diff --git a/.gitignore b/.gitignore index ed41e61..aedb6fc 100644 --- a/.gitignore +++ b/.gitignore @@ -117,6 +117,8 @@ src/token.json *.synctex.gz *.fdb_latexmk *.fls +*.bbl +*.blg ########## # SPHINX # diff --git a/paper/paper.intro.tex b/paper/paper.intro.tex index bbc6116..749b002 100644 --- a/paper/paper.intro.tex +++ b/paper/paper.intro.tex @@ -1,11 +1,11 @@ -On-call schedules for a fixed number of health-care providers are central to the efficient running of hospitals. Hospital departments provide services where patient needs, and thus the system's demands, often exceed the available supply. For example, it is important that a hospital department allocates its resources, such as the availability of a finite number of clinicians, optimally, to ensure the best possible service for its patients. Carefully allocated on-call schedules are meant to simultaneously ensure sufficient resources are provided to patients while not overworking clinicians to prevent costly mistakes [ref]. It is common practice for on-call schedules to be created manually. Yet manually-created schedules are prone to errors and potential for biases [ref]. First, when there is a large number of clinicians in a single department, or the constraints that need to be satisfied by the department are very complex, a manual method may not provide an optimal schedule. Second, such methods are likely to overlook certain constraints that must be maintained to have an operational department, such as XXXX. Third, manual scheduling is often time-consuming for the person developing the schedule. For these reasons, it is important to develop automated methods that can generate optimal schedules that satisfy the given constraints of the hospital department. \\ +On-call schedules for a fixed number of health-care providers are central to the efficient running of hospitals. Hospital departments provide services where patient needs, and thus the system's demands, often exceed the available supply. For example, it is important that a hospital department allocates its resources, such as the availability of a finite number of clinicians, optimally, to ensure the best possible service for its patients. Carefully allocated schedules are meant to simultaneously ensure sufficient resources are provided to patients while not overworking clinicians to prevent costly mistakes [ref]. It is common practice for on-call schedules to be created manually. Yet manually-created schedules are prone to errors and potential for biases [ref]. First, when there is a large number of clinicians in a single department, or the constraints that need to be satisfied by the department are very complex, a manual method may not provide an optimal schedule. Second, such methods are likely to overlook certain constraints that must be maintained to have an operational department, such as preventing many consecutive work blocks from being assigned or ensuring clinicians are allocated a specific amount of work blocks throughout the year. Third, manual scheduling is often time-consuming for the person developing the schedule. For these reasons, it is important to develop automated methods that can generate optimal schedules that satisfy the given constraints of the hospital department. \\ -Automated methods to optimize schedules have been studied and applied in many industries, including transportation [??], manufacturing [??], [...]. Of special interest to a clinician on-call scheduling problem are the approaches to schedule nurses, who often work in shifts. In the nurse scheduling problem, the goal is to find an optimal assignment of nurses to shifts that satisfies all of the hard constraints, such as hospital regulations, and as many soft constraints as possible, which may include nurse preferences. A wide variety of approaches, including exact and heuristic approaches, have been used to solve the nurse scheduling problem: integer linear programming [??], network flows [??], genetic algorithms [??], simulated annealing [??], and artificial intelligence [??]