A careful solution: patient scheduling in health care

Koole, G.M. [Promotor

Robust Appointment Scheduling for Random Service Time Using Min-Max Optimization

Appointment Scheduling is an increasingly challenging problem for service-centers, healthcare, production and transportation sector. Challenges include meeting growing demand and high expectation of service level among the customers and ensuring an efficient service system which reduces the expenditure related to idle times and under-utilization of the system. The problem becomes more complicated in the presence of processing time uncertainties. In this study, a Robust Appointment Scheduling model is developed using Min-max Optimization to provide appointment dates for a system with a single processor. The objective is to minimize the cost of the worst-case scenario under any realization of the processing time of the jobs. The proposed methodology requires less information regarding the uncertain parameters and can provide optimal solution while only considering the extreme bounds of the uncertain parameters. Therefore, it is applicable to any probability distribution of the uncertain parameters. The model is well suited for any general case appointment scheduling problem regardless of the application field. Since the problem is NP-hard, an Iterative Solution Procedure and a Dynamic Programming model are developed for solving larger instances of problem in polynomial time. In addition, propositions that support the robust model are provided along with theoretical proofs. Appointment scheduling of two case studies, a Dentist’s clinic and VIA Rail Canada are performed. Both case studies exhibit high performance of the proposed robust model in terms of cost savings and computational efforts. This work will contribute both to the literature related to uncertainty handling in decision making and to the industries, which aim to achieve an efficient service system

Submodularity and Its Applications in Wireless Communications

This monograph studies the submodularity in wireless communications and how to use it to enhance or improve the design of the optimization algorithms. The work is done in three different systems. In a cross-layer adaptive modulation problem, we prove the submodularity of the dynamic programming (DP), which contributes to the monotonicity of the optimal transmission policy. The monotonicity is utilized in a policy iteration algorithm to relieve the curse of dimensionality of DP. In addition, we show that the monotonic optimal policy can be determined by a multivariate minimization problem, which can be solved by a discrete simultaneous perturbation stochastic approximation (DSPSA) algorithm. We show that the DSPSA is able to converge to the optimal policy in real time. For the adaptive modulation problem in a network-coded two-way relay channel, a two-player game model is proposed. We prove the supermodularity of this game, which ensures the existence of pure strategy Nash equilibria (PSNEs). We apply the Cournot tatonnement and show that it converges to the extremal, the largest and smallest, PSNEs within a finite number of iterations. We derive the sufficient conditions for the extremal PSNEs to be symmetric and monotonic in the channel signal-to-noise (SNR) ratio. Based on the submodularity of the entropy function, we study the communication for omniscience (CO) problem: how to let all users obtain all the information in a multiple random source via communications. In particular, we consider the minimum sum-rate problem: how to attain omniscience by the minimum total number of communications. The results cover both asymptotic and non-asymptotic models where the transmission rates are real and integral, respectively. We reveal the submodularity of the minimum sum-rate problem and propose polynomial time algorithms for solving it. We discuss the significance and applications of the fundamental partition, the one that gives rise to the minimum sum-rate in the asymptotic model. We also show how to achieve the omniscience in a successive manner

