The 2010 challenge problem from the French Operations Research Society (FORS) required participants to determine a minimum-cost production and maintenance schedule for a group of power plants, leading to a mixed-integer programming problem with some non-linear constraints. To model the stochastic nature of demand on the power system, each schedule is evaluated for a number of scenarios. This paper describes an implementation of a method from a 2009 paper by George Pocheron and others, which was a response to the 2010 Challenge, but the file this paper refers to is no longer on the FORS Challenge website. The authors of this paper present an implementation using the CPLEX package version 12.1, and include detailed results for tests using a variety of systems and demand scenarios.

The Benders decomposition is a two-phase solution technique for programming problems with linear constraints. First, some variable values are fixed and/or some constraints relaxed, forming a simpler subproblem that is then solved in the second phase. Differential data from the solution is used to modify the fixed information and continue iterating. Interesting variations used in this paper include a preprocessing phase to detect possible pairs of conflicting constraints and a repair procedure in the second phase to deal with the non-linear constraints.

There is little about how the differential information from phase two is used in phase one. Moreover, the authors do not make clear what they have done beyond a straightforward application of the CPLEX package to the method described in the 2009 paper.