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Nurse Scheduling using Constraint Logic Programming.
Abstract and Figures
The nurse scheduling problem consists of assigning working shifts to each nurse on each day of a certain period of time. A typical problem comprises 600 to 800 assignments that have to take into account several requirements such as minimal allocation of a station, legal regulations and wishes of the personnel. This planning is a difficult and time-consuming expert task and is still done manually. INTERDIP is an advanced industrial prototype that supports semi-automatic creation of such rosters. Using the artificial intelligence approach, constraint reasoning and constraint programming, INTERDIP creates a roster interactively within some minutes instead of by hand some hours. Additionally, it mostly produces better results. INTERDIP was developed in collaboration with Siemens Nixdorf. It was presented at the Systems'98 Computer exhibition in Munich and several companies have inquired to market our system.
Figures - uploaded by Slim Abdennadher
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... The set of variables relevant to f i is referred to as the scope of f i , and denoted as x i ⊆ X. Formally, f i : xj ∈x i D xj → R + ∪ {∞}. 1 A solution is a value assignment for a subset ρ of variables from X that is consistent with their respective domains; i.e., it is a partial function θ : X → n i=1 D xi such that, for each x j ∈ X, if θ(x j ) is defined (i.e., x j ∈ ρ), then θ(x j ) ∈ D xj . The cost of an assignment ρ is the sum of the evaluation of the constraints involving all the variables in ρ. ...
... where Σ is the state space, defined as the set of all possible complete solutions. 1 For simplicity, we assume that tuples of variables are built according to a predefined ordering. ...
... [0] [1] [2] [3] on the information of the thread ID and, thus, avoiding accessing the scope S and assignment vectors R of the input and output bucket-tables. We now discuss how this process can be efficiently handled on the GPU kernels. ...
Discrete optimization is a central problem in artificial intelligence. The optimization of the aggregated cost of a network of cost functions arises in a variety of problems including (W)CSP, DCOP, as well as optimization in stochastic variants such as the tasks of finding the most probable explanation (MPE) in belief networks. Inference-based algorithms are powerful techniques for solving discrete optimization problems, which can be used independently or in combination with other techniques. However, their applicability is often limited by their compute intensive nature and their space requirements. This paper proposes the design and implementation of a novel inference-based technique, which exploits modern massively parallel architectures, such as those found in Graphical Processing Units (GPUs), to speed up the resolution of exact and approximated inference-based algorithms for discrete optimization. The paper studies the proposed algorithm in both centralized and distributed optimization contexts. The paper demonstrates that the use of GPUs provides significant advantages in terms of runtime and scalability, achieving up to two orders of magnitude in speedups and showing a considerable reduction in execution time (up to 345 times faster) with respect to a sequential version.
... To provide adequate care, healthcare professionals such as nurses are scheduled based on the needs of patients and work-hour regulations. This process takes hours of manual labour to complete [1], which amid a pandemic, takes precious time away from patient care. Our motivation for this research has to do with reducing costs and deficiencies in the current system, especially during COVID-19's unprecedented impact on the healthcare system on a global scale [2], [3]. ...
... Possible automation of a scheduling system has been documented since the sixties [4], [5], and provides valuable information on approaches that can be taken to tackle the issue of roster scheduling. More specifically, there is constant focus on providing roster scheduling for nurses [1], [6]. These works refer to this as the nurse scheduling problem (NSP) or nurse rostering problem (NRP). ...
... A prototype system tested at a hospital in Munich called INTERDIP uses Constraint Logic Programming (CLP) to solve scheduling problems using efficient, special-purpose algorithms [1]. CLP combines the advantages of logic programming and constraint solving to find solutions using chronological backtrack search to explore choices. ...
The nurse scheduling problem (NSP) deals with assigning nurses to shifts in a schedule. These assignments must be made based on several hard and soft constraints specific to each nurse. Our solution attempts to solve this problem for smaller-scale clinics or private offices by creating weekly schedules that require only two nurses per shift and have only two shifts per day. We used thirty-four nurses with no specific specializations and can complete all nurse-related activities required by the clinic as sample data. Each nurse in the data pool can be scheduled more than once a week. Using techniques from genetic algorithms and tabu search, our algorithm assesses multiple possible solutions and returns only the most viable schedule based on the soft constraints.
... Numerous approaches have been proposed to solve the NSP [8,9,10,11]. In addition to solving the NSP using exact methods, researchers have been proposing evolutionary methods based on meta-heuristics that works by eliciting candidate solutions while balancing between exploration and exploitation to escape local minima/maxima [12,13,14,15,16]. ...
