An attainable region (AR) analysis is a geometrically-based method of optimisation that has mainly been used for performing optimal reactor synthesis. The objective of the analysis is to find the complete set of all possible outcomes, a system can achieve from a given feed set using a given number of fundamental physical processes such as chemical reaction, mixing and heat transfer. From such an analysis one can find optimal pathways that can be used to obtain a desired product from a given feed. More importantly, these pathways can be interpreted to represent optimised process equipment. In a previous paper (Kauchali, S., McGregor, C., & Hildebrandt, D., 1999), we applied the AR theory to binary distillation where we constructed a constrained attainable region. We considered the optimum policy for the reflux ratio along the column where there was no cost associated with the processes used to control the reflux ratio. In this paper, we would like to investigate the effect of including costs for the processes used to control the reflux ratio on the operating policy and structure of the column. The attainable region, subject to the conditions discussed above, has been determined and the behaviour shown graphically in a composition, cost and reflux/reboil space. We discuss the effects of changing the reflux/reboil ratio along the length of the column and examine the implications of the results obtained from the construction of the constrained AR for the design of conventional distillation columns.