Mixed-integer programming models for an employee scheduling problem with multiple shifts and work locations

This paper is concerned with the problem of assigning employees to gas stations owned by the Kuwait National Petroleum Corporation (KNPC), which hires a firm to prepare schedules for assigning employees to about 86 stations distributed all over Kuwait. Although similar employee scheduling problems have been addressed in the literature, certain peculiarities of the problem require novel mathematical models and algorithms to deal with the specific nature and size of this problem. The problem is modeled as a mixed-integer program, and a problem size analysis based on real data reveals that the formulation is too complex to solve directly. Hence, a two-stage approach is proposed, where the first stage assigns employees to stations, and the second stage specifies shifts and off-days for each employee. Computational results related to solving the two-stage models directly via CPLEX and by specialized heuristics are reported. The two-stage approach provides daily schedules for employees for a given time horizon in a timely fashion, taking into consideration the employees' expressed preferences. This proposed modeling approach can be incorporated within a decision support system to replace the current manual scheduling practice that is often chaotic and has led to feelings of bias and job dissatisfaction among employees.