Solving combinatorial optimization problems involve satisfying a set of hard constraints while optimizing some objectives. In this context, exact or approximate methods can be used. While exact methods guarantee the optimal solution, they often come with an exponential running time as opposed to approximate methods that trade the solutions quality for a better running time. In this context, we tackle the Nurse Scheduling Problem (NSP). The NSP consist in assigning nurses to daily shifts within a planning horizon such that workload constraints are satisfied while hospitals costs and nurses preferences are optimized. To solve the NSP, we propose implicit and explicit approaches. In the implicit solving approach, we rely on Machine Learning methods using historical data to learn and generate new solutions through the constraints and objectives that may be embedded in the learned patterns. To quantify the quality of using our implicit approach in capturing the embedded constraints and objectives, we rely on the Frobenius Norm, a quality measure used to compute the average error between the generated solutions and historical data. To compensate for the uncertainty related to the implicit approach given that the constraints and objectives may not be concretely visible in the produced solutions, we propose an alternative explicit approach where we first model the NSP using the Constraint Satisfaction Problem (CSP) framework. Then we develop Stochastic Local Search methods and a new Branch and Bound algorithm enhanced with constraint propagation techniques and variables/values ordering heuristics. Since our implicit approach may not guarantee the feasibility or optimality of the generated solution, we propose a data-driven approach to passively learn the NSP as a constraint network. The learned constraint network, formulated as a CSP, will then be solved using the methods we listed earlier.
... With the expanding influence of computer technology on all walks of life, there are more and more cross applications of science and technology and medical treatment. Abdennadher and Schlenkef supported semi-automatic generation of scheduling tables by imitating some thinking modes of human beings based on the idea of constraint programming [29,30]. Cheng et al. [31] introduced and implemented a constraint-based nurse scheduling system by using a redundant modeling method. ...
The management of nursing scheduling in healthcare facilities have faced new challenges during the COVID-19 pandemic. With the rapid development of big data and artificial intelligence technology, data-driven intelligent medical services are what we need to study nowadays. This paper not only proposes reasonable solutions in areas such as refined nursing scheduling by using these scientific technologies to quickly realize the allocation of human resources in hospitals. It also accelerates the development of hospital informatization construction through computer technology, establishing a scientific and intelligent medical platform that meets the needs of users. Aiming at the problem of nursing scheduling in medical service data research, this paper proposes a complete plan by analyzing the development of the medical platform at this stage. Firstly, established an intelligent medical service platform, and studied the medical management from the perspective of data. Then, analyze the intelligent medical platform data by utilizing optimized algorithms, through reasonable analysis under various constraints, to get the basic nursing scheduling plan that meets the needs of medical institutions. Finally, considering the actual situation of emergency medical treatment, the decision classification model is introduced under the basic scheme to further screen out the optimal management scheme of modern medical treatment.
... Ongoing research studies are mostly based on heuristic algorithms and conventional linear programming optimization techniques which are mainly presented for homogeneous personnel shift scheduling [2,3]. Indeed, NSP can be performed by using the recently developed open-source artificial intelligence (AI) constraint optimization modules, resulting in more flexibility and cost effectiveness in maintaining the system to generate roster schedule [4]. As it is open sourced, source codes developed for different applications are usually contributed for knowledge and experience sharing, in that various software experts can collaborate on this open-source platform to develop a system of common interest in this NSP. ...
Objectives
A hospital ward usually comprises of about 50 nurses and a nurse duty roster is prepared monthly. It is common for nurses to make duty shift requests prior to scheduling. A ward manager normally spends more than a working day to manually prepare and subsequently to optimally adjust the schedule upon staff requests and hospital policies. This study aimed to develop an automatic nurse roster scheduling system with the use of open-source operational research tools by taking into account the hospital standards and the constraints from nurses.
Methods
Artificial intelligence and end user tools operational research tools were used to develop the code for the nurse duty roster scheduling system. To compare with previous research on various heuristics in employee scheduling, the current system was developed on open architecture and adopted with real shift duty requirements in a hospital ward.
Results
The schedule can be generated within 1 min under both hard and soft constraint optimization. All hard constraints are fulfilled and most nurse soft constraints could be met. Compared with those schedules prepared manually, the computer-generated schedules were more optimally adjusted as real time interaction among nurses and management personnel. The generated schedules were flexible to cope with daily and hourly duty changes by redeploying ward staff in order to maintain safe staffing levels.
