When evaluating investments in HPC systems ^{5}, the denominator of the BCR can be easy to find though one must make sure that all of the costs involved have been identified. However, the profit or cost savings due to the investment may not be nearly as easy to determine. The DARPA High Productivity Computing Systems (HPCS) program ^{6} has been working on determining the factors that play into the numerator and denominator of a BCR evaluation. In an article from the Winter 2004 Special Edition on HPC Productivity of the *International Journal of High Performance Computing Applications*^{7}, the HPCS research team used productivity as their measure and defined it in classic economic terms as utility divided by cost. This is very similar to the BCR equation:

To expand on the utility (benefit) and cost for an organization, Dr. Jeremy Kepner of MIT Lincoln Laboratory, a HPCS Productivity Team member, developed a high performance productivity framework and evaluation model. The HPCS productivity model looks past the traditional measures of high performance computing systems such as peak floating point operations per second (flops) and system demand, since they usually do not have much influence on productivity. The result is the (SK)3 formulation:

In other words, the productivity level of a high performance computing system is a function of the time saved by engineers and scientists in solving advanced problems, taking into account not only the cost of the system, but also the time required to train users on it, prepare the application code(s) for parallel processing, launch the application(s), and administer the system. This formulation is intended for a research-oriented institution like a university or national laboratory.

In an industry environment, where systems are used less for basic research and more for solving product design and development challenges (i.e., a “production” environment), the variables for determining BCR/productivity may very well be different. Rather than computing the time saved by users on the system, an industry user may be more concerned with the value of newly developed products, potential increases in market share, profits generated (or lost) using HPC systems, or the importance of the job to be completed (i.e., how much revenue or market share will the company be able to gain once this large, extremely important problem is solved). In the denominator, the “time to parallelize” is irrelevant because all of the parallel software running on the HPC system is purchased. Hence the “time to parallelize” is replaced by the “cost of software.” Also the launch time becomes minute in comparison to the software execution time. Again, we start with the basic formula: productivity (BCR) equals utility/benefit divided by cost. With the above changes, the new expanded BCR formulation follows.

In the next section, we use these two productivity (BCR) formulas with numerical examples to demonstrate their use.