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Resident scheduling in teaching hospitals

Autor: Sebastian Kraul

There are currently almost 60,000 medical residents in one of 57 specialist training programs in Germany. The cost pressures of hospitals and the changing view of the medical profession regarding the work-life balance have led to recruitment problems and low employee satisfaction in many places. A promising approach to counter this problem is through objective and structured training planning.

My dissertation mainly deals with medical residents‘ strategic and tactical-operative training scheduling. In addition to relieving the medical staff currently responsible for the planning process, a focus was to increase the predictability of a structured training. This allows hospitals to increase the quality of their training and, consequently, their attractiveness to other hospitals. In addition, supervisors from different departments can better assess the knowledge of residents and thus keep the level of service, which is particularly important in hospitals, permanently high even when changing residents.

From the residents‘ point of view, a well-structured training planning, in addition to ensuring the program duration, enables a high degree of information. Residents are therefore no longer surprised by a short-term department change – they are currently informed one or two weeks in advance about a change – and have a direct insight into their training progress.

In addition to the mathematical modeling of the problems and the development of exact and heuristic solution approaches, our cooperation partner München rechts der Isar made a practice-oriented verification of the methods by cross-checking the actual training schedules in close coordination with the responsible planner. It showed that the developed methods led to results usable in practice. In particular, we were able to identify bottlenecks in the hospital’s surgical portfolio, which strongly impacts training. Finally, the interactions within and outside the training process were analyzed, especially regarding fairness, continuity, and uncertainty.

Additional information on the results can be found on my project page on Research Gate.

OR News Mai 2022 (Nr.74)

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A Two-Stage Stochastic Optimisation Model for Urban Same-Day Delivery with Micro-Hubs

Autor: Charlotte Ackva

Facing the vast range of products in the e-commerce sector, more and more customers are purchasing online. To compete with the big online retailers, many local shops also offer a delivery service to their customers. However, conventional delivery by motorised vans is often inefficient due to low delivery volumes, access restrictions in city centres, and poor parking conditions.

To overcome these challenges, local shops start collaborating for joint transportation of parcels to the same region. For this, micro-hubs are used as intermediate storage and transhipment facilities. This increases consolidation opportunities in the delivery process: shops bring their goods to a close-by micro-hub. There, parcels are picked up by a shared vehicle for further transportation to other micro-hubs close to the parcels’ destinations. The shared vehicle is conducting a consistent tour, i.e. visiting the same micro-hubs at the same time every day. While this gives planning stability to storekeepers, customers, and drivers, finding an effective consistent schedule is challenging. Since customer orders vary from day to day, it highly depends on the consistent schedule which of these orders can be fulfilled. Figure 1 exemplarily shows a consistent schedule for two different demand realisations.


Figure 1: Example of a consistent tour for two different demand realisations (own illustration).

We formulate the problem as a two-stage stochastic optimisation model aiming to maximise the expected number of fulfilled customer orders. At the first stage, when demand is still unknown, the vehicle’s schedule is determined. At the second stage, the flow of parcels is decided based on the schedule from the first stage.

We apply the Progressive Hedging (PH) Algorithm to determine a consistent schedule. While convergence of PH is shown for convex programs, this does not hold true for integer programs anymore. Therefore, we investigate the performance of the algorithm for different parameter settings and different demand patterns. We find that PH performs rather poorly when demand is randomly distributed, but yields particularly good results when structural information of the demand distribution is available.