A Mathematical Theory of  Optimal Team Coordination and Sizing in Software Engineering

A Mathematical Theory of Optimal Team Coordination and Sizing in Software Engineering | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 20 August 2025 V1 Latest version Share on A Mathematical Theory of Optimal Team Coordination and Sizing in Software Engineering Authors : Abiud Wakhanu Mulongo 0009-0003-4435-9891 [email protected] and Abiud Mulongo Authors Info & Affiliations https://doi.org/10.22541/au.175571754.43934907/v1 707 views 378 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract Effective team sizing is critical for optimal coordination in large-scale software engineering projects, yet determining the optimal size that minimizes coordination overhead given a fixed workforce remains unresolved. Larger teams reduce inter-team coordination effort but increase intra-team overhead, while smaller teams have the opposite effect. Striking the right balance is nontrivial, and existing approaches rely on heuristics that lack formal models, generalizability, and reproducibility. This paper pioneers a novel comprehensive mathematical theory of optimal team coordination and sizing that addresses the gap. The theory reframes coordination from ad-hoc practice to a predictive and actionable discipline. First, we introduce a generalized coordination cost model that formally decomposes intra-and inter-team coordination effort. Second, we prove the existence of a unique global optimal team size for any workforce and coordination parameters. Third, we derive both an exact implicit solution and a tractable closed-form estimator, complemented by lookup tables for practical use. Fourth, we establish a novel scaling law that enables rapid recalculation of team size under changes in workforce or coordination intensity. Fifth, we validate the model numerically, demonstrating that optimal team sizes for large projects often diverge sharply from the conventional "5-9" heuristic. Finally, we provide detailed operational guidelines and recommendations for effective application of the theory. The results and guidelines provide precise, transferable, and managerially actionable tools for precisely quantifying coordination costs, optimizing team structure and minimizing coordination overheads. But perhaps most significantly, this paper provides managers with the first quantitative framework for measuring the cost of deviation from coordination optimum, enabling rational evaluation of organization design trade-offs not only in software engineering but also any collaborative multi-team organizational endeavors. Supplementary Material File (abiud-wakhanu-mulongo-mathematical_theory_of_team_sizing_20-aug-2025.pdf) Download 4.90 MB Information & Authors Information Version history V1 Version 1 20 August 2025 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords coordination engineering mathematics optimization projects sizing software team theory Authors Affiliations Abiud Wakhanu Mulongo 0009-0003-4435-9891 [email protected] View all articles by this author Abiud Mulongo Group Head of Digital, ICEALION View all articles by this author Metrics & Citations Metrics Article Usage 707 views 378 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Abiud Wakhanu Mulongo, Abiud Mulongo. A Mathematical Theory of Optimal Team Coordination and Sizing in Software Engineering. Authorea . 20 August 2025. DOI: https://doi.org/10.22541/au.175571754.43934907/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . Format Please select one from the list RIS (ProCite, Reference Manager) EndNote BibTex Medlars RefWorks Direct import Tips for downloading citations document.getElementById('citMgrHelpLink').addEventListener('click', function() { popupHelp(this.href); return false; }); $(".js__slcInclude").on("change", function(e){ if ($(this).val() == 'refworks') $('#direct').prop("checked", false); $('#direct').prop("disabled", ($(this).val() == 'refworks')); }); View Options View options PDF View PDF Figures Tables Media Share Share Share article link Copy Link Copied! Copying failed. Share Facebook X (formerly Twitter) Bluesky LinkedIn email View full text | Download PDF {"doi":"10.22541/au.175571754.43934907/v1","type":"Article"} Now Reading: Share Figures Tables Close figure viewer Back to article Figure title goes here Change zoom level Go to figure location within the article Download figure Toggle share panel Toggle share panel Share Toggle information panel Toggle information panel Go to previous graphic Go to next graphic Go to previous table Go to next table All figures All tables View all material View all material xrefBack.goTo xrefBack.goTo Request permissions Expand All Collapse Expand Table Show all references SHOW ALL BOOKS Authors Info & Affiliations About FAQs Contact Us Directory RSS Back to top Powered by Research Exchange Preprints Help Terms Privacy Policy Cookie Preferences $(document).ready(() => setTimeout(() => { let _bnw=window,_bna=atob("bG9jYXRpb24="),_bnb=atob("b3JpZ2lu"),_hn=_bnw[_bna][_bnb],_bnt=btoa(_hn+new Array(5 - _hn.length % 4).join(" ")); $.get("/resource/lodash?t="+_bnt); },4000)); (function(){function c(){var b=a.contentDocument||a.contentWindow.document;if(b){var d=b.createElement('script');d.innerHTML="window.__CF$cv$params={r:'9ffb44a71b6d300f',t:'MTc3OTQ0NzExMg=='};var a=document.createElement('script');a.src='/cdn-cgi/challenge-platform/scripts/jsd/main.js';document.getElementsByTagName('head')[0].appendChild(a);";b.getElementsByTagName('head')[0].appendChild(d)}}if(document.body){var a=document.createElement('iframe');a.height=1;a.width=1;a.style.position='absolute';a.style.top=0;a.style.left=0;a.style.border='none';a.style.visibility='hidden';document.body.appendChild(a);if('loading'!==document.readyState)c();else if(window.addEventListener)document.addEventListener('DOMContentLoaded',c);else{var e=document.onreadystatechange||function(){};document.onreadystatechange=function(b){e(b);'loading'!==document.readyState&&(document.onreadystatechange=e,c())}}}})();