We formulate and transform a real-world combinatorial problem into a constraint satisfaction problem: choose a restricted set of containers from a warehouse, such that the elements contained in the containers satisfy some restrictions and compatibility criteria. We set up a formal, mathematical model, describe the combinatorial problem and define a (nonlinear) system of equations, which describes the equivalent constraint satisfaction problem. Next, we use the framework provided by the Apache Commons Mathematics Library in order to implement a solution based on genetic algorithms. We carry out performance tests and show that a general approach, having business logic solely in the definition of the fitness function, can deliver satisfactory results for a real-world use-case in the manufacturing industry.