Hari Balasubramanian

Optimal Allocation of Surgery Blocks to Operating Rooms Under Uncertainty

The allocation of surgeries to operating rooms (ORs) is a challenging combinatorial optimization problem. There is also significant uncertainty in the duration of surgical procedures, which further complicates assignment decisions. In this paper, we present stochastic optimization models for the assignment of surgeries to ORs on a given day of surgery. The objective includes a fixed cost of opening ORs and a variable cost of overtime relative to a fixed length-of-day. We describe two types of models. The first is a two-stage stochastic linear program with binary decisions in the first stage and simple recourse in the second stage. The second is its robust counterpart, in which the objective is to minimize the maximum cost associated with an uncertainty set for surgery durations. We describe the mathematical models, bounds on the optimal solution, and solution methodologies, including an easy-to-implement heuristic. Numerical experiments based on real data from a large health-care provider are used to contrast the results for the two models and illustrate the potential for impact in practice. Based on our numerical experimentation, we find that a fast and easy-to-implement heuristic works fairly well, on average, across many instances. We also find that the robust method performs approximately as well as the heuristic, is much faster than solving the stochastic recourse model, and has the benefit of limiting the worst-case outcome of the recourse problem.

Heuristic scheduling of jobs on parallel batch machines with incompatible job families and unequal ready times

This research is motivated by a scheduling problem found in the diffusion and oxidation areas of semiconductor wafer fabrication, where the machines can be modeled as parallel batch processors. We attempt to minimize total weighted tardiness on parallel batch machines with incompatible job families and unequal ready times of the jobs. Given that the problem is NP-hard, we propose two different decomposition approaches. The first approach forms fixed batches, then assigns these batches to the machines using a genetic algorithm (GA), and finally sequences the batches on individual machines. The second approach first assigns jobs to machines using a GA, then forms batches on each machine for the jobs assigned to it, and finally sequences these batches. Dispatching and scheduling rules are used for the batching phase and the sequencing phase of the two approaches. In addition, as part of the second decomposition approach, we develop variations of a time window heuristic based on a decision theory approach for forming and sequencing the batches on a single machine.

Genetic algorithm based scheduling of parallel batch machines with incompatible job families to minimize total weighted tardiness

This research is motivated by a scheduling problem found in the diffusion and oxidation areas of semiconductor wafer fabrication, where the machines can be modelled as parallel batch processors. We attempt to minimize total weighted tardiness on parallel batch machines with incompatible job families. Given that the problem is NP-hard, we propose two different versions of a genetic algorithm (GA), each consisting of three different phases. The first version forms fixed batches, then assigns batches to the machines using a GA, and finally sequences the batches on individual machines. The second version assigns jobs to machines using a GA, then forms batches on each machine for the jobs assigned to it, and finally sequences these batches. Heuristics are used for the batching phase and the sequencing phase. For both these versions an additional fourth phase can be included wherein the sequenced batches are modified using pairwise swapping techniques. Using stochastically generated test data we show that algorithms of the first version of the GA outperform (1) traditional dispatching rules with respect to solution quality and (2) the algorithms of the second version with respect to both solution quality and computation time.

A Discrete Event Simulation Model to Evaluate Operational Performance of a Colonoscopy Suite

Background and Aims. Colorectal cancer, a leading cause of cancer death, is preventable with colonoscopic screening. Colonoscopy cost is high, and optimizing resource utilization for colonoscopy is important. This study’s aim is to evaluate resource allocation for optimal use of facilities for colonoscopy screening. Method. The authors used data from a computerized colonoscopy database to develop a discrete event simulation model of a colonoscopy suite. Operational configurations were compared by varying the number of endoscopists, procedure rooms, the patient arrival times, and procedure room turnaround time. Performance measures included the number of patients served during the clinic day and utilization of key resources. Further analysis included considering patient waiting time tradeoffs as well as the sensitivity of the system to procedure room turnaround time. Results. The maximum number of patients served is linearly related to the number of procedure rooms in the colonoscopy suite, with a fixed room to endoscopist ratio. Utilization of intake and recovery resources becomes more efficient as the number of procedure rooms increases, indicating the potential benefits of large colonoscopy suites. Procedure room turnaround time has a significant influence on patient throughput, procedure room utilization, and endoscopist utilization for varying ratios between 1:1 and 2:1 rooms per endoscopist. Finally, changes in the patient arrival schedule can reduce patient waiting time while not requiring a longer clinic day. Conclusions. Suite managers should keep a procedure room to endoscopist ratio between 1:1 and 2:1 while considering the utilization of related key resources as a decision factor as well. The sensitivity of the system to processes such as turnaround time should be evaluated before improvement efforts are made.

