In this paper, we investigate a stochastic appointment scheduling problem in an outpatient clinic with a single doctor. The number of patients and their sequence of arrivals are fixed, and the scheduling problem is to determine an appointment time for each patient. The service durations of the patients are stochastic, and only the mean and covariance estimates are known. We do not assume any exact distributional form of the service durations, and solve for distributionally robust schedules that minimize the expectation of the weighted sum of patients' waiting time and doctor's overtime. We formulate this scheduling problem as a convex conic optimization problem with a tractable semidefinite relaxation. Our model can be extended to handle additional support constraints of the service durations. Using the primal-dual optimality conditions, we prove several interesting structural properties of the optimal schedules. We develop an efficient semidefinite relaxation of the conic program, and show that we can still obtain near optimal solutions on benchmark instances in the existing literature. We apply our approach to develop a practical appointment schedule at an eye clinic that can significantly improve the efficiency of the appointment system in the clinic, compared to an existing schedule.

No abstract

ObjectiveIn China, patients increasingly choose to access already severely overcrowded higher level hospitals, leaving lower level facilities with low utilization rates. This situation undermines the effectiveness and efficiency of the health system. The situation tends to worsen despite policy measures aimed at improvement. We systematically review the factors affecting patient choice to synthesize scientific understanding of health system access in China. The review provides an evidence base for measures to direct patient flow towards lower level facilities.MethodsWe screened the peer-reviewed literature published from April 2009 to January 2016 that investigates Chinese patients’ choice of health care facilities at different levels and assessed 45 studies in total. We applied two structured forms to extract data on each study’s characteristics, methodology, and factors.Results of data synthesisThe results identified four factor types: 1) patient, 2) provider, 3) context and 4) composite: combined patient, provider, and/or context attributes. Patient factors are mentioned the most, but the evidence on patient factors is often inconclusive. Evidence suggests that the provider factors ‘drug variety’ and ‘equipment’, and composite factor ‘perceived quality’, push patients from lower levels towards higher levels.ConclusionUnderuse of primary care facilities and overcrowding of higher level facilities will likely be amplified by current demographic trends. Evidence suggests that improving drug availability, equipment and perceived quality of primary care services can improve the situation. Well-designed research that considers the interactions between factors is called for to better inform future interventions.

Abstract The underutilization of primary care in urban China threatens the efficiency and effectiveness of the Chinese health system. To guide patient flow to primary care, the Chinese government has rolled out a sequence of health care reforms which improve the affordability, the infrastructure and workforce of the primary care system. However, these measures have not yielded the desired effect on the utilization of primary care, which is lowest in urban areas. It is unclear how the factors identified to influence facility choice in urban China are actually impacting choice behaviour. We conducted a discrete choice experiment to elicit the quantitative impact of facility attributes when choosing a health care facility for first visit and analysed how the stated choice varies with these attributes. We found that the respondents placed different weights on the identified attributes, depending on whether they perceived their condition to be minor or severe. For conditions perceived as minor, the respondents valued visit time, equipment and medical skill most. For conditions perceived as severe, they placed most importance on equipment, travel time and facility size. We found that for conditions perceived as minor, only 14% preferred visiting a facility over opting out, a percentage which would more than double to 37% if community health centres were maximally improved. For conditions perceived as severe, improvements in community health centres may almost double first visits to primary care, mostly from patients who would otherwise choose higher-level facilities. Our findings suggest that for both severity conditions, improvements to medical equipment and medical skill at community health centres in urban China can effectively direct patient flow to primary care and promote the efficiency and effectiveness of the urban health system.

This paper studies how to schedule medical appointments with time-dependent patient no-show behavior and random service times. The problem is motivated by our studies of independent datasets from countries in two continents that unanimously identify a significant time-of-day effect on patient show-up probabilities. We deploy a distributionally robust model, which minimizes the worst-case total expected costs of patient waiting and service provider’s idling and overtime, by optimizing the scheduled arrival times of patients. This model is challenging because evaluating the total cost for a given schedule involves a linear program with uncertainties present in both the objective function and the right-hand side of the constraints. In addition, the ambiguity set considered contains discrete uncertainties and complementary functional relationships among these uncertainties (namely, patient no-shows and service durations). We show that when patient no-shows are exogenous (i.e., time-independent), the problem can be reformulated as a copositive program and then be approximated by semidefinite programs. When patient no-shows are endogenous on time (and hence on the schedule), the problem becomes a bilinear copositive program. We construct a set of dual prices to guide the search for a good schedule and use the technique iteratively to obtain a near-optimal solution. Our computational studies reveal a significant reduction in total expected cost by taking into account the time-of-day variation in patient show-up probabilities as opposed to ignoring it. This paper was accepted by David Simchi-Levi, optimization.