Optimizing a complex multi-objective personnel scheduling problem jointly complying with requests from customers and staff

This paper deals with a complex multi-objective personnel scheduling problem motivated by a real case. A multi-objective mixed integer linear programming formulation of the problem is proposed. Constraints are classified into mandatory and optional. The work introduces a solution approach, dubbed PRIMP (Prioritize & Improve), that enforces constraint satisfaction by adopting additional objective functions. All the (given and additional) objective functions are lexicographically ordered. The method sequentially solves single-objective problems, according to their priority. Each problem is first processed by an exact solver; if no optimal solution is found within a given time limit, the problem is then addressed heuristically. The proposed multi-stage method is efficient (it takes just a few minutes to produce a daily schedule) and effective, compared both to the manual approach followed by the company and to the method that optimally tackles each single-objective problem by means of a competitive mixed-integer linear programming solver. Experimental results indicate that PRIMP can produce high quality schedules, where a larger number of optional constraints are satisfied and both the global idle time of employees and the waiting time of customers is reduced. The approach is modular and easily adaptable to manage different objective functions and/or constraints.