Scheduling interfering job sets on parallel machines

We consider bicriteria scheduling on identical parallel machines in a nontraditional context: jobs belong to two disjoint sets, and each set has a different criterion to be minimized. The jobs are all available at time zero and have to be scheduled (non-preemptively) on m parallel machines. The goal is to generate the set of all non-dominated solutions, so the decision maker can evaluate the tradeoffs and choose the schedule to be implemented. We consider the case where, for one of the two sets, the criterion to be minimized is makespan while for the other the total completion time needs to be minimized. Given that the problem is NP-hard, we propose an iterative SPT-LPT-SPT heuristic and a bicriteria genetic algorithm for the problem. Both approaches are designed to exploit the problem structure and generate a set of non-dominated solutions. In the genetic algorithm we use a special encoding scheme and also a unique strategy - based on the properties of a non-dominated solution - to ensure that all parts of the non-dominated front are explored. The heuristic and the genetic algorithm are compared with a time-indexed integer programming formulation for small and large instances. Results indicate that the both the heuristic and the genetic algorithm provide high solution quality and are computationally efficient. The heuristics proposed also have the potential to be generalized for the problem of interfering job sets involving other bicriteria pairs.

Optimization of PSA Screening Policies: A Comparison of the Patient and Societal Perspectives

Objective. To estimate the benefit of PSA-based screening for prostate cancer from the patient and societal perspectives. Method. A partially observable Markov decision process model was used to optimize PSA screening decisions. Age-specific prostate cancer incidence rates and the mortality rates from prostate cancer and competing causes were considered. The model trades off the potential benefit of early detection with the cost of screening and loss of patient quality of life due to screening and treatment. PSA testing and biopsy decisions are made based on the patient’s probability of having prostate cancer. Probabilities are inferred based on the patient’s complete PSA history using Bayesian updating. Data Sources. The results of all PSA tests and biopsies done in Olmsted County, Minnesota, from 1993 to 2005 (11,872 men and 50,589 PSA test results). Outcome Measures. Patients’ perspective: to maximize expected quality-adjusted life years (QALYs); societal perspective: to maximize the expected monetary value based on societal willingness to pay for QALYs and the cost of PSA testing, prostate biopsies, and treatment. Results. From the patient perspective, the optimal policy recommends stopping PSA testing and biopsy at age 76. From the societal perspective, the stopping age is 71. The expected incremental benefit of optimal screening over the traditional guideline of annual PSA screening with threshold 4.0 ng/mL for biopsy is estimated to be 0.165 QALYs per person from the patient perspective and 0.161 QALYs per person from the societal perspective. PSA screening based on traditional guidelines is found to be worse than no screening at all. Conclusions. PSA testing done with traditional guidelines underperforms and therefore underestimates the potential benefit of screening. Optimal screening guidelines differ significantly depending on the perspective of the decision maker.

A lognormal approximation of activity duration in PERT using two time estimates

The success behind effective project management lies in estimating the time for individual activities. In many cases, these activity times are non-deterministic. In such situations, the conventional method (project evaluation and review technique (PERT)) obtains three time estimates, which are then used to calculate the expected time. In practice, it is often difficult to get three accurate time estimates. A recent paper suggests using just two time estimates and an approximation of the normal distribution to obtain the expected time and variance for that activity. In this paper, we propose an alternate method that uses only two bits of information: the most-likely and either the optimistic or the pessimistic time. We use a lognormal approximation and experimental results to show that our method is not only better than the normal approximation, but also better than the conventional method when the underlying activity distributions are moderately or heavily right skewed.

