Two stochastic optimization methods for shift design with uncertain demand. (February 2023) - Wu, Zhiying; Xu, Guoning; Chen, Qingxin; Mao, Ning
Highlights: A shift design model with a probability constraint on demand satisfaction is proposed. Two scenario-based approaches are introduced to solve the stochastic version of shift design model. Both stochastic methods achieve good performance in numerical experiments. Abstract: The purpose of this paper is to investigate the shift design problem with a probability constraint on demand satisfaction and to design the corresponding stochastic model so that the staffing for each shift can cope with stochastic demand. To solve this stochastic model, we propose two solution methods: a method involving average sample approximation and a two-stage heuristic algorithm based on statistics with a greedy strategy. Numerical results show that both methods can solve the stochastic model of this paper well, and the sample average approximation method outperforms the two-stage heuristic algorithm in terms of cost optimization. However, as the number of scenarios used to approximate realistic situations increases,  the superiority of the two-stage heuristic algorithm in terms of solution speed becomes progressively more significant.