The permutation flowshop is a widely applied scheduling model. In many real-world applications of this model, a minimum and maximum time-lag must be considered between consecutive
operations. We can apply this model to healthcare systems in which the minimum time-lag could
be the transfer times, while the maximum time-lag could refer to the number of hours patients
must wait. We have modeled a MILP and a constraint programming model and solved them using CPLEX to find exact solutions. Solution times for both methods are presented. We proposed
two metaheuristic algorithms based on genetic algorithm and solved and compared them with each
other. A sensitivity of analysis of how a change in minimum and maximum time-lags can impact
waiting time and Cmax of the patients is performed. Results suggest that constraint programming is
a more efficient method to find exact solutions and changes in the values of minimum and maximum
time-lags can impact waiting times of the patients and Cmax significantly
