Vikram Tiwari

Scheduling projects with heterogeneous resources to meet time and quality objectives

In service organizations, heterogeneity in workforce skills can lead to variation in end-product/service quality. The multi-mode, resource-constrained, project scheduling problem (MRCPSP), which assumes similar skills among resources in a given resource pool, accounts for differences in quality levels of individuals by assigning different activity durations depending on the skill level used. This approach is often inadequate to model the problem type investigated here. Using typical projects from the customer training division of a large telecommunications company (which motivated this research), a labor assignment problem using a successive work-time concept is formulated and solved using integer programming optimization procedures. The setting represents a multiple-project environment where projects are separate and independent, but require the same renewable resource mix for their completion. The paper demonstrates how the output of the model can be used to identify bottlenecks (or critical resource skills), and also demonstrates how cross-training the appropriately skilled groups or individuals can increase throughput. The approach guides decision-making concerning which workers to cross-train in order to extract the greatest benefits from worker-flexibility.

Value of a scheduled duration quantified in terms of equivalent numbers of historical cases.

BACKGROUND:Probabilistic estimates of case duration are important for several decisions on and soon before the day of surgery, including filling or preventing a hole in the operating room schedule, and comparing the durations of cases between operating rooms with and without use of specialized equipment to prevent resource conflicts. Bayesian methods use a weighted combination of the surgeon’s estimated operating room time and historical data as a prediction for the median duration of the next case of the same combination. Process variability around that prediction (i.e., the coefficient of variation) is estimated using data from similar procedures. A Bayesian method relies on a parameter, &tgr;, that specifies the equivalence between the scheduled estimate and the information contained in the median of a certain number of historical data. METHODS:Times from operating room entrance to exit (“case duration”) were obtained for multiple procedures and surgeons at 3 U.S. academic hospitals. A new method for estimating the parameter &tgr; was developed. RESULTS:(1) The method is reliable and has content, convergent, concurrent, and construct validity. (2) The magnitudes of the Somer’s D correlations between scheduled and actual durations are small when stratified by procedure (0.05–0.14), but substantial when pooled among all cases and procedures (0.58–0.78). This pattern of correlations matches that when medians (or means) of historical durations are used. Thus, scheduled durations and historical data are essentially interchangeable for estimating the median duration of a future case. (3) Most cases (79%–88%) either have so few historical durations (0–2) that the Bayesian estimate is influenced principally by the scheduled duration, or so many historical durations (>10) that the Bayesian estimate is influenced principally by the historical durations. Thus, the balance between the scheduled duration versus historical data has little influence on results for most cases. (4) Mean absolute predictive errors are insensitive to a wide range of values (e.g., 1–10) for the parameter. The implication is that &tgr; does not routinely need to be calculated for a given hospital, but can be set to any reasonable value (e.g., 5). CONCLUSIONS:Understanding performance of Bayesian methods for case duration is important because variability in durations has a large influence on appropriate management decisions the working day before and on the day of surgery. Both scheduled durations and historical data need to be used for these decisions. What matters is not the choice of &tgr; but quantifying the variability using the Bayesian method and using it in managerial decisions.

Explanation for the Near-Constant Mean Time Remaining in Surgical Cases Exceeding Their Estimated Duration, Necessary for Appropriate Display on Electronic White Boards

