Scheduling and Resource Allocation for Improving Service and Operations Management: Modelling, Solution Methods and Applications (especially in Healthcare)

本提案将开发模型和解决方案方法，以改进服务和运营管理应用程序中的调度和资源分配决策，特别是在医疗保健领域。目标是实现更好的服务水平（例如，更短的等待时间（直到服务日），及时的服务（在服务时）），降低服务/产品提供商的成本（例如，更少的加班，更低的容量需求）和更好地利用资源。提案的模型和方法在服务、医疗保健和制造业等不同行业中有许多实际应用。主要考虑两个方面：***联合预约和提前调度(CAAS)***广义多资源调度(GMRS)*** CAAS的目的是为一个服务系统找到一个最佳调度，其中工作（例如，客户，患者）随机到达系统（到达时间，数量，优先级和工作类型），并分配一个服务日。作业等待到服务当天，作业处理时间是随机的。作业在服务当天按照给定的顺序进行处理。目标是找到一个调度策略，使总预期成本最小化（在服务开始之前和服务开始期间）。调度策略包括确定服务的日期（date）和服务的时间（特定服务日的预约时间）。该成本包括服务当天的等待时间、服务当天的等待时间、服务器空闲时间和服务器超时时间。我将寻求以下问题的答案：***如何建模和解决CAAS问题？如何用不同的客观标准来解决CAAS问题，而不是最小化期望值（例如，成本的百分位数）？***如何确定每日加工的最佳作业顺序？***如何添加一个终端资源，让所有作业在处理后和离开系统之前停留一段时间？*** GMRS的目标是开发模型和解决方法，以找到一个排序时间表，使给定的一组作业（如手术）的处理成本最小化，这些作业将由多组资源（如外科医生和麻醉师）在多台机器（如手术室）上处理。这种模型的输出是使机器运行的总成本（常规时间和加班时间）最小化的最优机器数量和最优作业处理计划（分配资源）。当在机器上处理一个作业时，每个资源需要以顺序的方式工作，并且考虑到不同资源之间的延迟时间（例如，外科医生必须等待直到准备和麻醉完成）。更复杂的是，工作有不同的类型（例如，外科专业），资源是基于工作类型的。我将搜索以下问题的答案：***如何建模和求解GMRS？***如何建模和求解随机版本的GMRS，即工作持续时间是随机的？***如何用终端资源建模和解决GMRS ？

This proposal will develop models and solution methods to improve scheduling and resource allocation decisions in service and operations management applications, especially in healthcare. The goal is to achieve better service levels (e.g., shorter wait times (until service day), timely service (at the say of service)), lower cost to service/product providers (e.g., less overtime, lower capacity requirements) and better utilization of resources. There are many real-world applications for the proposal's models and methods in different industries such as service, healthcare and manufacturing. Two main areas are considered: *** Combined appointment and advance scheduling (CAAS)*** Generalized multi resource scheduling (GMRS)***The aim of CAAS is to find an optimum schedule for a service system where jobs (e.g., customers, patients) arrive to the system randomly (arrival times, quantity, priority and job types) and they are assigned a service day. Jobs wait until the day of the service and job processing times are stochastic. Jobs are processed in a given order in the day of the service. The goal is to find a scheduling policy that minimizes total expected cost (before the day of the service and during the day of the service). The scheduling policy consists of determining day of the service (date) and time of the service (appointment time for a given day of the service). The cost consists of wait time until the day of the service, wait time during the day of the service, idle time of the server, and overtime of the server. I will seek answers to:*** How to model and solve the CAAS problem?*** How to solve the CAAS problem with a different objective criterion other than minimizing the expected value (e.g., a percentile of the cost)? *** How to determine an optimal sequence of jobs for daily processing? *** How to add an end-resource where all jobs stay for some time after they are processed and before they leave the system?***The goal of GMRS is to develop models and solution methods to find a sequencing schedule minimizing processing costs for a given set of jobs (e.g., surgeries) to be processed on multiple machines (e.g., operating rooms) by multiple sets of resources (e.g., surgeons and anesthetists). The output of such a model is the optimum number of machines and optimum job processing schedule (with assigned resources) minimizing the total cost of running machines (regular time and overtime). When a job is processed on a machine, each resource needs to work in a sequential manner and lag times (e.g., a surgeon must wait until preparation and anesthesia are done) between different resources are considered. Further complication is that jobs have different types (e.g., surgical specialty), and resources are based on job types. I will search answers for the following questions: *** How to model and solve GMRS?*** How to model and solve a stochastic version GMRS, i.e., job durations stochastic?*** How to model and solve GMRS with an end-resource?