Abstract
The resource constrained scheduling problem involves the scheduling of a number of activities over time, where each activity consumes one or more resources per time period. For a feasible solution to exist, the total resource consumption per time period must not exceed the available resources. In addition, the order in which activities may be scheduled is determined by a precedence graph. In this paper, valid inequalities proposed for the resource flow-based formulation in previous studies are investigated to determine what effect they may have on computing times. It is shown empirically that improved computing times may be obtained if these valid inequalities are, in fact, omitted from the resource ow-based formulation. In addition, a heuristic is proposed for the generation of initial starting solutions and for estimating the extent of the scheduling horizon which, in turn, is required to calculate the latest starting times of activities. The computational results are based on well-known problem test instances as well as new randomly generated problem instances. Keywords: Scheduling, mixed integer linear programming, valid inequalities
Highlights
A solution to the resource constrained scheduling problem (RCSP) prescribes starting times of activities such that the total resource usage by the activities per time period is within a pre-specified resource capacity
The computational results reported in this paper show that constraint sets (7) and (8) may, have a detrimental effect on computing times for some problem instances when included in the formulation of resource flow RCSP models
The results show that by adopting the RFX formulation, 11% of the total number of J60 L instances are solved to optimality
Summary
A solution to the resource constrained scheduling problem (RCSP) prescribes starting times of activities such that the total resource usage by the activities per time period is within a pre-specified resource capacity. A note on flow-based formulations for solving resource constrained scheduling problems 23 successor activities according to the precedence graph), and let Ur be the upper limit on the quantity of resource r ∈ R that may be consumed per day. The computational results reported in this paper show that constraint sets (7) and (8) may, have a detrimental effect on computing times for some problem instances when included in the formulation of resource flow RCSP models. The purpose of solving the RGE heuristic is two-fold It provides a starting solution for the RCSP which may result in a speed-up of the MILP solver, and secondly, it provides an estimate of the scheduling horizon which, in turn, is required to calculate the latest starting times of activities.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
