A genetic algorithm for scheduling staff of mixed skills under multi-criteria

We consider the problem of scheduling staff with mixed skills. We formulate the problem as a multi-criteria optimization model, where the primary objective is to minimize the total cost for assigning staff to meet the manpower demands over time, the secondary objective is to seek a solution with the maximum surplus of staff among the solutions with almost same level of assigning cost, and the tertiary objective is to reduce the variation of staff surplus over different scheduling periods. This is a new model to handle the staff scheduling problem, which is motivated by the operational requirements in some local service organizations. We propose a new genetic algorithm (GA) to solve the problem. The proposed GA differs from traditional GAs in the following components: (1) it performs its parent selection by using a ranking scheme that considers successively the three criteria; (2) it uses a multi-point crossover operator based on the hamming distance between schedules; and (3) it adopts a heuristic to resolve the problem of infeasibility created by crossover operations. Computational results are reported, which show the effectiveness of the proposed approach in finding desirable solutions.