On the trade-off between staff-decomposed and activity-decomposed column generation for a staff scheduling problem.

In this paper a comparison is made between two decomposition techniques to solve a staff scheduling problem with column generation. In the first approach, decomposition takes place on the staff members, whereas in the second approach decomposition takes place on the activities that have to be performed by the staff members. The resulting master LP is respectively a set partitioning problem and a capacitated multi-commodity flow problem. Both approaches have been implemented in a branch-and-price algorithm. We show a trade-off between modeling power and computation times of both techniques.decomposition; staff scheduling; set partitioning; multi-commodity flow; branch-and-price; branch-and-price; programs;

Heuristic branch-and-price for building long term trainee schedules.

Branch-and-price is an increasingly important technique for solving large integer programming models. Staff scheduling has been a particularly fruitful area since these problems typically exhibit a decomposable structure. Beside computational efficiency branch-and-price produces two other important advantages in comparison with pure integer programming. Firstly, it often allows for a more accurate problem statement since many constraints which are hard to formulate in the integer program could be easily incorporated in the column generator. Secondly, a branch-and-price algorithm can easily be turned into an effective heuristic when optimality is no major concern. We illustrate these advantages for a medical trainee scheduling problem encountered at Oogziekenhuis Gasthuisberg Leuven and present some computational results together with implementation issues.Advantages; Area; Branch-and-price; Constraint; Efficiency; Heuristic; Integer programming; Model; Models; Problems; Research; Scheduling; Staff scheduling; Structure;

A heuristic procedure to solve the project staffing problem with discrete time/resource trade-offs and personnel scheduling constraints

Highlights • Project staffing with discrete time/resource trade-offs and calendar constraints. • An iterated local search procedure is proposed. • Different problem decomposition techniques are applied. Abstract When scheduling projects under resource constraints, assumptions are typically made with respect to the resource availability and activities are planned each with its own duration and resource requirements. In resource scheduling, important assumptions are made with respect to the staffing requirements. Both problems are typically solved in a sequential manner leading to a suboptimal outcome. We integrate these two interrelated scheduling problems to determine the optimal personnel budget that minimises the overall cost. Integrating these problems increases the scheduling flexibility, which improves the overall performance. In addition, we consider some resource demand flexibility in this research as an activity can be performed in multiple modes. In this paper, we present an iterated local search procedure for the integrated multi-mode project scheduling and personnel staffing problem. Detailed computational experiments are presented to evaluate different decomposition heuristics and comparison is made with alternative optimisation techniques

Quantitative methods of physician scheduling at hospitals

Masteroppgave i industriell økonomi og informasjonsledelse 2010 – Universitetet i Agder, GrimstadStaff scheduling at hospitals is a widely studied area within the fields of operation research and management science because of the cost pressure on hospitals. There is an interest to find procedures on how to run a hospital more economically and efficient. Many of the studies about staff scheduling at hospital have been done about nurses, which work under common labor law restrictions. The goal of nurse scheduling is to minimize the staffing cost and maximizing their preferences. While the operation rooms are the engine of the hospitals, the physicians are the fueling for the hospitals. Without the physicians the patients would not be treated well and the hospital would not earn money. This thesis studies the physician scheduling problem, which has not been studied so widely as the nurse scheduling problem. A limited number of literatures about this theme have been studied to answer the main research question: How can we categorize physician scheduling at hospitals? Studying the physician rostering problem on the search for efficiency and cost savings is an intricate process. One can read a lot about this theme develop a lot of models; and shape and test different hypotheses. However, to increase efficiency it is wise to make a plan of information to consider. The categories searched for within this literature review are the level of experience, the planning period, the field of specialty, the type of shifts, whether cyclic or acyclic schedules are used and also which models and methods are used to solve this problem. Level of experience was first divided between residents - that are still under education, and physicians - which are fully licensed. Physicians are medical trained doctors that provide medical treatment rather than surgical treatment in hospitals. After medical school, they have accomplished between three to seven years of residential internship before they obtain their license. The residents are still under education and must therefore participate in a number of assorted activities and patient treatments during their resident period to acquire their license. This situation for resident makes scheduling unique as they are in a learning period and staffing the hospital at the same time. The planning period is a category that is divided in three levels; short-term which lasts up to a month, midterm which lasts from one month up to six months and a long-term that lasts from six months up to one year. The field of specialty is divided between the specialties of the physicians. In the numerous departments at a hospital, the work is distinctive from one another. A normal workday in a department that is only open during the day can be quite different from a workday in an emergency department. Working in a hospital is unlike other type of jobs. A hospital or at least different departments in a hospital are open all day long, every day of the year. As a result, the hospital must be staffed all the time. The need for staffing varies during the day, the day of week; and during the different seasons, due to the fluctuation of the demands. An example for a solution is a variety of broad types of shifts. Scheduling these shift types can be made cyclic or acyclic. Qualitative method has been used in this master’s thesis. The research question is a typically quantitative method starting with “how”. And to answer it, this thesis builds on a definite number of case studies. These case studies are limited to concern only about physician and resident scheduling problem written in English. These cases are primarily scientific articles and conference handouts. The cases are read - and interesting information is registered in a case study database. The findings have shown different use of planning period after the level of experience. Few studies have been done with short-term planning period; physicians are mostly scheduled for a midterm planning period, whereas residents are mostly scheduled with a long-term planning period. Most studies have scheduled physicians and residents for a day, evening and night shift, often in a combination with some kind of on-call shift. The field of specialty that is most studied is within emergency medicine. As the work in an emergency department is stressful, it is a complex task to make good schedules that satisfies the physicians and residents working there. Exact approaches are the most used modeling technique used for physician scheduling

Solving the medical student scheduling problem using simulated annealing

We consider the medical student scheduling (MSS) problem, which consists of assigning medical students to internships of different disciplines in various hospitals during the academic year to fulfill their educational and clinical training. The MSS problem takes into account, among other constraints and objectives, precedences between disciplines, student preferences, waiting periods, and hospital changes. We developed a local search technique, based on a combination of two different neighborhood relations and guided by a simulated annealing procedure. Our search method has been able to find the optimal solution for all instances of the dataset proposed by Akbarzadeh and Maenhout (Comput Oper Res 129: 105209, 2021b), in a much shorter runtime than their technique. In addition, we propose a novel dataset in order to test our technique on a more challenging ground. For this new dataset, which is publicly available along with our source code for inspection and future comparisons, we report the experimental results and a sensitivity analysis

Applications of Mathematical Programming in Personnel Scheduling

In the few decades of its existence, mathematical programming has evolved into an important branch of operations research and management science. This thesis consists of four papers in which we apply mathematical programming to real-life personnel scheduling and project management problems. We develop exact mathematical programming formulations. Furthermore, we propose effective heuristic strategies to decompose the original problems into subproblems that can be solved effciently with tailored mathematical programming formulations. We opt for solution methods that are based on mathematical programming, because their advantages in practice are a) the exibility to easily accommodate changes in the problem setting, b) the possibility to evaluate the quality of the solutions obtained, and c) the possibility to use general-purpose solvers, which are often the only software available in practice

Crew Planning at Netherlands Railways: Improving Fairness, Attractiveness, and Efficiency

The development and improvement of decision support voor crew planning at Netherlands Railways (NS