Quadratic Scheduling Problems
As noted in Chapter 4.2, the operations scheduling problem (OSP) with machine independent quadratic interaction costs is identical with the graph partitioning problem (GPP). We compare in this chapter these alternative formulations for the OSP in this special case. By comparing the two formulations we do not mean an empirical comparison, but rather an analytical comparison such as the one carried out by Padberg and Sung  for four different formulations of the traveling salesman problem. This guarantees that our results have validity for any numerical calculations based on the formulations that we propose in Chapters 4.2 and 4.3. In the second half of this chapter we derive some results on the facial structure of the OSP.
KeywordsLinear Programming Relaxation Linear Relaxation Polyhedral Cone Linear Description Proper Face
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