An Efficient Decision-Making Approach for the Planning of Diagnostic Services in a Segmented Healthcare System

In this paper, we address a decision-making problem related to the requirement of costly equipment by medical diagnostic services in a segmented public healthcare system comprising several institutions and private providers. The problem is motivated by a real-world case of the Mexican healthcare system. The aim of this study is to determine which hospitals can provide the service, their capacity levels, the allocation of demand in each institution, and the referral of patients to other institutions or private providers while minimizing annual investment costs and operating costs required to satisfy demand. A mixed-integer linear programming model that takes into account different characteristics such as patient acuity levels, types of equipment, and demand variation through time is introduced. The model was empirically assessed to evaluate its impact on the decision-making process. A sensitivity analysis to evaluate solution behavior for variations of critical parameters was performed. The results showed that some values could generate a significant effect on the total costs for the service coverage and in the efficiency of the service, whereas overall results indicated the usefulness of the model. While this model is valuable to aid this decision-making problem, it is limited to medium-size instances of up to 90 facilities. To solve the problems with larger instances, a two-phase heuristic algorithm is proposed. In the first phase, the method uses a greedy construction mechanism, and in the second phase, it attempts to improve the solution. Empirical evidence on large instances shows that good solutions with low computing times are reached in comparison with the exact method.