A branch and price algorithm for the resource constrained home health care vehicle routing problem

We consider the vehicle routing problem with resource constraints motivated by a home health care application. We propose a branch and price algorithm to solve the problem. In our problem, we consider different types of patients that require a nurse or a health aid or both. The patients can be serviced by the appropriate vehicles that may carry a nurse, or a health aid or both. The number of nurses and health aids are limited. We also need to satisfy time window constraints for each patient. We try to find feasible routes to minimize the total distance travelled. Our proposed branch and price scheme utilizes a label correcting algorithm with ng-relaxation and a heuristic pricing method. We demonstrate the effectiveness of our algorithm on random problem instances that we have generated based on Solomon instances upto 100 patients.