. \\ +Automated methods to optimize schedules have been studied and applied in many industries, including transportation \cite{aickelin_improved_2006, goel_truck_2012, gunther_combined_2010}, manufacturing \cite{al-yakoob_mixed-integer_2007, al-yakoob_column_2008, alfares_simulation_2007}, retail \cite{chapados_retail_2011, nissen_automatic_2010} and military \cite{horn_scheduling_2007, laguna_modeling_2005}. Of special interest to a clinician on-call scheduling problem are the approaches to schedule nurses, who often work in shifts. In the nurse scheduling problem, the goal is to find an optimal assignment of nurses to shifts that satisfies all of the hard constraints, such as hospital regulations, and as many soft constraints as possible, which may include nurse preferences. A wide variety of approaches, including exact and heuristic approaches, have been used to solve the nurse scheduling problem: integer linear programming \cite{azaiez_0-1_2005, trilling_nurse_2006, widyastiti_nurses_2016}, network flows \cite{el_adoly_new_2018}, genetic algorithms \cite{aickelin_exploiting_2000, jan_evolutionary_2000, kawanaka_genetic_2001}, simulated annealing \cite{jaszkiewicz_metaheuristic_1997}, and artificial intelligence \cite{abdennadher_nurse_nodate, li_hybrid_2003}. A comprehensive literature review of these and other methods applied to nurse rostering is presented in \cite{burke_state_2004}. \\ %An extensive literature review of these and other methods is presented by [??]. We will briefly summarize the main ideas of some of these approaches. \\ SM - don't need to introduce that you will do this for this type of paper I think - would do in a thesis chapter though. Many of these approaches were designed to satisfy the requirements of a specific hospital department which causes a large number of variables and constraints to be incorporated into the problem formulation. While these department-specific approaches allow end-users to find precise schedules that satisfy the needs of the department and the preferences of the nurses and clinicians in that department, they are difficult to readily adapt to other departments in the same hospital or other hospitals. % explain why hard to adapt?... what makes their generalizablility/adaptability limited? -Moreover, the large number of variables and constraints also leads to computational complexity issues [ref], especially when using exact methods for finding the solution. In this paper, we tackle a version of the nurse scheduling problem arising from a case study of one clinical division, providing two different services simultaneously (general infectious disease (ID) consults; and HIV consults service) at St. Michael's Hospital in Toronto, Canada. Our goal is to (1) present a simple integer linear programming formulations for the scheduling problem as developed for the hospital, and describe the adaptability of the formulation to solving similar problems in other departments; (2) compare the performance of the ILP scheduler to the results of the manual approach; and (3) analyze the robustness of the algorithm in difficult instances of the problem. \\ +Moreover, the large number of variables and constraints also leads to computational complexity issues \cite{goos_complexity_1996}, especially when using exact methods for finding the solution. In this paper, we tackle a version of the nurse scheduling problem arising from a case study of one clinical division, providing two different services simultaneously (general infectious disease (ID) consults; and HIV consults service) at St. Michael's Hospital in Toronto, Canada. Our goal is to (1) present a simple integer linear programming formulations for the scheduling problem as developed for the hospital, and describe the adaptability of the formulation to solving similar problems in other departments; (2) compare the performance of the ILP scheduler to the results of the manual approach; and (3) analyze the robustness of the algorithm in difficult instances of the problem. \\ % present a simple formulation for the problem developed and tested at the hospital after switching from a manual approach to scheduling; and (2) analyze the performance of integer linear programming in solving difficult instances of the problem and compare the results with those of the manual approach; and (3) describe the adaptability of the formulation as a basic framework for solving similar problems in other departments. \\ %make #3 an objective We begin by describing the problem in Section \ref{sec:problem}, and presenting our ILP formulation in Section \ref{sec:methods}. Next, we compare the results of our formulation to manually-created schedules, and evaluate the performance of the algorithm on simulated data in Section \ref{sec:results}. Finally, we discuss and interpret the results in Section \ref{sec:discussion}. % list the main contents/elements of the paper. \ No newline at end of file diff --git a/paper/paper.methods.tex b/paper/paper.methods.tex index cc6d949..47ba35d 100644 --- a/paper/paper.methods.tex +++ b/paper/paper.methods.tex @@ -89,6 +89,4 @@ \subsection{Objectives} \label{sec:meth-objectives} \begin{equation} \alpha \bar{Q}_1(X) + \beta \bar{Q}_2(Y) + (1 - \alpha - \beta) \bar{Q}_3(Z) \end{equation} -with $0 \leq \alpha, \beta \leq 1$. \\ - -[...] \ No newline at end of file +with $0 \leq \alpha, \beta \leq 1$. \\ \ No newline at end of file diff --git a/paper/paper.pdf b/paper/paper.pdf index 6e2d675..b0b5437 100644 Binary files a/paper/paper.pdf and b/paper/paper.pdf differ diff --git a/paper/paper.tex b/paper/paper.tex index 66697e2..7b861c4 100644 --- a/paper/paper.tex +++ b/paper/paper.tex @@ -19,4 +19,6 @@ \input{paper.results.tex} \section{Discussion} \label{sec:discussion} \input{paper.discussion.tex} + \bibliographystyle{unsrt} + \bibliography{references} \end{document} \ No newline at end of file diff --git a/paper/references.bib b/paper/references.bib new file mode 100644 index 0000000..9ed2245 --- /dev/null +++ b/paper/references.bib @@ -0,0 +1,342 @@ + +@article{burke_state_2004, + title = {The {State} of the {Art} of {Nurse} {Rostering}}, + volume = {7}, + issn = {1094-6136}, + url = {http://link.springer.com/10.1023/B:JOSH.0000046076.75950.0b}, + doi = {10.1023/B:JOSH.0000046076.75950.0b}, + abstract = {Nurse rostering is a complex scheduling problem that affects hospital personnel on a daily basis all over the world. The need for quality software solutions is acute for a number of reasons. In particular, it is very important to efficiently utilise time and effort, to evenly balance the workload among people and to attempt to satisfy personnel preferences. A high quality roster can lead to a more contented and thus more effective workforce.}, + language = {en}, + number = {6}, + urldate = {2019-08-27}, + journal = {Journal of Scheduling}, + author = {Burke, Edmund K. and De Causmaecker, Patrick and Berghe, Greet Vanden and Van Landeghem, Hendrik}, + month = nov, + year = {2004}, + pages = {441--499} +} + +@article{azaiez_0-1_2005, + title = {A 0-1 goal programming model for nurse scheduling}, + volume = {32}, + issn = {03050548}, + url = {https://linkinghub.elsevier.com/retrieve/pii/S0305054803002491}, + doi = {10.1016/S0305-0548(03)00249-1}, + abstract = {In this study, a computerized nurse-scheduling model is developed. The model is approached through a 0-1 linear goal program. It is adapted to Riyadh Al-Kharj hospital Program (in Saudi Arabia) to improve the current manual-made schedules. The developed model accounts both for hospital objectives and nurses’ preferences, in addition to considering some recommended policies that are displayed in the literature. Hospital objectives include ensuring a continuous service with appropriate nursing skills and sta ng size, while avoiding additional costs for unnecessary overtime. Nurses preferences, which are deduced from a survey conducted on-purpose for the sake of this study, include mainly fairness considerations, in terms of ratio of night shifts and weekends o , in addition to avoiding isolated days on and o . The model is implemented in an experimental phase of six-month period using LINGO and is considered to perform reasonably well, based both on some quality criteria displayed in the literature and on the feedback obtained from a second survey, that has been developed to assess the scheduling system performance.}, + language = {en}, + number = {3}, + urldate = {2019-08-27}, + journal = {Computers \& Operations Research}, + author = {Azaiez, M.N. and Al Sharif, S.S.}, + month = mar, + year = {2005}, + pages = {491--507} +} + +@article{trilling_nurse_2006, + title = {{NURSE} {SCHEDULING} {USING} {INTEGER} {LINEAR} {PROGRAMMING} {AND} {CONSTRAINT} {PROGRAMMING}}, + volume = {39}, + issn = {14746670}, + url = {https://linkinghub.elsevier.com/retrieve/pii/S1474667015360602}, + doi = {10.3182/20060517-3-FR-2903.00340}, + language = {en}, + number = {3}, + urldate = {2019-08-27}, + journal = {IFAC Proceedings Volumes}, + author = {Trilling, Lorraine and Guinet, Alain and Magny, Dominiue Le}, + year = {2006}, + pages = {671--676} +} + +@article{widyastiti_nurses_2016, + title = {Nurses {Scheduling} by {Considering} the {Qualification} using {Integer} {Linear} {Programming}}, + volume = {14}, + issn = {2302-9293, 1693-6930}, + url = {http://www.journal.uad.ac.id/index.php/TELKOMNIKA/article/view/2913}, + doi = {10.12928/telkomnika.v14i3.2913}, + abstract = {One of problems that frequently occurs in hospital management is nurses scheduling problem. A suitable schedule is needed in order to avoid fatigue, both physically and psychologically, which subsequently may deteriorate their performance. Nurse scheduling is commonly designed by the head of nurse manually. In this research, nurse scheduling problem is modeled by considering the qualification of the nurses and the model has the form of integer linear programming. The objective of the model is to maximize the number of nurse’s day-offs. Then optimization problem is implemented to nurses scheduling in the High Care Unit and the Emergency room of Rumah Sehat Terpadu Dompet Dhuafa Parung Bogor.