendations have been provided.