A THEORETICALLY CORRECT RESOURCE USAGE VISUALIZATION FOR THE RESOURCE-CONSTRAINED PROJECT SCHEDULING PROBLEM

The cumulative resource constraints of the resource-constrained project scheduling problem (RCPSP) do not treat the resource demands as geometric rectangles, that is, activities are not necessarily assigned to the same resource units over their processing times. In spite of this fact, most papers on resource-constrained project scheduling mainly in the motivation phase use a strip packing of rectangles (SPR) like visualization to illustrate the resource allocation. A novice researcher inspired by the "artistic" SPR visualization may think that the "rectangles" are essential elements of the RCPSP, and that the RCPSP is a special counter-intuitive strip packing problem (SPP) which can be solved without explicitly defined strip packing constraints. In this context "artistic" means, that we have to use a "drawing tool" to produce a SPR like visualization, because the standard model of the RCPSP knows nothing about the rectangles. In the RCPSP, the rectangles can be torn vertically and horizontally, which is absurd in the SPP, and the existence of a cumulative solution is only a necessary but not sufficient condition of the existence of the SPR like visualization, as proven by several researchers. Therefore the popular SPR visualization is theoretically wrong and misleading, and hides a real problem, which is connected to the dedicated resource assignment. In this paper, we prove that replacing the rectangles with a set of strips with unit height we can always generate a theoretically correct strip packing of strips (SPS) like dedicated assignment, where dedicated means that each demand unit is served by exactly one resource unit over its duration without "hidden" transfer time and cost.

کلیدواژه ها:

resource-constrained project scheduling ، resource-profile visualization ، strip-packing of strips ، spatial resource constraint ، commulated resource constraint