A simulation-based neighbourhood search algorithm to schedule multi-category patients at a multi-facility health care diagnostic centre

A key operational decision faced by a multi-facility health care diagnostic centre serving different patient categories (for example: Health Check-up Patient (HCP), Out-Patient (OP), Emergency Patient (EP), or In-Patient) is whom to serve next at a particular facility. In this paper, we model random arrival of these patients belonging to different categories and priorities at multiple diagnostic facilities over a finite planning horizon. We formulate a mathematical model for sequential decision-making under uncertainty using Markov Decision Process (MDP) with the objective of maximising net revenue and use dynamic programming (DP) to solve it. To address dimensionality and scalability issue of MDP, we provide a decentralised MDP (D_MDP) formulation. We develop simulation-based neighbourhood search algorithm to improve DP solution for D_MDP. We compare these solutions with three other rule-based heuristics using simulation.