No abstract

Generally, the utilization of traditional scheduling methods represents a complex and cumbersome task for most project managers. Using the existing tools often requires long preparation, and the quality of the graphical output of the planning job is suboptimal. The lack of accuracy in the representation of the execution process diminishes the reliability of the schedule. This article proposes a new planning approach that that can simulate the real conditions of projects. The concepts of graphical scheduling models are analyzed to position the new chronographic approach among other graphical scheduling techniques. The theoretical concept, the mathematical model, and the graphical approach for this new planning method are summarized. Among other features, the proposed chronographic method allows the internal division of activities and relationships as a function of quantities, and new realistic types of floats are proposed. The output may be represented on numerous levels of hierarchical detail or as a combination of these levels. The result is modeling that produces improved visual clarity, increased flexibility, and more adaptability to changes for construction projects.Key words: planning, scheduling, modeling, time-scaled, chronographic method, Gantt, critical path method, precedence.

Since the late 1950s, researchers have studied the soft logic of scheduling, in particular the precedence constraint between activities used to compute the critical path. However, by proposing only external constraints and simulating work production through lags, the precedence logic lacks precision. These gaps diminish the reliability of the schedule and impair the internal monitoring of activity interdependencies. Chronographic logic addresses such limitations by introducing the internal division and proposing internal monitoring as a function of production. This paper proposes the concept of probabilistic production-based dynamic functions which would replace internal divisions with a mathematical function that permits the tracking of the dynamic interdependencies between two in-progress activities. A case study compares the overall schedule calculation using traditional precedence logic with the dynamic production-based function. This simulation was designed to investigate the overall impact on the critical path and the criticality of each activity. The result is a new method of implementing scheduling logic that takes into account the impact of the internal changes of workload and allows the use of internal margins. These self-adaptations provide a better simulation of construction-site conditions which help to produce more realistic results. NotationA current achieved quantity of the predecessor B current achieved quantity of the successor Bx n binomial curves delta_a gap allowed to start the elementary quantity of the successor; delta_b gap allowed to postpone the beginning of the elementary quantity of the predecessor D i activity duration I activity code K branches code n elementary steps that divide an activity N number of completed periods of the predecessor Na elementary number corresponding to the quantity A Nb elementary number corresponding to the quantity B Q i estimated quantity of work of activity i Q iy quantity of work related to the first internal division of the predecessor activity Q jy quantity of work related to the start of the successor activity S i activity start date U m temporal function X i predecessor activity code, X j successor activity code X n activity number DQ iy probabilistic gap

Abstract-The more complex a project is, the more attractive non-traditional project delivery methods like Design-Build become. These delivery methods allow decisions with several options to be postponed. To account for these alternatives, existing generalized scheduling methods integrate decisions into their processes; however, these methods only use traditional precedence dependencies for network calculations. This paper contributes to the existing body of knowledge by extending the traditional logic and modeling execution alternatives using chronographic time-scaled point-to-point relations, production-based dynamic relations and function dependencies between ongoing activities. Using the Monte-Carlo simulation, the paper simulates the impact of operations and reworks uncertainties for the execution alternatives. For companies, this approach represents scheduling constraints in a flexible manner and provides a feasible solution for modeling the complexity of real-world projects.