<abstract xmlns="http://www.w3.org/1999/xhtml"><p> The inaugural challenge of the 2016 Creative Construction Conference has posed two related questions on how many possible criticality constellations with different behaviors for delays and acceleration exist and how said constellations can occur for nonlinearly and monotonously progressing activities that have continuous relations. This paper systematically solves these questions by performing a thorough literature review, assembling theoretical foundations for link constellations, performing a computer simulation of all possible permutations, and providing a mathematical proof by contradiction. It is found that (for the initially assumed self-contained activities in a network schedule that exhibit only a linearly growing production), three newly hypothesized criticality constellations cannot exist. Nonlinear activity constellations with diverging or converging relative pro­ductivities are examined next. Lags in networks become buffers in linear schedules. It is found that a nonlinear curvature of the progress may induce middle-to-middle relations besides those between start and finish. If multiple curvatures are allowed, then partial segments can form relations, which increase the number of criticality constellations. This paper is extended from the 2017 Procedia Engineering conference version. </p></abstract>

The inaugural challenge of the 2016 Creative Construction Conference has posed two related questions on how many possible criticality constellations with different behaviors for delays and acceleration exist and how said constellations can occur for nonlinearly and monotonously progressing activities that have continuous relations. This paper systematically solves these questions by performing a thorough literature review, assembling theoretical foundations for link constellations, performing a computer simulation of all possible permutations, and providing a mathematical proof by contradiction. It is found that (for the initially assumed self-contained activities in a network schedule that exhibit only a linearly growing production), three newly hypothesized criticality constellations cannot exist. Nonlinear activity constellations with diverging or converging relative pro­ductivities are examined next. Lags in networks become buffers in linear schedules. It is found that a nonlinear curvature of the progress may induce middle-to-middle relations besides those between start and finish. If multiple curvatures are allowed, then partial segments can form relations, which increase the number of criticality constellations. This paper is extended from the 2017 Procedia Engineering conference version.

Precedence permutation patterns creating criticality constellations: Exploring a conjecture on nonlinear activities with continuous links

Organization, Technology and Management in Construction: an International Journal

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

The inaugural challenge of the 2016 Creative Construction Conference has posed two related questions on how many possible criticality constellations with...

Precedence permutation patterns creating criticality constellations: Exploring a conjecture on nonlinear activities with continuous links

Data publikacji: 17 lut 2018

Zakres stron: 1674 - 1683

Otrzymano: 31 sie 2017

Przyjęty: 23 lis 2017

DOI: https://doi.org/10.1515/otmcj-2016-0023

Słowa kluczowe
precedence diagramming, link constellations, continuous precedence relations, classification of critical activities

© 2018 Gunnar Lucko, Yi Su, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Precedence permutation patterns creating criticality constellations: Exploring a conjecture on nonlinear activities with continuous links

Data publikacji: 17 lut 2018

Zakres stron: 1674 - 1683

Otrzymano: 31 sie 2017

Przyjęty: 23 lis 2017

DOI: https://doi.org/10.1515/otmcj-2016-0023

Słowa kluczoweprecedence diagramming, link constellations, continuous precedence relations, classification of critical activities

© 2018 Gunnar Lucko, Yi Su, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Słowa kluczowe
precedence diagramming, link constellations, continuous precedence relations, classification of critical activities