Nurse scheduling problem by considering total number of required nurses as well as nurses' preferences for working shifts: An algorithmic game-theoretic approach

In this paper, nurse scheduling problem (NSP) is studied by minimizing the total number of the required nurses as well as by maximizing the nurses’ preferences for working shifts. In this setting, hospital’s managers set the total number of the required nurses while nurse-chiefs select the required part-timers and then assign shifts to all nurses including the full-timers and the selected part-timers. Obviously, competition between the managers and nurse-chiefs to make decisions leads to a conflict between their objectives. In this point of view, a two-player game-theoretic framework can be established between them to set decisions. To our knowledge, this study is the first one that develops the game-theoretic approach to solve the NSP. In this setting, four game-theoretic models, including Managers-Stackelberg, Nurses-Stackelberg, Nash, and Centralized, are proposed based on the various competitive and cooperative interactions between the players. Moreover, a mathematical programming model is developed to obtain the equilibrium strategies. It is found that the managers and nurse-chiefs gain their best responses under the Managers-Stackelberg and Nurses-Stackelberg games, respectively. In the Nash game, they make decisions in order to meet their objectives, mostly. Moreover, the equilibrium strategies given by the Managers-Stackelberg and Centralized games are the same.