ADVISORY ARTICLE
By Alexander Apostolov, PhD
Sofia, Bulgaria
Introduction
Since my initial article on the Combination-Permutation Algorithm (CPA) for portfolio allocation [1] was published, I have continued to work on this issue.
Building on the previous formulation [1], this article presents the “new and improved formulation” of the algorithm. It also explains the rationale behind CPA, the possibilities for its implementation, and the research it enables.
The Rationale Behind CPA
The typical approach to portfolio allocation involves sequential steps such as project prioritization, selection, scheduling, sequencing, and staging to avoid resource contention. The exact steps and their sequence may vary, and some of them are sometimes combined, but in any case, this approach has inherent fundamental problems.
According to this approach, the portfolio goal (such as maximizing profit) can be achieved by making the best decisions at each step of the process. In other words, the resource allocation problem is broken down into subproblems that are solved separately. It seems logical that the best solutions to each subproblem should provide the best solution to the overall problem.
However, the portfolio goal depends on multiple factors that must be taken into account in their entirety at the same time. The very first step in the typical process leads to a suboptimal solution that cannot be corrected in subsequent steps. Each following step results in a suboptimal solution within an already limited, suboptimal region of possible solutions. Thus, the suboptimality accumulates.
The sum of local optimizations is not equivalent to global optimization.
Some computer games tempt players with large prizes to try to distract them from the goal of the game. Similarly, each step in the allocation of a project portfolio tempts with the prize of the best solution to the corresponding subproblem. This is a classic greedy trap. Nonetheless, if the excitement of the portfolio allocation game is more important than the goal, we can ignore the outcome and enjoy the process.
Let’s assume that the first step of the allocation limits the maximum portfolio profit to 90% of the theoretically possible one. The second and third steps limit the maximum profit to 90% of the maximum that can be achieved after the previous step. Thus, the three steps limit the portfolio profit to 73% of the maximum possible one. So far, we have generated systemic waste (waste of local optimization) of 27% of the maximum possible portfolio profit.
More…
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How to cite this article: Apostolov, A. (2026). Advancing the Combination-Permutation Algorithm, PM World Journal, Vol. XV, Issue II, February. Available online at https://pmworldjournal.com/wp-content/uploads/2026/02/pmwj161-Feb2026-Apostolov-Advancing-the-Combination-Permutation-Algorithm.pdf
About the Author
Alexander Apostolov
Sofia, Bulgaria
Alexander Apostolov holds a Master’s degree in Economics and a PhD in Project Management and Sustainable Development. He has 25 years of experience in project management for new product development, construction, IT, events, and more.
He is currently the managing director of a project management consulting firm and the Lean Project Management Foundation. His interests lie in the development and implementation of holistic project management methods and tools.
Alexander Apostolov can be reached at contact@leanpm.org and www.leanpm.org.
