Decision model for hiring doctor’s assistants in rheumatology

The client, a rheumatology center, would like to change the process of treating rheumatology patients.
The problem: Rheumatologists are over-utilized, working overtime, whereas patients face long waiting lists and cannot be seen as often as necessary. The idea at the rheumatology center was that follow-up visits can be be handled by a doctor’s assistant and only problematic cases the patient will be seen by the doctor. Having patients seen by the doctor’s assistant would be a new process that has not registered with the insurances yet.
This problem is particularly pressing for the doctors because there is a cap on how many patients can be billed per quarter (thus the straight profitability lines (blue) in Fig. 1 and 2 for the scenarios without an assistant).

The questions: Does it financially make sense to hire an assistant, and if so, how many? How high must the billing rate be that the insurances will be charged with? How many more patients can be treated that way/ must be treated that way to still be profitable?

The solution: Characteristic for this problem was that there are two unknown variables that influence each other. We broke this down: Under consideration of different factors (number of cases, time per patient, etc., doctor’s assistant’s salary), we came up with two thresholds:
1. For a given number of cases, how high does the billing rate have to be in order to be profitable? See Fig. 1.

Profit subject to Billing rate
Fig. 1: Profitability subject to the billing rate for the newly introduced doctor’s assistant

2. For a given billing rate, how many cases must be accepted by the doctor’s office in order to be profitable? See Fig. 2.

Profit subject to number of cases
Fig. 2: Profitability subject to the number of cases handled if a doctor’s assistant is hired

Feedback: “Everybody was so thrilled by the solution Svenja found. The physicians loved to be able to see how many more patients they can treat using the new concept.”

Selection of Physicians with multiple objectives

The client, a health insurance company, provides physicians with recommendations for referrals to specialists.
The problem: Select the top 5 specialists among a long list of different specialty doctors with different costs and quality scores. The drive time for the patient must not exceed 60 minutes.

The solution: Two objectives, maximizing quality and minimizing cost, with different scales had to be incorporated into the objective function of this optimization problem. A visual solution of this problem is depicted in Fig. 3.
Read more about how to solve multi-objective problems here.

cost-vs-quality
Fig. 3: Visualization of Optimization Problem: Cost vs. quality for selected specialists. Orange: best alternatives, Blue: Other

Feedback: “Svenja is incredibly knowledgeable on this topic and makes OR look easy.”

Facility Layout Planning for Hospitals

The transportation processes for patients, personnel, and material in large and complex maximum-care hospitals with many departments can consume significant resources and thus induce substantial logistics costs. These costs are largely determined by the allocation of the different departments and wards in possibly multiple connected hospital buildings. We develop a hierarchical layout planning approach based on an analysis of organizational and operational data from the Hanover Medical School, a large and complex university hospital in Hanover, Germany. The purpose of this approach is to propose locations for departments and wards for a given system of buildings such that the consumption of resources due to those transportation processes is minimized. We apply the approach to this real-world organizational and operational data set as well as to a fictitious hospital building and analyze the algorithmic behavior and resulting layout.
This was a theoretical problem, and was published here: Article about Facility Layout Planning

 

We present a model and an algorithmic procedure to analyze closed cyclic queues that are subject to blocking. We consider the first two moments of the processing time and present the fitting of phase-type distributions such that the number of phases and transitions is minimal. Using phase-type distributions, we enable the analysis of queuing systems with processing times with any coefficient of variation.
This was a theoretical problem, and was published here: Article about Markov-chain model and algorithmic procedure