An important property of answer generation strategies for functional logic programming (FLP) languages is the complete exploration of the solution space. Integrating constraints into FLP proves to be useful in many cases, as the resulting constraint functional logic programming (CFLP) offers more facilities and more efficient operational semantics. CFLP can be achieved using conditional rewrite systems with a narrowing-based operational semantics. A common idea to improve the efficiency of such operational semantics is to use specific algorithms from operations research as constraint solvers. If the algorithm does not return a complete set of solutions, the property of completeness might be lost. We present a real world timetabling problem illustrating this approach. We propose an algorithm, obtained as an integration of three known optimization algorithms for the linear assignment problem (LAP), enumerating solutions to the LAP in order of increasing weight, such that the answer generation is complete again. We show, how the narrowing process can be tailored to use this algorithm and provide an efficient way to solve the timetable generation problem.