Demand and Capacity Management for Medical Practices

This thesis on tactical demand and capacity management for medical practices consists of four main parts. In the first part, we analyze the general planning and control decisions that need to be taken by a practice manager when opening and then running a medical practice. We further present a best-case data set containing all relevant information on interactions between patient and practice. We compare several real-world appointment data sets to this best-case data set, commenting on the consequences of not collecting specific data. We discuss the fundamental problem of defining model parameters from data and give recommendations for modelers and practitioners to bridge the gap between theory and practice. In the second part, we present a flexible analytical queueing model to investigate the relationship between the physician\u27s daily capacity, the panel size, and the distribution of indirect waiting times of patients. Essential features of the basic model are the consideration of queue length-dependent parameters such as the appointment request rate, the no-show probability, and the rescheduling probability. We present several extensions to the basic model, including the consideration of queue length-dependent service times. Finally, we investigate the model behavior by conducting extensive numerical experiments. In the third part, we propose deterministic integer linear programs that decide on the intake of new patients into panels over time, considering the future panel development. Here, we minimize the deviation between the expected panel workload and the physician\u27s capacity over time. We classify panel patients and define transition probabilities from one class to another from one period to the next. Experiments are conducted with parameters based on real-world data. We use the programs to define upper bounds on the number of patients in a patient class to be accepted in a period through solving the programs several times with different demand inputs. When we use those upper bounds in a stochastic discrete-event environment, the expected differences between workload and capacity can be significantly reduced over time, considering several future periods instead of one in the optimization. Using a detailed classification of new patients decreases the expected differences further. In the last part, we present further integer linear programs to decide on the intake of new patients. For example, we consider several physicians with overlapping panels and capacities as decision variables. Last but not least, we investigate how the queueing model and the panel management programs could be combined

Stochastic Optimization Approaches for Outpatient Appointment Scheduling under Uncertainty

Outpatient clinics (OPCs) are quickly growing as a central component of the healthcare system. OPCs offer a variety of medical services, with benefits such as avoiding inpatient hospitalization, improving patient safety, and reducing costs of care. However, they also introduce new challenges for appointment planning and scheduling, primarily due to the heterogeneity and variability in patient characteristics, multiple competing performance criteria, and the need to deliver care within a tight time window. Ignoring uncertainty, especially when designing appointment schedules, may have adverse outcomes such as patient delays and clinic overtime. Conversely, accounting for uncertainty when scheduling has the potential to create more efficient schedules that mitigate these adverse outcomes. However, many challenges arise when attempting to account for uncertainty in appointment scheduling problems. In this dissertation, we propose new stochastic optimization models and approaches to address some of these challenges. Specifically, we study three stochastic outpatient scheduling problems with broader applications within and outside of healthcare and propose models and methods for solving them. We first consider the problem of sequencing a set of outpatient procedures for a single provider (where each procedure has a known type and a random duration that follows a known probability distribution), minimizing a weighted sum of waiting, idle time, and overtime. We elaborate on the challenges of solving this complex stochastic, combinatorial, and multi-criteria optimization problem and propose a new stochastic mixed-integer programming model that overcomes these challenges in contrast to the existing models in the literature. In doing so, we show the art of, and the practical need for, good mathematical formulations in solving real-world scheduling problems. Second, we study a stochastic adaptive outpatient scheduling problem which incorporates the patients’ random arrival and service times. Finding a provably-optimal solution to this problem requires solving a MSMIP, which in turn must optimize a scheduling problem over each random arrival and service time for each stage. Given that this MSMIP is intractable, we present two approximation based on two-stage stochastic mixed-integer models and a Monte Carlo Optimization approach. In a series of numerical experiments, we demonstrate the near-optimality of the appointment order (AO) rescheduling policy, which requires that patients are served in the order of their scheduled appointments, in many parameter settings. We also identify parameter settings under which the AO policy is suboptimal. Accordingly, we propose an alternative swap-based policy that improves the solution of such instances. Finally, we consider the outpatient colonoscopy scheduling problem, recognizing the impact of pre-procedure bowel preparation (prep) quality on the variability of colonoscopy duration. Data from a large OPC indicates that colonoscopy durations are bimodal, i.e., depending on the prep quality they can follow two different probability distributions, one for those with adequate prep and the other for those with inadequate prep. We define a distributionally robust outpatient colonoscopy scheduling (DRCOS) problem that seeks optimal appointment sequence and schedule to minimize the worst-case weighted expected sum of patient waiting, provider idling, and provider overtime, where the worst-case is taken over an ambiguity set characterized through the known mean and support of the prep quality and durations. We derive an equivalent mixed-integer linear programming formulation to solve DRCOS. Finally, we present a case study based on extensive numerical experiments in which we draw several managerial insights into colonoscopy scheduling.PHDIndustrial & Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/151727/1/ksheha_1.pdfDescription of ksheha_1.pdf : Restricted to UM users only