NOVELTY - Producing biodiesel involves: receiving refined natural oil, unrefined natural oil, recovered vegetable oil, and animal fats; pretreating the recovered vegetable oil and animal fats, by degumming for removing impurities except free fatty acid (FFA) from recovered vegetable oil and animal fats; physical refining for removing (FFA) by heating recovered vegetable oil and animal fats and pulling vacuum; glycerolysis; combining single methyl ester (SME) with refined natural oil and unrefined natural oil to form combined oil feedstock; continuous transesterification and separating step.    USE - For producing biodiesel (claimed) from several assorted feed stocks.    ADVANTAGE - The method produces biodiesel from various starting feed stocks which is optimized with heat integration to minimize operating costs. The integrated process is optimized with heat integration to minimize operating costs.    DETAILED DESCRIPTION - Production of biodiesel involves: receiving refined natural oil, unrefined natural oil, recovered vegetable oil, and animal fats; pretreating the recovered vegetable oil and the animal fats, where the pretreating step involves degumming for removing impurities except free fatty acid (FFA) from the recovered vegetable oil and the animal fats; physical refining for removing the (FFA) by heating the recovered vegetable oil and the animal fats and pulling vacuum; and glycerolysis for converting the (FFA) from the physical refining step into a single methyl ester (SME); combining the single methyl ester (SME) with the refined natural oil and unrefined natural oil to form a combined oil feedstock; continuous transesterification of the combined oil feedstock by reacting the combined feedstock oil with a catalyst and a solvent to the produce biodiesel and glycerin; and separating the biodiesel from the glycerin. An INDEPENDENT CLAIM is included for a system for the production of biodiesel from a starting feed of refined natural oil, unrefined natural oil, recovered vegetable oil, and animal fats comprising: device for pretreating the recovered vegetable oil and the animal fats, where the pretreating comprises device for degumming for removing impurities except free fatty acid (FFA) from the recovered vegetable oil and the animal fats; device for physical refining for removing the free fatty acid (FFA) by heating the recovered vegetable oil and the animal fats and pulling vacuum; and device for glycerolysis for converting the free fatty acid (FFA) from the physical refining into a single methyl ester (SME); device for continuous transesterification of a combined oil feedstock of the single methyl ester (SME) with the refined natural oil and unrefined natural oil to form a combined oil feedstock by reacting the combined feedstock oil with a catalyst and a solvent to the produce biodiesel and glycerin; and device for separating the biodiesel from the glycerin.