Traditionally operational business decision models are represented and executed using business rules and decision management systems which utilize various rules engines. Such systems usually force human modelers to write rules for all possible combinations of decision variables to find one possible decision. In particular, this is true for decision models which follow the DMN standard. Alternatively, the same decision model can be represented using an optimization engine such as a constraint solver that does not need to know how to behave in all possible situations and is capable to automatically find multiple feasible decisions and even the optimal one. However, it is very difficult to represent all DMN constructs using only constraint programming facilities. Both these extreme approaches, rule engines and constraint solvers, have their limitations. This paper investigates the third way for business decision modeling when the entire decision model is split into several sub-models, some of which can be represented and executed using rule engines while others-using constraint or linear solvers. We demonstrate this approach using Decision Management Community Challenges and utilizing open source products "OpenRules" (for business decision models) and "Java Solver" (for optimization models) with various off-the-shelf constraint and linear solvers.