Challenges and solutions for the integrated recovery room planning and scheduling problem during COVID-19 pandemic.

This study presents an efficient solution for the integrated recovery room planning and scheduling problem (IRRPSP). The complexity of the IRRPSP is caused by several sources. The problem combines the assignment of patients to recovery rooms and the scheduling of caregivers over a short-term planning horizon. Moreover, a solution of the IRRPSP should respect a set of hard and soft constraints while solving the main problem such as the maximum capacity of recovery rooms, the maximum daily load of caregivers, the treatment deadlines, etc. Thus, the need for an automated tool to support the decision-makers in handling the planning and scheduling tasks arises. In this paper, we present an exhaustive description of the epidemiological situation within the Kingdom of Saudi Arabia, especially in Jeddah Governorate. We will highlight the importance of implementing a formal and systematic approach in dealing with the scheduling of recovery rooms during extreme emergency periods like the COVID-19 era. To do so, we developed a mathematical programming model to present the IRRPSP in a formal way which will help in analyzing the problem and lately use its solution for comparison and evaluation of our proposed approach. Due to the NP-hard nature of the IRRPSP, we propose a hybrid three-level approach. This study uses real data instances received from the Department of Respiratory and Chest Diseases of the King Abdulaziz Hospital. The computational results show that our solution significantly outperforms the results obtained by CPLEX software with more than 1.33% of satisfied patients on B1 benchmark in much lesser computation time (36.27 to 1546.79 s). Moreover, our proposed approach can properly balance the available nurses and the patient perspectives.

A decomposition - construction approach for solving the home health care scheduling problem.

Solving NP-hard Combinatorial Optimization Problems (COP) is a complex process as it deals with difficult cases essentially when using classical modeling techniques that may fail in handling real-life problems efficiently. In this context, Hierarchical Optimization Models (HOM) can be viewed as an effective alternative for modeling numerous difficult optimization problems. Their efficiency is explained by their ability to relax the COP complexity by decomposing it hierarchically into a set of weaker and easier interconnected subproblems. Recently, the HOM has been effectively used to model NP-hard COPs in many fields such as healthcare, supply chain, transport, economic, etc. In this paper, we will use the HOM to model the Home Health Care Scheduling Problem (HCSP). The proposed model will divide the HCSP into three subproblems namely the grouping, the assignment, and the routing subproblems. The result of the decomposition phase is represented using a Hierarchical Directed Acyclic Graph (HDAG) showing a graph of interconnected subproblems as nodes and their decomposition and/or dependency links as edges. The paper embeds also a generic algorithm for traversing the obtained HDAG to visit all nodes in the order satisfying the decomposition and dependency edges. Each visited problem is then solved using a specific algorithm. The developed approach was applied to solve a real-life instance from Zealand Company and the obtained results outperform other known approaches.