Conclusions
An economical but yet highly efficient and user friendly solution to nurse roster scheduling system has been developed and adopted using open-source operational research methodology. The open-source platform is found to perform satisfactorily in scheduling application. The system can be implemented to different wards in hospitals and be regularly updated with new hospital polices and nurse manpower by hospital information personnel with training in artificial intelligence.
... (2) constraint logic programming (Abdennadher & Schlenker, 1999), which can utilize specialized constraint solving techniques to search for the best scheduling choices; (3) mixed integer programming (Peters et al., 2019), where all scheduling constraints and objectives are related linearly; (4) satisfiability modulo theories (Erkinger & Musliu, 2017), which can be used to encode the scheduling constraints in first-order formulas and support solving large problems; and (5) evolutionary algorithms (Moi et al., 2021;Peters et al., 2019), which are inspired by the biological principle of evolutionary and have been successfully applied. Besides above work, some heuristics (Shao & Xin, 2019) and hybrid approaches (Bai et al., 2010) can also be found. ...
Effective staff scheduling is a critical activity of successful software development management. Due to its difficulty and broad applications in many service delivery scenarios, staff scheduling has been studied for several decades. However, most existing work focus on constructing the working schedules based on a given workforce size. This paper tries to solve a prerequisite issue before performing staff scheduling, i.e., testing whether the already existed manpower can meet the scheduling requirements. Though it is possible to use network flow theory or artificial intelligence (AI) methods like genetic algorithms to solve this problem, their time complexities could be too high to be used for large problem sizes. This paper proposes a constructive method that can derive the minimum staff number for three scheduling problem variants in a linear running time, and in the meantime a corresponding working schedule that can satisfy all the problem constraints can be produced. We not only theoretically show the lower bound for the computation time complexity of our proposed method but also prove its correctness. Moreover, based on the derived minimum staff number, we further explore the genetic algorithm for generating the schedule and compare its performance with our method. The experiments show that our method outperforms the baselines in terms of both effectiveness and efficiency.
... This evaluation is largely dependent on the constraints defned in a specifc scheduling domain. As such, scheduling has been defned as a problem concerning the satisfaction of a series of constraints, which may be either hard or soft [1,5]. Hard constraints must be satisfed, whereas soft constraints, under which constraints for preferences generally fall, are considered implicitly when creating a schedule but may be violated [5]. ...
... The assignment of shifts in a company is a classical management problem that is usually referred to as the "nurse scheduling problem". It has been treated in different ways, for instance through the application of constraint logic programming [23]. Another example of this kind of study of management problems can be seen in [24], in which the authors deal with some non-standard shift types by means of a redundant modeling approach. ...
This article discusses a theoretical construction based on the graph theory to rework the space of potential partitions in envy-free distribution. This work has the objective of applying Sperner’s lemma to the distribution of three rotating shifts for three workers who are to cover a 24 h job position in a company. As a novel feature, worker’s preferences have been modeled as functions of probability for the three shifts, according to salary offers for said shifts. Envy-free allocation was achieved, since each worker received their preferred shift without the need for negotiation between agents in conflict. Adaptation to the type of dynamic situations that arise with rotating shifts, as well as the consideration of probabilistic preferences by workers are some of the main novelties of this work.
The Nurse Scheduling Problem (NSP) is a well-known
NP-hard combinatorial optimization problem. Solving
the NSP involves assigning feasible shift patterns to nurses,
satisfying hard constraints while optimizing objectives such as
penalty costs. Various approaches have been proposed to tackle
the NSP, explicitly using exact or approximate methods, or
implicitly using machine learning models. Exact techniques, e.g.,
Mixed-Integer Linear Programming (MILP), are often time consuming while approximation methods such as metaheuristics
trade running time for the quality of the solution returned.
In this paper, we propose an exact alternative method to
model and solve the NSP using the Constraint Satisfaction
Problem (CSP) framework. More precisely, we use the Weighted
Constraint Satisfaction Problem (WCSP) to capture all the
constraints related to working requirements, in addition to the
quantified nurses’ preferences (represented as weights) over
shift patterns. Solving the WCSP (corresponding to a given
NSP instance) consists of finding an optimal solution satisfying
all the constraints while optimizing the objective function (total
weight). To solve the WCSP, we have adopted a variant of the
Branch & Bound (B&B) algorithm, enhanced with constraint
propagation and variables/values ordering heuristics. To assess
the time efficiency of this new B&B variant, we conducted
an experimental study on several NSP instances. The results
show that our algorithm is able to return optimal schedules in
acceptable running times.
