Planning methods using data envelopment analysis and markov systems

Abstract

This paper explores the extension of a modelling framework that integrates data envelopment analysis (DEA) and markov systems, into a two-stage setting. In a recent paper in EJOR, a single-stage DEA-markov hybrid model was introduced, establishing a research direction blending these seemingly distinct approaches to address the attainability problem in workforce planning. Markov systems are widely used in scenarios where a population system (e.g., staff profiles, patients with chronic conditions) begins the planning horizon in a specific state and aims to transition to a new state by the end of the horizon. Although it is common for this horizon to encompass multiple steps, this hybrid model considered attainability within a single-step horizon. In the current study, we investigate problems in two phases and integrate a network DEA approach with markovian population systems under various assumptions, resulting into new variations of the relevant models. The decision maker (DM) can specify potential future outcomes (e.g., personnel flows) in consecutive steps in time, and use DEA to identify feasible courses of action through convexity (or even use the second stage in a normative manner to identify optimal flows). The two-stage DEA model captures the DM’s relative preferences for future states and provides measures of efficacy of potential flows relative to the ultimate desired state. Consequently, the organization can plan interventions to enhance the probability of achieving some anticipated goal. The paper includes illustrations using data from workforce planning and concludes with a discussion on relevant issues in healthcare, circular economy and social radicalization.