Erlang loss bounds for OT–ICU systems

Abstract

In hospitals, patients can be rejected at both the operating theater (OT) and the intensive care unit (ICU) due to limited ICU capacity. The corresponding ICU rejection probability is an important service factor for hospitals. Rejection of an ICU request may lead to health deterioration for patients, and for hospitals to costly actions and a loss of precious capacity when an operation is canceled.There is no simple expression available for this ICU rejection probability that takes the interaction with the OT into account. With c the ICU capacity (number of ICU beds), this paper proves and numerically illustrates a lower bound by an M|G|c|c system and an upper bound by an M|G|c-1|c-1 system, hence by simple Erlang loss expressions.The result is based on a product form modification for a special OT-ICU tandem formulation and proved by a technically complicated Markov reward comparison approach. The upper bound result is of particular practical interest for dimensioning an ICU to secure a prespecified service quality. The numerical results include a case study.

Bloody fast blood collection

“…Despite its slightly unrealistic additional assumption, this analytic result might be quite useful to establish reasonable approximations for queue lengths and possibly a safe estimate (upper bound) for the congestion probability of the collection site, in line with the result in Van Dijk and Kortbeek [66].…”

“…Another, even more technical and formal option would be to use a stochastic comparison approach. This has been shown for a network somewhat similar to the blood collection site, containing two stations, by van Dijk and Kortbeek [66]. For the queueing network based on the blood collection site, the details would be even more complex.…”

Healthcare Optimization : Current Status and Vitalization Suggestions

“…Revere and Black (2003), van den Heuvel et al(2005), Woodard(2005), Carrigan andKujawa(2006), De Koning et al(2006), Lee and Lee(2010), Najmuddin et al(2010), Han et al(2011) 자원관리 Fletcher et al(2006, van Houdenhoven et al(2007), van Houdenhoven et al(2008), van Dijk andKortbeek(2009), Raikundalia et al(2011), Creemers et al(2012), Zonderland and Timmer(2012) ( (Bartolozzi et al, 2000). Kim et al(2012) …”

Integrated decision making in healthcare : an operations research and management science perspective

“…Third, backlogs may be created in emergency rooms or surgical recovery units [104,206,217,375,376]. Fourth, elective admissions or surgeries may have to be postponed, by which surgical waiting lists may increase [7,112,208,523,524], which negatively impacts the health condition of (possibly critical) patients [478,484]. Finally, to accommodate a new admission in critical care units, one may predischarge a less critical patient to a general ward [152,517].…”

“…Units with a substantial fraction of scheduled patients can in general operate under a higher average utilization [217]. The effect of variability in length of stay on care unit size requirements is shown to be less pressing than often thought by hospital managers [217,484]. Reducing the average length of stay shows far more potential.…”