Mixed-integer linear programming and constraint programming formulations for solving resource availability cost problems

We consider the resource availability cost problem and two extensions through general temporal constraints and calendar constraints. With general temporal constraints minimum and maximum time lags between the activities can be ensured. Calendar constraints are used to model breaks in the availability of a resource, e.g., weekends or public holidays of resource types that equal staff. Especially if long-term and capital-intensive projects are under consideration, resource availability cost problems should be applied because in such projects it is more important to minimize the cost than, e.g., the project duration. We present mixed-integer linear programming (MILP) formulations as well as constraint programming (CP) models for the three problems. In a performance study we compare the results of the MILP formulations solved by cplex and the CP models solved by the lazy clause generation solver chuffed on benchmark instances from literature and also introduce new benchmarks. Our CP models close all open instances for resource availability cost problems from the literature.