Solving Employee Timetabling Problems Using Boolean Satisfiability

The employee timetabling problem (ETP) is concerned with assigning a number of employees into a given set of shifts over a fixed period of time, e.g. a week, while meeting the employee´s preferences and organizational work regulations. The problem also attempts to optimize the performance criteria and distribute the shifts equally among the employees. The problem is considered a classical NP-complete optimization problem. It has received intensive research during the past few years given its use in industries and organizations. Several formulations and algorithms based on local search have been proposed to solve ETPs (Dowsland, 1998; Kragelund, 1997; Meisels et al., 1997; and Meisels and Schaerf, 2003). In this paper, we propose a complete approach using integer linear programming (ILP) to solve these problems. The ILP model of interest is developed and solved using the generic ILP solver CPLEX and the Boolean satisfiability ILP solver PBS. Experimental results indicate that the proposed model is tractable for reasonable-sized ETP problems