Approximation results on resource leveling problems

Abstract

This work deals with resource leveling problems. A set of jobs is given as well as a resource level representing a capacity that may be exceeded at some cost. Jobs have integer processing times, must be scheduled non-preemptively and consume one unit of resource while processed. More precisely, the objective to be maximized is the resource use below the resource level, i.e., the complementary of the total overload cost.

Two main families of problems are investigated: either with or without precedence constraints. The case with no precedence constraints is shown to admit an EPTAS; a quasi-linear time approximation algorithm with constant ratio $\frac{7}{8}$ is also provided. The case with precedence constraints is shown to be significantly harder to solve as it does not admit a PTAS under some classical complexity assumption. Approximation algorithms with constant ratios are provided for special cases with in-tree precedence graph or with fixed resource level.