In prevailing scientific papers it is assumed that waiting time for an appointment and the quality of care do not influence clients’ choice behavior. Therefore, the decision is only about the facilities’ locations and the number of servers per facility. However, it has been shown that this assumption yields suboptimal results in terms of participation. In this contribution we consider clients’ utility function to include variables denoting the waiting time for an appointment and the quality of care. Both variables are defined as functions of a facility’s utilization. At first glance, this yields a mixed integer non–linear model formulation. As commonly modeled in empirical choice studies, we assume that the waiting time for an appointment can be considered to be categorial, i. e. the variable takes on only a few discrete values. The minimum quantity requirement (as a proxy for quality of care) is considered as a categorial variable as well, i. e., it indicates whether a facility satisfies the requirement or not. These assumptions allow us to employ a segmentation approach to formulate a mixed integer linear program. We show that the problem can be solved to optimality in acceptable time, applying GAMS / CPLEX to our instances, based on both artificial data as well as in the context of a case study based on empirical data.
Keywords: discrete choice modeling, facility location, discrete optimization, logit, health care, congestion, waiting time
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| Graphical representation of waiting time level determination. |