BACKGROUND: Consider a case that has been ongoing for longer than the scheduled duration. The anesthesiologist estimates that there is 1 hour remaining. Forty-five minutes later the case has not yet finished, and closure has not yet started. We showed previously that the mean (expected) time remaining is approximately 1 hour, not 15 minutes. The relationship is a direct mathematical consequence of the log-normal probability distributions of operating room (OR) case durations. We test the hypothesis that, with an accurate probabilistic model, until closure begins the estimated mean time remaining would be the mean time from the start of closure to OR exit. METHODS: Among the 311,940 OR cases in a 7-year time series from 1 hospital, there were 3962 cases for which (1) there had been previously at least 30 cases of the same combination of scheduled procedure(s), surgeon, and type of anesthetic and (2) the actual OR time exceeded the 0.9 quantile of case duration before the case started. A Bayesian statistical method was used to calculate the mean (expected) minutes remaining in the case at the 0.9 quantile. The estimate was compared with the actual minutes from the time of the start of closure until the patient exited the OR. RESULTS: The mean ± standard error of the pairwise difference was 0.2 ± 0.4 minutes. The Bayesian estimate for the 0.9 quantile was exceeded by 10.2% ± 0.01% of cases (i.e., very close to the desired 10.0% rate). CONCLUSIONS: If a case is taking longer than the expected (scheduled) duration, closure has not yet started, and someone in the OR is asked how much time the case likely has remaining, the value recorded on a clipboard for viewing later should be the estimated time remaining (e.g., “1 hour”) not an end time (e.g., “5:15 PM”). Electronic whiteboard displays should not show that the estimated time remaining in the case is less than the mean time from start of closure to OR exit. Similarly, if closure has started, the expected time remaining that is displayed should not be longer than the mean time from closure to OR exit. Finally, our results match previous reports that, before a case starts, statistical methods can reliably be used to assist in decisions involving the longest amount of time that cases may take (e.g., conflict checking for resources, filling holes in the OR schedule, and preventing holes in the schedule).

Predicting case volume from the accumulating elective operating room schedule facilitates staffing improvements.

Background:Precise estimates of final operating room demand can only be made 1 or 2 days before the day of surgery, when it is harder to adjust staffing to match demand. The authors hypothesized that the accumulating elective schedule contains useful information for predicting final case demand sufficiently in advance to readily adjust staffing. Methods:The accumulated number of cases booked was recorded daily, from which a usable dataset comprising 146 consecutive surgical days (October 10, 2011 to May 7, 2012, after removing weekends and holidays), and each with 30 prior calendar days of booking history, was extracted. Case volume prediction was developed by extrapolation from estimates of the fraction of total cases booked each of the 30 preceding days, and averaging these with linear regression models, one for each of the 30 preceding days. Predictions were verified by comparison with actual volume. Results:The elective surgery schedule accumulated approximately three cases per day, settling at a mean ± SD final daily volume of 117 ± 12 cases. The model predicted final case counts within 8.27 cases as far in advance as 14 days before the day of surgery. In the last 7 days before the day of surgery, the model predicted the case count within seven cases 80% of the time. The model was replicated at another smaller hospital, with similar results. Conclusions:The developing elective schedule predicts final case volume weeks in advance. After implementation, overly high- or low-volume days are revealed in advance, allowing nursing, ancillary service, and anesthesia managers to proactively fine-tune staffing up or down to match demand.

Modeling anesthetic times. Predictors and implications for short-term outcomes

BACKGROUND Little is known about the predictors of anesthetic times and impact of anesthetic and operative times on patient outcomes. METHODS We documented operative case length, anesthetic induction time length, and anesthetic recovery time length in 1713 consecutive patients who underwent elective vascular surgical interventions. We recorded patient and procedure-related characteristics that might influence the anesthetic time length, including a variable for possible July effect. Multivariate linear regression was used to model the length of anesthetic times. Multivariate logistic regression was used to model the impact of anesthetic and operative time lengths on a composite outcome of perioperative (30-d postoperative) death, myocardial infarction, cardiac arrhythmias, stroke, and congestive heart failure. RESULTS Statistically significant predictors of anesthetic induction time included body mass index, anesthesia type, and procedure type. Statistically significant predictors of anesthetic recovery time included operative case length, procedure type, and anesthesia type. After adjusting for the statistically significant covariates of total blood transfusion, history of coronary artery disease, and procedure type, there was a trend for increased likelihood of the composite end point as a function of operative time (odds ratio, 1.14; 95% confidence interval, 0.97-1.33; P = 0.09), which did not reach statistical significance. Multivariate analysis showed no association between the anesthetic time and composite end point. CONCLUSIONS Modeling individually anesthetic induction and recovery time on the basis of operative and anesthetic procedure characteristics is feasible. Anesthetic and operative times do not impact perioperative morbidity and mortality.

