In a nutshell, maintenance scheduling has to decide which parts of the g= enerating units or the transmission infrastructure to shut down during time= windows with reduced energy demand at an acceptable failure risk so that p= rofit losses/costs are minimal. In principle this requires to combine integ= er maintenance decisions with complex physical models on technical restrict= ions (ramping, power flow, etc.) as well as with stochastic models for the = development of supply (e.g. due to wind and solar energy), demand and price= s. Further restrictions include the necessary equipment and personnel. Beca= use each single component is mathematically already a challenge, the main b= ody of literature can be found in engineering journals while so far there i= s very limited coverage by mathematical journals.

In the past, solution techniques only considered a coarse discretization= of the time horizon (weekly time steps) and the problem was decomposed int= o single production units (fossil fuel power plants, hydro-electric units,.= ..). Stochastic aspects were considered at the unit level with scenario mod= eling for hydro inputs and marginal costs. For the optimization over = a single unit Dynamic Programming is a simple and efficient approach.

Nowadays, models are using a finer discretization (daily time steps). Te= chnical coupling constraints between the different production units are inc= orporated (for eg. limited ressources to perform certain operations). The m= ain solution methods are local search heuristics, decomposition approaches = (Bender's, Dantzig Wolfe and Lagrangean Relaxation) and occasional Mixed In= teger Programming (MIP) or Model Predictive Control (MPC) models.

In practice MIP approaches require small time windows for the schedule o= f maintenance. Local search approaches are less restrictive but don't provi= de proofs of optimality. A flurry of approaches for this problem have been = developed in the 2010 ROADEF Challenge. There is much room for future work = in mathematical methodology. Stochastic models should cover aspects like de= mands, renewable productions, delays in maintenance operations and availabi= lity of power plants (failures, efficiency,...). A highly desirable aim is = to achieve stability of the computed schedule with respect to small modific= ations in the input. In deregulated markets game theoretic aspects en= ter because an independent system operator must approve time windows in vie= w of the proposals of several competitors.

**Contributors**:

Prof. Christoph Helmberg, TU Chemnitz

Prof. Etienne de Klerk, Tilburg University

Dr Thomas Triboulet, EDF

Dr. Fabrizio Lacalandra, QuanTek