Improving Clinical Access and Continuity through Physician Panel Redesign

BackgroundPopulation growth, an aging population and the increasing prevalence of chronic disease are projected to increase demand for primary care services in the United States.ObjectiveUsing systems engineering methods, to re-design physician patient panels targeting optimal access and continuity of care.DesignWe use computer simulation methods to design physician panels and model a practice’s appointment system and capacity to provide clinical service. Baseline data were derived from a primary care group practice of 39 physicians with over 20,000 patients at the Mayo Clinic in Rochester, MN, for the years 2004–2006. Panel design specifically took into account panel size and case mix (based on age and gender).MeasuresThe primary outcome measures were patient waiting time and patient/clinician continuity. Continuity is defined as the inverse of the proportion of times patients are redirected to see a provider other than their primary care physician (PCP).ResultsThe optimized panel design decreases waiting time by 44% and increases continuity by 40% over baseline. The new panel design provides shorter waiting time and higher continuity over a wide range of practice panel sizes.ConclusionsRedesigning primary care physician panels can improve access to and continuity of care for patients.

Dynamic allocation of same-day requests in multi-physician primary care practices in the presence of prescheduled appointments

Appointments in primary care are of two types: 1) prescheduled appointments, which are booked in advance of a given workday; and 2) same-day appointments, which are booked as calls come during the workday. The challenge for practices is to provide preferred time slots for prescheduled appointments and yet see as many same-day patients as possible during regular work hours. It is also important, to the extent possible, to match same-day patients with their own providers (so as to maximize continuity of care). In this paper, we present a mathematical framework (a stochastic dynamic program) for same-day patient allocation in multi-physician practices in which calls for same-day appointments come in dynamically over a workday. Allocation decisions have to be made in the presence of prescheduled appointments and without complete demand information. The objective is to maximize a weighted measure that includes the number of same-day patients seen during regular work hours as well as the continuity provided to these patients. Our experimental design is motivated by empirical data we collected at a 3-provider family medicine practice in Massachusetts. Our results show that the location of prescheduled appointments – i.e. where in the day these appointments are booked – has a significant impact on the number of same-day patients a practice can see during regular work hours, as well as the continuity the practice is able to provide. We find that a 2-Blocks policy which books prescheduled appointments in two clusters – early morning and early afternoon – works very well. We also provide a simple, easily implementable policy for schedulers to assign incoming same-day requests to appointment slots. Our results show that this policy provides near-optimal same-day assignments in a variety of settings.

The impact of case mix on timely access to appointments in a primary care group practice

At the heart of the practice of primary care is the concept of a physician panel. A panel refers to the set of patients for whose long term, holistic care the physician is responsible. A physician’s appointment burden is determined by the size and composition of the panel. Size refers to the number of patients in the panel while composition refers to the case-mix, or the type of patients (older versus younger, healthy versus chronic patients), in the panel. In this paper, we quantify the impact of the size and case-mix on the ability of a multi-provider practice to provide adequate access to its empanelled patients. We use overflow frequency, or the probability that the demand exceeds the capacity, as a measure of access. We formulate problem of minimizing the maximum overflow for a multi-physician practice as a non-linear integer programming problem and establish structural insights that enable us to create simple yet near optimal heuristic strategies to change panels. This optimization framework helps a practice: (1) quantify the imbalances across physicians due to the variation in case mix and panel size, and the resulting effect on access; and (2) determine how panels can be altered in the least disruptive way to improve access. We illustrate our methodology using four test practices created using patient level data from the primary care practice at Mayo Clinic, Rochester, Minnesota. An important advantage of our approach is that it can be implemented in an Excel Spreadsheet and used for aggregate level planning and panel management decisions.