}, + language = {en}, + number = {3}, + urldate = {2019-08-27}, + journal = {TELKOMNIKA (Telecommunication Computing Electronics and Control)}, + author = {Widyastiti, Maya and Aman, Amril and Bakhtiar, Toni}, + month = sep, + year = {2016}, + pages = {933} +} + +@article{el_adoly_new_2018, + title = {A new formulation and solution for the nurse scheduling problem: {A} case study in {Egypt}}, + volume = {57}, + issn = {11100168}, + shorttitle = {A new formulation and solution for the nurse scheduling problem}, + url = {https://linkinghub.elsevier.com/retrieve/pii/S111001681730282X}, + doi = {10.1016/j.aej.2017.09.007}, + abstract = {Nurse Scheduling Problem (NSP) is the assignment of a number of nurses to a number of shifts in order to satisfy hospital’s demand. The objectives of NSP are the minimization of the overall hospital cost, and the maximization of nurses’ preferences while taking into consideration the governmental rules and hospital standards. In this article, a proposed mathematical model for the NSP is presented, which is based on the idea of multi-commodity network flow model. The proposed model was verified using hypothetical instances as well as benchmark instances, then, it is applied to a real case study in an Egyptian hospital. The results demonstrate the advantage of using the proposed model in generating schedule required to solve the problem. Furthermore, it proves the superiority of the obtained schedule to those generated manually by the supervisor head nurse as it improves the level of nurses’ satisfaction by creating fair schedule system take care about nurses’ preferences as well as decreases the overall overtime cost by 36\%.}, + language = {en}, + number = {4}, + urldate = {2019-08-27}, + journal = {Alexandria Engineering Journal}, + author = {El Adoly, Ahmed Ali and Gheith, Mohamed and Nashat Fors, M.}, + month = dec, + year = {2018}, + pages = {2289--2298} +} + +@article{aickelin_exploiting_2000, + title = {Exploiting problem structure in a genetic algorithm approach to a nurse rostering problem}, + volume = {3}, + copyright = {Copyright © 2000 John Wiley \& Sons, Ltd.}, + issn = {1099-1425}, + url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/%28SICI%291099-1425%28200005/06%293%3A3%3C139%3A%3AAID-JOS41%3E3.0.CO%3B2-2}, + doi = {10.1002/(SICI)1099-1425(200005/06)3:3<139::AID-JOS41>3.0.CO;2-2}, + abstract = {There is considerable interest in the use of genetic algorithms to solve problems arising in the areas of scheduling and timetabling. However, the classical genetic algorithm (GA) paradigm is not well equipped to handle the conflict between objectives and constraints that typically occur in such problems. In order to overcome this, successful implementations frequently make use of problem specific knowledge. This paper is concerned with the development of a GA for a nurse rostering problem at a major U.K. hospital. The structure of the constraints is used as the basis for a co-evolutionary strategy using co-operating subpopulations. Problem-specific knowledge is also used to define a system of incentives and disincentives, and a complementary mutation operator. Empirical results based on 52 weeks of data show how these features are able to improve an unsuccessful canonical GA to the point where it is able to provide a practical solution to the problem. Copyright © 2000 John Wiley \& Sons, Ltd.}, + language = {en}, + number = {3}, + urldate = {2019-08-27}, + journal = {Journal of Scheduling}, + author = {Aickelin, Uwe and Dowsland, Kathryn A.}, + year = {2000}, + keywords = {co-evolution, genetic algorithms, heuristics, manpower scheduling}, + pages = {139--153} +} + +@inproceedings{jan_evolutionary_2000, + title = {Evolutionary algorithms for nurse scheduling problem}, + volume = {1}, + doi = {10.1109/CEC.2000.870295}, + abstract = {The nurse scheduling problem (NSPs) represents a difficult class of multi-objective optimisation problems consisting of a number of interfering objectives between the hospitals and individual nurses. The objective of this research is to investigate difficulties that occur during the solution of NSP using evolutionary algorithms, in particular genetic algorithms (GA). As the solution method a population-less cooperative genetic algorithm (CGA) is taken into consideration. Because contrary to competitive GAs, we have to simultaneously deal with the optimization of the fitness of the individual nurses and also optimization of the entire schedule as the final solution to the problem in hand. To confirm the search ability of CGA, first a simplified version of NSP is examined. Later we report a more complex and useful version of the problem. We also compare CGA with another multi-agent evolutionary algorithm using pheromone style communication of real ants. Finally, we report the results of computer simulations acquired throughout the experiments.