Using Constraint Satisfaction Problem approach to solve human resource allocation problems in cooperative health services

In developing countries, the increasing utilization of health services, due to a great life expectancy, is followed by a reduction in incomes from the public health system and from private insurance companies, to the payment of medical procedures. Beyond this scenery, it is mandatory an effective hospital cost control though the utilization of planning tools. This work is intended to contribute to the reduction of hospital costs, proposing a new tool for planning human resources utilization in hospital plants. Specifically, it is proposed a new tool for human resources allocation in health units. The solution to the allocation problem uses the CSP technique (Constraint Satisfaction Problem) associated with the backtracking search algorithm. With the objective of enhancing the backtracking search algorithm performance a new heuristics is proposed. Through some simulations the performance of the proposed heuristics is compared to the other heuristics previously published in literature: remaining minimum values, forward checking and grade heuristics. Another important contribution of this work is the mathematical modeling of the constraints, that could be unary, multiple, numeric and implicit constraints. In the results it is presented a case study of a human resource allocation in a cooperative health service. Based on the results, it is proposed that for a real allocation problems solution, the best approach is to combine the remaining minimum values heuristics with the grade heuristics, to select the best unit allocation to be filled, and then use the proposed heuristic to select the best physician to the chosen unit allocation. This association shows a satisfactory result for the human resource allocation problem of the case study, with an algorithm convergence time of 46.7 min with no backtracks. The same problem when manually resolved took about more than 50 h.