Keywords: construction engineering, scheduling, project total float, RCPSP, RCTPF.

Critical path has long been central to the analysis of non-resource constrained projects. This issue becomes more crucial when resource constraints are introduced. Even in simple resource constrained projects, alternative resource allocations are often possible, resulting in a choice of schedules with identical project durations, but different critical sequences. An activity may be critical in one schedule, but have considerable float (flexibility) in another. In such situations an analysis of floats plays an important and crucial role, making the development of new float measures a central issue in project scheduling.

In a previous study we presented a new and innovative approach - the resource constrained project total float (RCTPF) - to the calculation of the resource constrained project scheduling problem (RCPSP). This algorithm was geared toward the calculation of the total float of each activity in order to maximize the total float of the project. The RCTPF is in essence a flexibility measure which is geared toward enhancing the schedule robustness by maximizing the project total float. The greater the RCTPF is, the better the solution (the robustness) is. However, this measure, although it significantly improves the flexibility of the solution, is still, in some cases, not necessarily the best solution from the project robustness point of view.

In order to solve this problem, the paper introduces a new measure for calculating project total float based on the existing RCTPF measure. This new measure - dispersal resource-constrained total project float measure (D-RCTPF) - is aimed at maximizing the number of activities in the project that have a total float.

The D-RCTPF is based on the assertion that in many cases the distribution of the total amount of float within the activities is more significant than the existence of float or its amount and can significantly improve and enhance the project robustness. In the D-RCTPF the "best" schedule is a schedule in which both the RCTPF and the Ds measures are maximal. However, in most cases these two measures do not reach their optimum in the same feasible schedule. For this reason, the "second best schedule" will be the one preferred by the project manager according to the nature of the activities. Theoretically the optimal schedule searching process is formulated as a mixed integer linear programming (MILP) problem, which can be solved directly for small-scale projects in reasonable time.

The presented resource conflict oriented MILP model, can be used as a new resource constrained project scheduling model in its own right.

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