Capacity planning for a network of community health services

Highlights

• Developed queuing model to predict blocking at each stage of a generalized network.

• Coupled queuing model with an Non-Linear Integer Program to optimize capacity.

• Developed an innovated simulated annealing method to solve Integer program.

• Tested approach on a network of 6 stages using data provided by health authority.

• Developed two simulation models to validate our capacity planning approach.

Abstract

Community care services are becoming increasingly important to health delivery as patients live longer but with chronic disease. In this research, we propose a queuing network approach to capacity planning for a network of services. We take advantage of existing heuristics that calculate the probability of blocking for a given capacity plan and utilize the output of these heuristics to run a simulated annealing approach to optimize capacity allocation across the network subject to a performance guarantee related to the sum of the blocking probabilities. We apply this model to a local health region with a network of six services – acute care, long term care, assisted living, home care, rehabilitation and chronic care. We test the results of the optimization model through a simulation that incorporates more realism than is possible in the queuing model and that also allows us to determine the transient behaviour of the system as it transitions from current capacity levels to the those proposed by the optimization model.

Introduction

It is a well-known truth that many if not all developed countries are experiencing increasing health care expenditures. While it is perhaps a sign of affluence that we can spend so much of our GDP on health care, it remains true that current growth is unsustainable and that many if not all developed countries are finding it challenging to weigh the relative merits of various health care expenditures in an effort to reduce the overall cost. It is also a well-known truth that a large portion of health care expenditures are consumed by the elderly in acute care and that the proportion of the population over the age of 65 is steadily increasing. Quite often, these patients remain in the hospital much longer than necessary simply due to the lack of space in a more appropriate service in the community such as rehabilitation, assisted living or long term care. This phenomenon has become sufficiently endemic that patients who have been cleared for discharge but remain in the hospital for want of capacity in the community are now labelled as “alternate level of care” (ALC) patients. In Canada, the challenge of managing ALC patients has become perhaps the most significant impediment to running acute care efficiently. Even as far back as 2009, over 50,000 patients waited in hospital due to delays in arranging post-discharge care accounting for 16% of total patient days in all Ontario hospitals. By 2013, the percentage had dropped to 14% but has since stabilized at this level (Office of the Auditor General of Ontario, 2015). The impact of these extended stays can be felt in congestion in emergency departments leading to long wait times as well as cancelled surgeries due to the lack of an available ward bed. In addition, the added time in the hospital is quite often deleterious to the health of the patient. For all these reasons, many developed countries are seeking to better plan for the sub-acute needs of elderly patients that are best met outside of acute care.

Through this research, we build a model of a network with n different stages (or services) where demand can move between stages in any fashion – including returning to stages already visited. We take advantage of methodologies available in the literature to model the effect of blocking on service performance in a queuing network. This allows us to estimate the probability of blocking at each stage of the network and the expected number of patients waiting at each stage for transfer. While this model is useful, it provides no optimization. Moreover, since the method for calculating the blocking probabilities involves a heuristic algorithm rather than a closed-form solution, it is not straightforward to utilize the outputs of the queuing network model in an optimization framework. Thus we develop a simulated annealing approach to determine the capacity allocations at each stage for a given demand stream that minimizes the total cost subject to a constraint on the sum of the blocking probabilities across all stages. Finally we test the validity of the combined queuing network with optimization approach using a simulation model that incorporates non-homogenous patient flow probabilities and lengths of stay (based on age and gender) and that allows us to determine the impact of a graduated capacity build-up.

We apply our model to a real case study of a region with six different stages – home care (HC), assisted living (AL), long term care (LTC), chronic care (CC), rehabilitation (R) and acute care (AC). The first three form a continuum of care from services offered in the home (HC) where the health care provider comes to the patient, to services offered in an independent living arrangement (AL) to finally the 24 hour services provided in LTC. Chronic care serves patients with chronic conditions that are sufficiently complex to preclude them from taking advantage of the first three types of services. Rehabilitation provides short term services primarily to post-acute patients in order to enable them to either function independently or else to be able to function in one of the other sub-acute facilities. The two primary entry points into this network of sub-acute services is through acute care or else directly from the community into home care with a much smaller stream entering directly to LTC. However, transfers can occur between any two stages in the model and exits from the network can occur from any stage. Thus, the system we are looking to model and which we call the Community Care Network (CCN) can be displayed as in Fig. 1.