Workforce sizing and scheduling in Telemedecine

远程医疗是利用电信和信息技术提供远程医疗服务。患者和医疗专家之间的虚拟交互可以是预先录制的，也可以是实时完成的。在这种互动中，医疗保健专家就患者是治疗他/她的症状、等待看他/她的常规医生、去诊所还是去急诊室哪个更好提供建议。在这个项目中，我们与对话合作，这是一家总部位于蒙特利尔的初创公司，为加拿大公司提供先进和负担得起的移动医疗服务。对话组织雇佣了不同类型的医疗专家。虽然员工从周一到周五的工作时间是从早上8点到晚上8点，但患者可以在一天中的任何时间登录这款应用。Dialog目前通过估计比率来衡量和安排员工队伍：一名护士每小时可以服务的聊天次数/到达系统的病人数量，助理数量/护士数量。此外，对一名医疗专家每段时间可以提供的聊天次数的估计不包括员工的资历和经验。这种规划方法往往导致无法聘请适当数量的医疗专家，导致服务水平下降(即患者在获得服务之前等待很长时间)，并导致护士过度使用，因为他们通常被分配到加班时间，分配给更多的病人，超出了他们的处理能力。因此，该项目的目标是为对话提供一个决策支持工具，以确定工作人员的规模和日程安排。这涉及到建模和解决方案方面的几个挑战。我们面临着复杂的工作规则、需求的多变性和不确定性以及规划范围的长度。为了应对这些挑战，我们提出了一个两阶段随机规划模型。该模型将包括需求中的不确定性，以提供强大的人员配备和调度决策，以更好地对患者需求的变化做出反应。我们相信，这样的项目的实施将有助于减少患者的等待时间，提高满意度。此举亦应可纾缓诊所和医院的挤迫情况。

Telemedicine is the use of telecommunication and information technology to provide healthcare from adistance. The virtual interaction between the patient and the healthcare expert can be either pre-recorded ordone in real-time. In this interaction, a healthcare expert offers advice on whether it is better for the patient totreat his/her symptoms, wait to see his/her regular doctor, go to a clinic, or go to an emergency room. In thisproject, we collaborate with Dialogue, a Montreal-based start-up that provides progressive and affordablehealthcare, accessible on mobile, for Canadian companies. Dialogue employs different types of healthcareexperts. Although employees work from 8am to 8pm from Monday to Friday, patients can log into the app atany time of the day. Dialogue currently dimensions and schedules the workforce by estimating ratios: numberof chats a nurse can serve per hour/number of patients arriving to the system, number of assistants/number ofnurses. Moreover, the estimate of the number of chats that a healthcare expert can serve per time period doesnot include the level of seniority and the experience of the employee. This planning method often results in theinability to hire an appropriate number of healthcare experts, in a decrease in the service level (i.e. patientsusually wait a long time before being served), and in the over-utilization of nurses as they are usually allocatedto overtime and they are assigned to more patients than they can handle. The objective of this project istherefore to provide Dialogue with a decision-support tool to staff dimensioning and scheduling. This involvesseveral challenges from the modeling and solution perspectives. We face complex work regulations, demandvariability and uncertainty and the length of the planning horizon. In order to address these challenges, wepropose to use a two-stage stochastic programming model. This model will include uncertainty in demands toprovide robust staffing and scheduling decisions that will react, in a better way, to changes in patients'requirements. We believe that the implementation of such a project will contribute to reducing patients' waittime and improving satisfaction. This should also relieve congestion in clinics and hospitals.