Cranes have come to symbolize building construction itself. They perform indispensable services in moving materials and components vertically and horizontally. Used since antiquity, their history is interrelated with the development of new power sources that replaced man and mule, first steam and later internal combustion, diesel, and electric engines. Mobile cranes can be rapidly deployed to lift heavy loads. New models with telescoping booms and all-terrain travel capability, compact urban machines, and even hybrids with tower cranes are beginning to replace the familiar lattice boom truck cranes. Mobile cranes have dominated the North American market, but a cultural change appears to be taking place toward tower cranes for building projects. Tower cranes, common in Europe for decades, are globally gaining in popularity with surging real estate developments. Ideal for dense urban environments and coming with a small footprint, they are available in a growing diversity of sizes and configurations. Sophis...

This paper describes a new integrated method of linear schedule analysis using singularity functions. These functions have previously been used for structural analysis and are newly applied to scheduling. Linear schedules combine information on time and amount of work for each activity. A general model is presented with which activities and their buffers can be mathematically described in detail. The algorithm of the new method forms the body of the paper, including the steps of setting up initial equations, calculating pairwise differences between them, differentiating these to obtain the location of any minima, and deriving the final equations. The algorithm consolidates the linear schedule under consideration of all constraints and, thus, automatically generates the minimum overall project duration. The model distinguishes time and amount buffers, which bears implications for the definition and derivation of the critical path. Future research work will address float and resource analysis using the new model.

The analysis of project schedules is among the central tasks of construction managers. Parallel to the well-known critical path method, linear scheduling techniques have been researched. The two most fully developed existing methods, the linear scheduling model and the repetitive scheduling method, are reviewed. Based on a discussion of a published example, the new mathematical analysis method for linear and repetitive schedules is introduced. The productivity scheduling method is based on singularity functions that provide a flexible and powerful mathematical model for construction activities and their buffers that are characterized by their linear or repetitive nature. The steps of formulating initial equations, stacking and consolidating them, and deriving information about their criticality are described in detail. The mathematical approach of the new method allows an integrated treatment of activities regardless of the number of changes in productivity within them and does not depend on the graphical...

Resources perform or enable physical operations and thus are vital on construction projects, yet are subject to various constraints. Their use within a project schedule must therefore be carefully planned. A major objective is optimizing when they are active within the float of noncritical activities to avoid disruptive and costly fluctuations. This paper builds on analyzing criticality of linear schedules with the unique singularity functions. The new approach keeps resources intact and derives one flexible equation for the complete resource profile of a schedule, including any timing or resource rate changes. Another equation models its first moment of area to minimize the objective function toward a level profile. A genetic algorithm is suitable for an iterative optimization. The parameters of its chromosomes are recombined evolutionarily and can model any permutation. Analyzing a road project illustrates how singularity functions integrate resource optimization with its linear schedule and facilitate a subsequent optimization.

The ability of construction contractors to plan and manage cash flow is critical for their economic success. The cumulative interaction of outflows (labor, materials, and equipment costs) and inflows (progress payments less retainage) creates a profile with a complex zigzag shape. This could only be modeled by simplification, e.g., as values tabulated at discrete times; averaged S-curves without peaks; or envelopes of all possible constellations. Neither is suited for a fully integrated model that dynamically links schedules with their cash flows for optimization. Therefore, singularity functions, whose components define ranges of behavior between cutoffs, are used to flexibly yet accurately model cash flow profiles and their various payment terms. The new approach augments construction project management toward an integrated planning model and is validated with an example from the literature. Optimization with a simulated annealing algorithm shifts activity positions in a randomized but directed search f...

This paper describes how float can be calculated exactly for linear schedules by using singularity functions. These functions originate in structural engineering and are newly applied to scheduling. They capture the behavior of an activity or buffer and the range over which it applies and are extensible to an infinite number of change terms. This paper builds upon the critical path analysis for linear schedules, which takes differences between singularity functions and differentiates them. It makes several important case distinctions that extend the earlier concept of rate float. Time and location buffers act along different axis directions. Together with different productivities between and within activities, this can create a complex pattern of critical and noncritical segments. Depending on starts and finishes, areas of float precede or follow these noncritical segments. The schedule of a small project is reanalyzed with case distinctions to demonstrate in detail what float types are generated.