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Sculptured dies cavity roughing (SDCR) is a multi-dimensional optimization problem that requires the simultaneous decision of several variables. The most frequent discussion in SDCR is the simultaneous decision on tool selection and cutting plane determination in order to minimize machining (roughing) time. This study consider the trade-off between roughing and finishing time which represented by residual volume in roughing process by applying machining efficiency as the objective of the proposed algorithm. The machining efficiency for each set of tool selection depend on the determination of cutting plane. Therefore this multi-dimensional problem is classified as a complex combinatorial problem and there is need for 2 dimensional problems formulation. This study proposed binary coding to represent the problem, by which enumeration of the problem could be well structured and the coding and decoding process of 2 dimensional problem could be simplified in order to search and identify the optimum result. The algorithm has produced the optimum result and empirically shown 10% of improvement of machining efficiency when compared to result from the simulator and better machining efficiency when compared to smallest-tool-possible (STP) and smallest residual possible (SRP). (Keywords : Sculptured dies cavity roughing, enumeration, binary coding, Fibonacci, climbing stairs problem) [ABSTRACT FROM AUTHOR]