New pseudo polynomial algorithms for a partial resource-constrained project scheduling problem

Abstract

The resource-constrained project scheduling problem (RCPSP) aims to arrange activities to be processed by limit renewable resources. In real life, not all resources are constrained, nor do all activities face resource restrictions in a project. The RCPSP may emerge in parts of the project, which could be named as the partial RCPSP. In this paper, we consider a typical partial RCPSP that arranging $ K $ renewable resources to execute $ H $ parallel activities in a project for minimum makespan. In particular, we consider the problem under hypotheses that $ N=2 $ and $ N<H\le 2N $. We study the problem from the perspective of 'resource-unconstrained$ \rightarrow $resource-constrained', and discover the relationships between 'scheduling the $ H $ activities' and 'project makespan'. Based on the relationships, we redescribe the problem as new formats, which include only the $ H $ considered activities instead of all activities and emphasize the positions of theses activities on the activity-chains, and then present pseudo polynomial time algorithms for the problem under the hypotheses of $ N=2 $. We evaluate the performance of our algorithms, and present detailed computational results of instances that evaluate the efficiency and competitiveness of our procedure. For example, computational experiments test that about 0.008 seconds average is required for exactly disposing 300 parallel activities using our algorithms, while about 432 seconds average is required using general exact approaches. The proposed theories and methodologies can be extended to general partial RCPSP and some important types of RCPSP (such as reactive RCPSP). Furthermore, the obtained results may enlighten ideas and more effective theoretical tools for general RCPSP/MS-RCPSP.