}, + booktitle = {Proceedings of the 2000 {Congress} on {Evolutionary} {Computation}. {CEC}00 ({Cat}. {No}.00TH8512)}, + author = {Jan, A. and Yamamoto, M. and Ohuchi, A.}, + month = jul, + year = {2000}, + keywords = {ant communication, computer simulation, Contracts, cooperative genetic algorithm, evolutionary algorithms, Evolutionary computation, genetic algorithms, Genetic algorithms, hospitals, Hospitals, human resource management, Mathematical model, Mathematical programming, medical administrative data processing, multi-agent evolutionary algorithm, multi-agent systems, multi-objective optimisation, nurse scheduling problem, optimization, pheromone style communication, Processor scheduling, scheduling, Scheduling algorithm, search, search problems}, + pages = {196--203 vol.1} +} + +@inproceedings{kawanaka_genetic_2001, + title = {Genetic algorithm with the constraints for nurse scheduling problem}, + volume = {2}, + doi = {10.1109/CEC.2001.934317}, + abstract = {The Nurse Scheduling Problem (NSP) is a problem of allocating shifts (day and night shifts, holidays, and so on) for nurses under various constraints. Generally, NSP has a lot of constraints. As a result, it needs a lot of knowledge and experience to construct the scheduling table with its constraints, and it is usually done by the head nurse or the authority in hospitals. Some research on NSP using genetic algorithms (GA) is reported. Conventional methods take the constraints into the fitness function. However, if it reduces the fitness value a lot to the parts of solution against the constraints, it causes useless search, because most of the chromosomes are selected in the initial population or in the change by the genetic operations. If it doesn't reduce the fitness value so much, the final solution has some parts against the constraints. Some of them are established by the Labor Standards Act or the Labor Union Act, so the solution has to be modified. As a result, it is difficult to acquire an effective scheduling table automatically. The paper studies the method of coding and genetic operations with their constraints for NSP. The exchange of shifts is done to satisfy the constraints in the coding and after the genetic operations. We apply this method to NSP using actual shifts and constraints being used in a hospital. It shows that an effective scheduling table satisfying the constraints is acquired by this method.}, + booktitle = {Proceedings of the 2001 {Congress} on {Evolutionary} {Computation} ({IEEE} {Cat}. {No}.01TH8546)}, + author = {Kawanaka, H. and Yamamoto, K. and Yoshikawa, T. and Shinogi, T. and Tsuruoka, S.}, + month = may, + year = {2001}, + keywords = {Biological cells, chromosomes, constraint theory, fitness function, fitness value, genetic algorithm, genetic algorithms, Genetic algorithms, Genetic mutations, genetic operations, Heuristic algorithms, Hospitals, human resource management, initial population, Labor Standards Act, Labor Union Act, medical administrative data processing, NSP, nurse scheduling problem constraints, scheduling, scheduling table, search problems, shift allocation}, + pages = {1123--1130 vol. 2} +} + +@article{jaszkiewicz_metaheuristic_1997, + title = {A metaheuristic approach to multiple objective nurse scheduling}, + volume = {22}, + number = {3}, + journal = {Foundations of Computing and Decision Sciences}, + author = {Jaszkiewicz, Andrzej}, + year = {1997}, + pages = {169--184} +} + +@inproceedings{li_hybrid_2003, + address = {New York, NY, USA}, + series = {{SAC} '03}, + title = {A {Hybrid} {AI} {Approach} for {Nurse} {Rostering} {Problem}}, + isbn = {978-1-58113-624-1}, + url = {http://doi.acm.org/10.1145/952532.952675}, + doi = {10.1145/952532.952675}, + abstract = {This paper presents a hybrid AI approach for a class of overconstrained Nurse Rostering Problems. Our approach comes in two phases. The first phase solves a relaxed version of problem which only includes hard rules and part of nurses' requests for shifts. This involves using a forward checking algorithm with non-binary constraint propagation, variable ordering, random value ordering and compulsory backjumping. In the second phase, adjustments with descend local search and tabu search are applied to improved the solution. This is to satisfy the preference rules as far as possible. Experiments show that our approach is able to solve this class of problems well.