Mixed-Integer Rounding Enhanced Benders Decomposition for Multiclass Service-System Staffing and Scheduling with Arrival Rate Uncertainty
针对客户到达量不确定的多类服务系统，提出一个整合人员配置与排班的随机整数规划模型，并用混合整数舍入技术增强Benders分解算法来高效求解，相比分开决策能降低排班成本。
We study server scheduling in multiclass service systems under uncertainty in the customer arrival volumes. Common practice in such systems is to first identify staffing levels and then determine schedules for the servers that cover these levels. We propose a new stochastic integer programming (SIP) model that integrates these two decisions, which can yield lower scheduling costs by exploiting the presence of alternative server configurations that yield similar quality of service. We find that a branch-and-cut algorithm based on Benders decomposition may fail due to the weakness of the relaxation bound. We propose a novel application of mixed-integer rounding to improve the Benders cuts used in this algorithm, a technique that is applicable to any SIP with integer first-stage decision variables. Numerical examples illustrate the computational efficiency of the proposed approach and the potential benefit of solving the integrated model compared to considering the staffing and scheduling problems separately. This paper was accepted by Yinyu Ye, optimization.