CHIP is a new logic language combining the declarative aspects of logic programming with the efficiency of constraint solving techniques. It has been designed to tackle real world constrained search problems. It extends usual Prolog-like logic languages by introducing three new computation domains namely finite domain restricted terms, boolean terms and linear rational terms. For each of them CHIP uses specialized constraint solving techniques: consistency techniques for finite domains, equation solving in Boolean algebra and a symbolic simplex-like algorithm for rationals. CHIP has been successfully applied to a large number of industrial problems especially in the areas of planning, scheduling and circuit design. For all these problems the flexibility and the efficiency of CHIP has been systematically demonstrated.
Constraint Logic Programming (CLP) is a merger of two declarative paradigms: constraint solving and logic programming. Although a relatively new field, CLP has progressed in several quite different directions. In particular, the early fundamental concepts have been adapted to better serve in different areas of applications. In this survey of CLP, a primary goal is to give a systematic description of the major trends in terms of common fundamental concepts. The three main parts cover the theory, implementation issues, and programming for applications.
This paper describes a nurse scheduling system, the heart of which poses the scheduling decision as a large multiple-choice programming problem whose objective function quantifies preferences of individual nursing personnel concerning length of work stretch, rotation patterns, and requests for days off. The constraints provide for minimum numbers of nursing personnel of each skill class to be assigned to each day and shift of a four- or six-week scheduling period. The problem is solved by a modification of J. L. Balintfy and C. R. Blackburn's algorithm for multiple-choice programming problems. Included is a description of the implementation of the scheduling system on nursing units of several hospitals.
The constraint satisfaction problem (CSP) formalization has been a productive tool within Artificial Intelligence and related areas. The finite CSP (FCSP) framework is presented here as a restricted logical calculus within a space of logical representation and reasoning systems. FCSP is formulated in a variety of logical settings: theorem proving in first order predicate calculus, propositional theorem proving (and hence SAT), the Prolog and Datalog approaches, constraint network algorithms, a logical interpreter for networks of constraints, the constraint logic programming (CLP) paradigm and propositional model finding (and hence SAT, again). Several standard, and some not-so-standard, logical methods can therefore be used to solve these problems. By doing this we obtain a specification of the semantics of the common approaches. This synthetic treatment also allows algorithms and results from these disparate areas to be imported, and specialized, to FCSP; the special properties of FCSP are exploited to achieve, for example, completeness and to improve efficiency. It also allows export to the related areas. By casting CSP both as a generalization of FCSP and as a specialization of CLP it is observed that some, but not all, FCSP techniques lift to CSP and thereby to CLP. Various new connections are uncovered, in particular between the proof-finding approaches and the alternative model-finding approaches that have arisen in depiction and diagnosis applications.
A constraint satisfaction problem involves finding values for variables subject to constraints on which combinations of values are allowed. In some cases it may be impossible or impractical to solve these problems completely. We may seek to partially solve the problem, in particular by satisfying a maximal number of constraints. Standard backtracking and local consistency techniques for solving constraint satisfaction problems can be adapted to cope with, and take advantage of, the differences between partial and complete constraint satisfaction. Extensive experimentation on maximal satisfaction problems illuminates the relative and absolute effectiveness of these methods. A general model of partial constraint satisfaction is proposed.
Constraint satisfaction problems (CSPs) involve finding values for variables subject to constraints on which combinations of values are permitted. This paper develops a concept of interchangeability of CSP values. Fully Interchangeable values can be substituted for one another in solutions to the problem. Removing all but one of a set of fully interchangeable values can simplify the search space for the problem without effectively losing solutions. Refinements of the interchangeability concept extend its applicability. Basic properties of interchangeablity and complexity parameters are established. A hierarchy of local interchangeability is defined that permits recognition of some interchangeable values with polynomial time local computation. Computing local interchangeability at any level in this hierarchy to remove values before backtrack search is guaranteed to be cost effective for some CSPs. Several forms of weak interchangeability are defined that permit eliminating values without losing all solutions. Interchangeability can be introduced by grouping values or variables, and can be recalculated dynamically during search. The idea of interchangeability can be abstracted to encompass any means of recovering the solutions involving one value from the solutions involving another.