Continuous Preemption Problems
In this chapter we are concerned with project scheduling problems involving preemption of activities at arbitrary points in time. We survey the literature on preemptive project scheduling and propose a classification scheme for these problems. We then consider a project scheduling problem under continuous preemption, flexible resource allocation, and generalized feeding precedence relations between the activities. After providing a formal problem statement we reduce the problem to a canonical form only containing nonpositive completion-to-start time lags and investigate structural issues like necessary feasibility conditions and preemption gains. Next, we develop an MILP formulation that encodes a schedule as a sequence of slices containing sets of activities that are simultaneously in progress. Moreover, feasibility tests, preprocessing methods, and a column-generated based lower bound on the minimum project duration are presented. Finally, we report on the results of an experimental performance analysis of the MILP model for the project duration problem.
KeywordsColumn generation Continuous preemption Makespan minimization Mixed-integer linear programming formulation Project scheduling Resource constraints
The authors are indebted to Dr. Jean Damay for providing the benchmark results of the KSD-30 instances.
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