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.