A Unified Quantitative Model for Project Management with Singularity Functions

摘要

Construction project management is essentially an ongoing optimization process with multiple constraints consisting of scope (quality), time, and cost. These constraints are interrelated and compete with each other, which require an integrated method to express the complete project efficiently. Furthermore, unifying the multi-objective model should maintain necessary details of sub-models and accurately reflect the true situation of the project. This paper provides a unified way to describe the project mathematically with singularity functions, both effectively and efficiently. The contribution to the body of knowledge is threefold: First, sub-models with two constraints are modeled by point-slope formulas which includes linear schedule (time, quantity), cash flow (time, cost), and resource usage (resource, time). Second, the triple objective model is expanded to the point-vector formula with singularity functions without weakening its sub-model's intricacy and accuracy. Third, all possible models with combinations of the three dimensions are expressed mathematically, graphically, and their possible applications are discussed. Different from 4D CAD and BIM that coordinate rich building information in databases at a practical level, this study explores comprehensively modeling projects in multiple dimensions synchronously at a conceptual level. Such unified quantitative model may lead to new analytical and optimization approaches for construction management.