CAREER: Resource Allocation Under Uncertainty

整数规划是一种强大的技术，用于解决本质上是组合的问题，例如人员调度问题。为了确保满足整数规划模型的假设，通常必须对所研究的系统应用强简化假设。离散事件仿真是评估复杂系统预期性能的一种强大技术。人们可以在（离散事件）仿真模型中模拟几乎任意的复杂性。这个CAREER奖旨在将这两种管理科学技术联系起来，试图提供一种强大的优化方法，允许极大的模型复杂性。连接这些方法的方法要求仿真满足各种结构属性，并且这些结构信息可以传递给整数程序。本研究的重点是确定联动成功的一般条件，确定减少该方法计算需求的方法，并探索各种应用方法和领域。除了对管理科学理论的潜在贡献外，本研究的潜在应用还包括呼叫中心人员配置和救护车分配。在呼叫中心人员配置问题中，人们希望以最小化人员成本的方式分配人员轮班，同时确保客户服务令人满意。许多呼叫中心表现出复杂的客户路由和其他特征，这意味着模拟是预测给定员工水平的客户服务的首选方法。以比目前更低的成本获得满意的客户服务是可能的。在救护车分配问题中，人们试图确定何时何地放置救护车，以确保对呼叫的满意响应时间。同样，可能需要模拟来预测响应时间性能，并且可能以比当前情况更低的成本获得令人满意的响应时间性能。

Integer programming is a powerful technique for solving problems that are combinatorial in nature, such as staff scheduling problems. To ensure that the assumptions underlying integer programming models are satisfied, one must typically apply strong simplifying assumptions to the system under study. Discrete event simulation is a powerful technique for estimating the performance that can be expected from complex systems. One can model virtually arbitrary complexity in (discrete-event) simulation models. This CAREER award aims to link these two management science techniques in an attempt to provide a powerful optimization approach that allows great model complexity. The approach to linking these methods requires that the simulation satisfies various structural properties, and that this structural information can be communicated to the integer program. The focus of this research is in identifying general conditions under which the linkage will be successful, identifying methods to reduce the computational requirements of the approach, and exploring various application methods and areas.In addition to potential contributions to the theory of management science, potential applications of this research include call centre staffing and ambulance allocation. In the call centre staffing problem one wishes to assign staff to shifts in a way that minimizes staffing costs, while ensuring that customer service is satisfactory. Many call centres exhibit complex customer routing and other characteristics that mean that simulation is the preferred method for predicting customer service for a given staffing level. It may be possible to achieve satisfactory customer service at less cost than is currently the case. In the ambulance allocation problem, one is trying to determine when and where to place ambulances to ensure satisfactory response time performance to calls. Again, simulation may be needed to predict response time performance, and again, it may be possible to achieve satisfactory response time performance at less cost than is currently the case.