|Ph.D Student||Zychlinski Noa|
|Subject||Time-Varying Fluid Networks with Blocking: Models Supporting|
Patient Flow Analysis in Hospitals
|Department||Department of Industrial Engineering and Management||Supervisors||Professor Emeritus Avishai Mandelbaum|
|Dr. Izack Cohen|
|Full Thesis text|
This thesis was motivated by the bed blocking problem, which occurs when elderly hospital patients are ready to be discharged, but must remain in the hospital until a bed in a geriatric institution becomes available. Bed blocking has become a challenge to healthcare operators due to its economic implications and quality-of-life effect on patients. Indeed, hospital-delayed patients, who cannot access their most appropriate treatment (e.g. rehabilitation), prevent new admissions. Moreover, bed blocking is costly since a hospital bed is more expensive to operate than a geriatric bed.
The first part of this thesis focuses on analyzing the bed blocking problem, in order to improve the joint operation of hospitals and geriatric institutions. To this end, we develop a mathematical fluid model, which accounts for blocking, mortality and readmission?all significant features of the discussed environment. The comparison between our fluid model, a two-year data set from a hospital chain and simulation results shows that our model is accurate and useful. Then, for bed allocation decisions, the fluid model and especially its offered-load counterpart turn out insightful and easy to implement. Our analysis yields a closed-form expression for bed allocation decisions, which minimizes the sum of underage and overage costs. The proposed solution demonstrates that significant reductions in cost and waiting list length are achievable, as compared to current operations.
A more comprehensive view of the system we analyze in the first section, can be achieved by including Emergency Department (ED) boarded patients, waiting for admission to hospital wards. This analysis should also include finite waiting rooms and customer loss when they are full. Accordingly, we set out to model and analyze time-varying tandem networks with blocking and finite waiting rooms throughout the network. These models capture the essential characteristics of our first model-namely, time-variation and blocking; in this case, however, accommodating customer loss requires reflection analysis. We conclude this section by providing operational insights on network performance of tandem flow lines, in a broader perspective that goes beyond hospital networks.
The first two sections of the thesis focus on Blocking After Service (BAS). The third section, however, focuses on the Blocking Before Service (BBS) mechanism. BBS arises in telecommunication networks, production lines and healthcare systems.
We begin by modeling the stochastic queueing network of time-varying tandem networks with finite buffers throughout the network; then, we develop its corresponding fluid limit and provide design/operational insights regarding BAS/BBS mechanisms; in particular, on network throughput and job loss rate.