Derivation and out-of-sample validation of a modeling system to predict length of surgery.

BACKGROUND We performed a retrospective study to compare the precision of a regression model (RM) system with the precision of the standard method of surgical length prediction using historical means (HM). METHODS Data were collected on patients who underwent carotid endarterectomy and lower-extremity bypass. Multiple linear regression was used to model the operative time length (OTL). The precision of the RM versus HM in predicting case length then was compared in a validation dataset. RESULTS With respect to carotid endarterectomy, surgeon, surgical experience, and cardiac surgical risk were significant predictors of OTL. For lower-extremity bypass, surgeon, use of prosthetic conduit, and performance of a sequential bypass or hybrid procedure were significant predictors of OTL. The precision of out-of-sample prediction was greater for the RM system compared with HM for both procedures. CONCLUSIONS A regression methodology to predict case length appears promising in decreasing uncertainty about surgical case length.

Association of Health Literacy With Postoperative Outcomes in Patients Undergoing Major Abdominal Surgery

Importance Low health literacy is known to adversely affect health outcomes in patients with chronic medical conditions. To our knowledge, the association of health literacy with postoperative outcomes has not been studied in-depth in a surgical patient population. Objective To evaluate the association of health literacy with postoperative outcomes in patients undergoing major abdominal surgery. Design, Setting, and Participants From November 2010 to December 2013, 1239 patients who were undergoing elective gastric, colorectal, hepatic, and pancreatic resections for both benign and malignant disease at a single academic institution were retrospectively reviewed. Patient demographics, education, insurance status, procedure type, American Society of Anesthesiologists status, Charlson comorbidity index, and postoperative outcomes, including length of stay, emergency department visits, and hospital readmissions, were reviewed from electronic medical records. Health literacy levels were assessed using the Brief Health Literacy Screen, a validated tool that was administered by nursing staff members on hospital admission. Multivariate analysis was used to determine the association of health literacy levels on postoperative outcomes, controlling for patient demographics and clinical characteristics. Main Outcomes and Measures The association of health literacy with postoperative 30-day emergency department visits, 90-day hospital readmissions, and index hospitalization length of stay. Results Of the 1239 patients who participated in this study, 624 (50.4%) were women, 1083 (87.4%) where white, 96 (7.7%) were black, and 60 (4.8%) were of other race/ethnicity. The mean (SD) Brief Health Literacy Screen score was 12.9 (SD, 2.75; range, 3-15) and the median educational attainment was 13.0 years. Patients with lower health literacy levels had a longer length of stay in unadjusted (95% CI, 0.95-0.99; P = .004) and adjusted (95% CI, 0.03-0.26; P = .02) analyses. However, lower health literacy was not significantly associated with increased rates of 30-day emergency department visits or 90-day hospital readmissions. Conclusions and Relevance Lower health literacy levels are independently associated with longer index hospitalization lengths of stay for patients who are undergoing major abdominal surgery. The role of health literacy needs to be further evaluated within surgical practices to improve health care outcomes and use.

Use of simulation to assess a statistically driven surgical scheduling system

BACKGROUND To maximize operating room (OR) utilization, better estimates of case duration lengths are needed. We used computerized simulation to determine whether scheduling OR cases using a statistically driven system that incorporates patient and surgery-specific factors in the process of case duration prediction improves OR throughput and utilization. METHODS We modeled surgical and anesthetic length of vascular surgical procedures as a function of patient and operative characteristics using a multivariate linear regression approach (Predictive Modeling System [PMS]). Mean historical operative time per surgeon (HMS) and mean anesthetic time were also calculated for each procedure type. A computerized simulation of scheduling in a single OR performing vascular operations was then created using either the PMS or the HMS. RESULTS Compared to HMS, scheduling the operating room using the PMS increased throughput by a minimum of 15% (99.8% cumulative probability, P < 0.001). The PMS was slightly more likely to lead to overtime (mean 13% versus 11% of operative days during a calendar year, P < 0.001). However, the overtime lasted longer in the HMS group (mean 140 versus 95 min per day of overtime, P < 0.001). PMS was associated with lower OR underutilization rate (mean 23% versus 34% of operative days, P < 0.001) and less lengthy OR underutilization (mean 120 versus 193 min per day of underutilization, P < 0.001). CONCLUSIONS This computerized simulation demonstrates that using the PMS for scheduling in a single operating room increases throughput and other measures of surgical efficiency.

