Thesubjectofthisbookisthenested partitions method(NP), arelativelynew
optimization method that has been found to be very e?ective solving
discrete optimization problems. Such discrete problems are common in
many practical applications and the NP method is thus useful in diverse
application areas. It can be applied to both operational and planning
problems and has been demonstrated to e?ectively solve complex problems
in both manufacturing and service industries. To illustrate its broad
applicability and e?ectiveness, in this book we will show how the NP
method has been successful in solving complex problems in planning and
scheduling, logistics and transportation, supply chain design, data
mining, and health care. All of these diverse app-
cationshaveonecharacteristicincommon: theyallleadtocomplexlarge-scale
discreteoptimizationproblemsthatareintractableusingtraditionaloptimi-
tion methods. 1.1 Large-Scale Optimization
IndevelopingtheNPmethodwewillconsideroptimization problemsthatcan be
stated mathematically in the following generic form: minf(x), (1.1) x?X
where the solution space or feasible region X is either a discrete or
bounded ? set of feasible solutions. We denote a solution to this
problem x and the ? ? objective function value f = f (x