unweighted CFG propagator from [7]. Decompositions were slower than decompositions of the unweighted CFG constraint as the former uses integers instead of Booleans.

In the second set of experiments, we assigned weight 1 to activity productions, like Ai → ai, and post an additional cost function Pm j=1 zj that is minimized. Pm j=1 zj is the number of slots in which employees worked. Results are presented in Table1. We improved on the best solution found in the first model in 4 benchmarks and proved optimality in one. The decomposition of the weighted CFG constraint was slightly slower than the monolithic propagator, while entailment improved performance in most cases.

![0_image_0.png](0_image_0.png)

is the number of employees, **cost** shows the total number of slots in which employees worked in the best solution, **time** is the time to find the best solution, bt is the number of backtracks to find the best solution, BT is the number of backtracks in one hour, Opt shows if optimality is proved, Imp shows if a lower cost solution is found by the second model

## References