A Novel Method of Evaluating Key Factors for Success in a Multifaceted Critical Care Fellowship Using Data Envelopment Analysis

BACKGROUND: The current system of summative multi-rater evaluations and standardized tests to determine readiness to graduate from critical care fellowships has limitations. We sought to pilot the use of data envelopment analysis (DEA) to assess what aspects of the fellowship program contribute the most to an individual fellow’s success. DEA is a nonparametric, operations research technique that uses linear programming to determine the technical efficiency of an entity based on its relative usage of resources in producing the outcome. DESIGN: Retrospective cohort study. SUBJECTS AND SETTING: Critical care fellows (n = 15) in an Accreditation Council for Graduate Medical Education (ACGME) accredited fellowship at a major academic medical center in the United States. METHODS: After obtaining institutional review board approval for this retrospective study, we analyzed the data of 15 anesthesiology critical care fellows from academic years 2013–2015. The input-oriented DEA model develops a composite score for each fellow based on multiple inputs and outputs. The inputs included the didactic sessions attended, the ratio of clinical duty works hours to the procedures performed (work intensity index), and the outputs were the Multidisciplinary Critical Care Knowledge Assessment Program (MCCKAP) score and summative evaluations of fellows. RESULTS: A DEA efficiency score that ranged from 0 to 1 was generated for each of the fellows. Five fellows were rated as DEA efficient, and 10 fellows were characterized in the DEA inefficient group. The model was able to forecast the level of effort needed for each inefficient fellow, to achieve similar outputs as their best performing peers. The model also identified the work intensity index as the key element that characterized the best performers in our fellowship. CONCLUSIONS: DEA is a feasible method of objectively evaluating peer performance in a critical care fellowship beyond summative evaluations alone and can potentially be a powerful tool to guide individual performance during the fellowship.

Measuring Emergency Department Patient Population Acuity.

BACKGROUND Emergency department (ED) acuity is the general level of patient illness, urgency for clinical intervention, and intensity of resource use in an ED environment. The relative strength of commonly used measures of ED acuity is not well understood. METHODS We performed a retrospective cross-sectional analysis of ED-level data to evaluate the relative strength of association between commonly used proxy measures with a full spectrum measure of ED acuity. Common measures included the percentage of patients with Emergency Severity Index (ESI) scores of 1 or 2, case mix index (CMI), academic status, annual ED volume, inpatient admission rate, percentage of Medicare patients, and patients seen per attending-hour. Our reference standard for acuity is the proportion of high-acuity charts (PHAC) coded and billed according to the Centers for Medicare and Medicaid Services Ambulatory Payment Classification (APC) system. High-acuity charts included those APC 4 or 5 or critical care. PHAC was represented as a fractional response variable. We examined the strength of associations between common acuity measures and PHAC using Spearmans rank correlation coefficients (rs ) and regression models including a quasi-binomial generalized linear model and linear regression. RESULTS In our univariate analysis, the percentage of patients ESI 1 or 2, CMI, academic status, and annual ED volume had statistically significant associations with PHAC. None explained more than 16% of PHAC variation. For regression models including all common acuity measures, academic status was the only variable significantly associated with PHAC. CONCLUSION Emergency Severity Index had the strongest association with PHAC followed by CMI and annual ED volume. Academic status captures variability outside of that explained by ESI, CMI, annual ED volume, percentage of Medicare patients, or patients per attending per hour. All measures combined only explained only 42.6% of PHAC variation.