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 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.

The Hydro Unit Commitment problem (HUC) specific to hydroelectric plants is part of the electricity production planning problem, called Unit Commitment Problem (UCP).More specifically, the studied case is that of the HUC with a single plant, denoted 1-HUC.The plant is located between two reservoirs.The horizon is discretized in time periods.The plant operates at a finite number of points defined as pairs of the generated power and the corresponding water flow.Several constraints are considered.Each reservoir has an initial volume, as well as window resource constraints, defined by a minimum and maximum volume per time period.At each time period, there is an additional positive, negative or zero intake of water in the reservoirs.The case of a price-taker revenue maximization problem is considered.An efficient exact A* variant, so called HA*, is proposed to solve the 1-HUC accounting for window constraints, with a reduced search space and a dedicated optimistic heuristic.This variant is compared to a classical Resource Constrained Shortest Path Problem (RCSPP) algorithm and a Mixed Integer Linear Programming formulation solved with CPLEX.Results show that the proposed algorithm outperforms both concurrent alternatives in terms of computational time in average on a set of realistic instances, meaning that HA* exhibits a more stable behavior with a larger number of instances solved.