}, + urldate = {2019-08-27}, + booktitle = {Proceedings of the 2003 {ACM} {Symposium} on {Applied} {Computing}}, + publisher = {ACM}, + author = {Li, Haibing and Lim, Andrew and Rodrigues, Brian}, + year = {2003}, + note = {event-place: Melbourne, Florida}, + pages = {730--735} +} + +@article{abdennadher_nurse_nodate, + title = {Nurse {Scheduling} using {Constraint} {Logic} {Programming}}, + abstract = {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 di cult and time-consuming expert task and is still done manually. INTERDIP1 is an advanced industrial prototype that supports semi-automatic creation of such rosters. Using the arti cial 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.}, + language = {en}, + author = {Abdennadher, Slim and Schlenker, Hans}, + pages = {6} +} + +@inproceedings{aickelin_improved_2006, + series = {Lecture {Notes} in {Computer} {Science}}, + title = {Improved {Squeaky} {Wheel} {Optimisation} for {Driver} {Scheduling}}, + isbn = {978-3-540-38991-0}, + abstract = {This paper presents a technique called Improved Squeaky Wheel Optimisation (ISWO) for driver scheduling problems. It improves the original Squeaky Wheel Optimisation’s (SWO) effectiveness and execution speed by incorporating two additional steps of Selection and Mutation which implement evolution within a single solution. In the ISWO, a cycle of Analysis-Selection-Mutation-Prioritization-Construction continues until stopping conditions are reached. The Analysis step first computes the fitness of a current solution to identify troublesome components. The Selection step then discards these troublesome components probabilistically by using the fitness measure, and the Mutation step follows to further discard a small number of components at random. After the above steps, an input solution becomes partial and thus the resulting partial solution needs to be repaired. The repair is carried out by using the Prioritization step to first produce priorities that determine an order by which the following Construction step then schedules the remaining components. Therefore, the optimisation in the ISWO is achieved by solution disruption, iterative improvement and an iterative constructive repair process performed. Encouraging experimental results are reported.}, + language = {en}, + booktitle = {Parallel {Problem} {Solving} from {Nature} - {PPSN} {IX}}, + publisher = {Springer Berlin Heidelberg}, + author = {Aickelin, Uwe and Burke, Edmund K. and Li, Jingpeng}, + editor = {Runarsson, Thomas Philip and Beyer, Hans-Georg and Burke, Edmund and Merelo-Guervós, Juan J. and Whitley, L. Darrell and Yao, Xin}, + year = {2006}, + keywords = {Construction Step, Nurse Rostering, Nurse Schedule, Schedule Problem, Solution Disruption}, + pages = {182--191} +} + +@article{goel_truck_2012, + title = {Truck driver scheduling in {Australia}}, + volume = {39}, + issn = {0305-0548}, + url = {http://www.sciencedirect.com/science/article/pii/S0305054811001559}, + doi = {10.1016/j.cor.2011.05.021}, + abstract = {In September 2008 new regulations for managing heavy vehicle driver fatigue entered into force in Australia. According to the new regulations there is a chain of responsibility ranging from drivers to dispatchers and shippers and thus, carriers must explicitly consider driving and working hour regulations when generating truck driver schedules. This paper presents and studies the Australian Truck Driver Scheduling Problem (AUS-TDSP) which is the problem of determining whether a sequence of locations can be visited within given time windows in such a way that driving and working activities of truck drivers comply with Australian Heavy Vehicle Driver Fatigue Law.}, + number = {5}, + urldate = {2019-08-27}, + journal = {Computers \& Operations Research}, + author = {Goel, Asvin and Archetti, Claudia and Savelsbergh, Martin}, + month = may, + year = {2012}, + keywords = {Hours of service regulations, Vehicle scheduling}, + pages = {1122--1132} +} + +@inproceedings{gunther_combined_2010, + series = {Lecture {Notes} in {Business} {Information} {Processing}}, + title = {Combined {Working} {Time} {Model} {Generation} and {Personnel} {Scheduling}}, + isbn = {978-3-642-12494-5}, + abstract = {Workforce management is comprised of several phases, such as working time model generation and personnel scheduling. The combination of these phases has significant potential, especially for volatile personnel demand. This article shows that the concepts for the automatic generation of working time models already used in retail can be transferred to personnel scheduling in the logistics industry. Through this, the assignment of personnel can be accurately adapted to personnel demand. The results suggest the use of heuristics, especially meta-heuristics such as the evolution strategy or constructive methods which are adapted to the problem at hand.