Energetic Reasoning and Bin-Packing Problem for bounding a parallel machine problem
Résumé
This paper deals with an extension of energetic reasoning, using some efficient lower bounds of the bin-packing problem, to get tight lower bounds for the P|r i , q i |C max. The link between P||C max and bin-packing problem is well-known. Our purpose is to extend the use of efficient lower bounds of the bin-packing problem to P|r i , q i |C max. We focus on some time-intervals, to compute the mandatory parts of activities within this time-interval and then to deduce an associated bin-packing instance. Thus, lower bounds of the bin-packing problem are used to get new satisfiability tests for the parallel machine problem. We also propose to extend the classical time-bound adjustments of release dates and deadlines to efficiently use bin-packing lower bounds. Experimental results that prove the efficiency of our approach on several kind of instances are reported.