Assigning multi-skill configurations to multiple servers with a Scenario-Based Planning and Recombination Approach

This work deals with a dynamic problem arising from an outpatient healthcare facility. Patients with varying priorities arrive throughout the day, each with specific service requests that must be satisfied within target times. Failure to meet these targets incurs weighted tardiness penalties. Additionally, patients may choose to leave the system if subjected to prolonged waiting times, leading to further weighted penalties. The outpatient facility is equipped with multiple identical servers, each capable of providing a finite subset of services, referred to as configurations. The objective is to dynamically assign configurations, selected from a predefined set, to servers by minimizing the sum of weighted tardiness and abandonment penalties. Assignments are not fixed statically but can be dynamically changed over time to cope with the service requests. To address this problem, we propose a Scenario-Based Planning and Recombination Approach (SBPRA) that integrates an inner Reduced Variable Neighborhood Search. Differently from the traditional Scenario-Based Planning Approach (SBPA), which makes decisions based only on the solutions of individual scenarios, our approach solves an optimization problem to produce an additional solution that offers the best balance among the scenario solutions. Extensive tests on realistic instances show that SBPRA generates solutions that are 38% on average more effective than those generated by SBPA. Overall, the proposed approach can optimize resource allocation, mitigate the impact of patient abandonment, and improve the performance of the outpatient healthcare facility.