Personnel scheduling: A literature review

We provide a comprehensive overview of the typical decisions to be made in resource capacity planning and control in health care, and a structured review of relevant articles from the field of Operations Research and Management Sciences (OR/MS) for each planning decision. The contribution of this paper is twofold. First, to position the planning decisions, a taxonomy is presented. This taxonomy provides health care managers and OR/MS researchers with a method to identify, break down and classify planning and control decisions. Second, following the taxonomy, for six health care services, we provide an exhaustive specification of planning and control decisions in resource capacity planning and control. For each planning and control decision, we structurally review the key OR/MS articles and the OR/MS methods and techniques that are applied in the literature to support decision making.

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Taxonomic classification of planning decisions in health care: a structured review of the state of the art in OR/MS

https://repositorio.inesctec.pt/bitstream/123456789/3167/1/PS-06772.pdf

Operations Research in Healthcare: a survey

This paper presents a review and classification of the literature regarding workforce planning problems incorporating skills. In many cases, technical research regarding workforce planning focuses very hard on the mathematical model and neglects the real life implications of the simplifications that were needed for the model to perform well. On the other hand, many managerial studies give an extensive description of the human implications of certain management decisions in particular cases, but fail to provide useful mathematical models to solve workforce planning problems. This review will guide the operations researcher in his search to find useful papers and information regarding workforce planning problems incorporating skills. We not only discuss the differences and similarities between different papers, but we also give an overview of the managerial insights. The objective is to present a combination of technical and managerial knowledge to encourage the production of more realistic and useful solution techniques.

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Workforce Planning Incorporating Skills: State of the Art

Workforce planning incorporating skills: State of the art

Constructing duty schedules for nurses at large hospitals is a difficult problem. The objective is usually to ensure that there is always sufficient staff on duty, while taking into account individual preferences with respect to work patterns, requests for leave and financial restrictions, in such a way that all employees are treated fairly. The problem is typically solved via mixed integer programming or heuristic (local) search methods in the operations research literature. In this paper the problem is solved using a tabu search approach as a case study at Stikland Hospital, a large psychiatric hospital in the South African Western Cape, for which a computerized decision support system with respect to nurse scheduling was developed. This decision support system, called NuRoDSS (short for Nurse Rostering Decision Support System) is described in some detail.

Finding good nurse duty schedules: a case study

In certain shared resource applications, such as file access scheduling for a network of computer users, some level of conflict between the elements of the schedule is tolerable. A scheduling problem of this nature may be modelled as a generalisation of the classical vertex colouring problem for graphs, called the maximum degree graph colouring problem. In this paper we present four algorithmic procedures for solving the maximum degree graph colouring problem. The first two of these algorithms (a simple heuristic and a tabu search metaheuristic) produce approximate solutions, while the other two algorithms are exact. The runtime efficiencies of and the solution qualities produced by these procedures are tested with respect to a number of graph benchmarks from the literature.

Algorithms for a shared resource scheduling problem in which some level of conflict is tolerable

A typical ground-based air defence (GBAD) environment comprises defended assets on the ground which require protection from enemy aircraft entering the defended airspace. Protection against these aircraft is afforded by means of pre-deployed ground-based weapon systems that are assigned to engage these enemy aircraft according to some pre-specified criterion or set of criteria. The conditions under which human operators have to propose assignments of weapon systems to engage these aircraft are severely stressful since time is a critical factor and there is no room for error. Some progress has already been made with respect to the design of computerised threat evaluation and weapon assignment (TEWA) decision support systems (DSSs) within the context of a GBAD system. However, the weapon assignment (WA) component within such a TEWA DSS is typically based on a single criterion (objective). The aim in this paper is to model the WA problem as a multiobjective decision problem. A list of relevant factors (related to objectives) is identified by means of feedback received from a WA questionnaire which was completed by a number of military experts. For illustrative purposes, two objectives, namely the cost of assigning weapon systems for engagement and the accumulated survival probabilities of observed threats as a result of these engagements, were isolated from these factors in order to derive a bi-objective WA model. This model is solved in the context of a simulated, but realistic, GBAD environment by means of an existing multiobjective solution technique called the Nondominated Sorting Genetic Algorithm II.

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A multiobjective approach towards weapon assignment in a ground-based air defence environment

A new course entitled "Methods of Operations Research (OR)" was introduced at the Department of Applied Mathematics of Stellenbosch University during the second half of 2001. The aim of this course was to introduce students of OR to the trauma of mathematical modelling in real-world scenarios, instead of merely teaching them a number of theoretical OR-related topics in the form of a lecture-driven course with an examination at the end. Therefore this project-driven course, which is offered in collaboration with a number of partners in industry, is assessed on a continued evaluation basis, by means of written reports and oral presentations by students, after having physically, or at least virtually, visited real-world OR application sites. The objectives of the course, its structure and contents, as well as lessons learnt and some student feedback are described in this paper. A selection of projects used in the course are described in some detail in an appendix.

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Methods of OR: A new graduate course

In this paper we solve (approximately) the problem of finding the minimum number
of colours with which the vertices of a complete, balanced, multipartite graph G may
be coloured such that the maximum degrees of all colour class induced subgraphs are
at most some specified integer d 2 N. The minimum number of colours in such a
colouring is referred to as the &#916(d)–chromatic number of G. The problem of finding
the &#916(d)–chromatic number of a complete, balanced, multipartite graph has its roots
in an open graph theoretic characterisation problem and has applications conforming
to the generic scenario where users of a system are in conflict if they require access
to some shared resource. These conflicts are represented by edges in a so–called
resource access graph, where vertices represent the users. An efficient resource access
schedule is an assignment of the users to a minimum number of groups (modelled by
means of colour classes) where some threshold d of conflict may be tolerated in each
group. If different colours are associated with different time periods in the schedule,
then the minimum number of groupings in an optimal resource access schedule for
the above set of users is given by the &#916(d)–chromatic number of the resource access
graph. A complete balanced multipartite resource access graph represents a situation
of maximum conflict between members of different user groups of the system, but
where no conflict occurs between members of the same user group (perhaps due to an
allocation of diverse duties to the group members). Keywords : Graph/vertex colouring, chromatic number, maximum degree. ORiON Vol. 23 (1) 2007: pp. 29-49

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I Nieuwoudt

Papers

Finding good nurse duty schedules: a case study

Algorithms for a shared resource scheduling problem in which some level of conflict is tolerable

A multiobjective approach towards weapon assignment in a ground-based air defence environment

Methods of OR: A new graduate course

On the ?(d) - chromatic number of a complete balanced multipartite graph