}, + language = {en}, + booktitle = {Advanced {Manufacturing} and {Sustainable} {Logistics}}, + publisher = {Springer Berlin Heidelberg}, + author = {Günther, Maik and Nissen, Volker}, + editor = {Dangelmaier, Wilhelm and Blecken, Alexander and Delius, Robin and Klöpfer, Stefan}, + year = {2010}, + keywords = {constructive heuristic, evolution strategy, workforce management, workforce scheduling, working time model}, + pages = {210--221} +} + +@article{al-yakoob_mixed-integer_2007, + title = {Mixed-integer programming models for an employee scheduling problem with multiple shifts and work locations}, + volume = {155}, + issn = {1572-9338}, + url = {https://doi.org/10.1007/s10479-007-0210-4}, + doi = {10.1007/s10479-007-0210-4}, + abstract = {This paper is concerned with the problem of assigning employees to gas stations owned by the Kuwait National Petroleum Corporation (KNPC), which hires a firm to prepare schedules for assigning employees to about 86 stations distributed all over Kuwait. Although similar employee scheduling problems have been addressed in the literature, certain peculiarities of the problem require novel mathematical models and algorithms to deal with the specific nature and size of this problem. The problem is modeled as a mixed-integer program, and a problem size analysis based on real data reveals that the formulation is too complex to solve directly. Hence, a two-stage approach is proposed, where the first stage assigns employees to stations, and the second stage specifies shifts and off-days for each employee. Computational results related to solving the two-stage models directly via CPLEX and by specialized heuristics are reported. The two-stage approach provides daily schedules for employees for a given time horizon in a timely fashion, taking into consideration the employees’ expressed preferences. This proposed modeling approach can be incorporated within a decision support system to replace the current manual scheduling practice that is often chaotic and has led to feelings of bias and job dissatisfaction among employees.}, + language = {en}, + number = {1}, + urldate = {2019-08-27}, + journal = {Annals of Operations Research}, + author = {Al-Yakoob, Salem M. and Sherali, Hanif D.}, + month = nov, + year = {2007}, + keywords = {Employee scheduling, Manpower scheduling, Mixed-integer programming, Partitioning, Two-stage approach}, + pages = {119--142} +} + +@article{al-yakoob_column_2008, + title = {A column generation approach for an employee scheduling problem with multiple shifts and work locations}, + volume = {59}, + issn = {0160-5682}, + url = {https://doi.org/10.1057/palgrave.jors.2602294}, + doi = {10.1057/palgrave.jors.2602294}, + abstract = {This paper is concerned with the problem of assigning employees to a number of work centres taking into account employees' expressed preferences for specific shifts, off-days, and work centres. This particular problem is faced by the Kuwait National Petroleum Corporation that hires a firm to prepare schedules for assigning employees to about 86 stations distributed all over Kuwait. The number of variables in a mixed-integer programming model formulated for this problem is overwhelming, and hence, a direct solution to even the continuous relaxation of this model for relatively large-scale instances is inconceivable. However, we demonstrate that a column generation method, which exploits the special structures of the model, can readily solve the continuous relaxation of the model. Based on this column generation construct, we develop an effective heuristic to solve the problem. Computational results indicate that the proposed approach can facilitate the generation of good-quality schedules for even large-scale problem instances in a reasonable time.}, + number = {1}, + urldate = {2019-08-27}, + journal = {Journal of the Operational Research Society}, + author = {Al-Yakoob, S. M. and Sherali, H. D.}, + month = jan, + year = {2008}, + keywords = {column generation, employee scheduling, mixed-integer programming, optimization, scheduling}, + pages = {34--43} +} + +@article{alfares_simulation_2007, + title = {A {Simulation} {Approach} for {Stochastic} {Employee} {Days}-{Off} {Scheduling}}, + volume = {27}, + issn = {0228-6203}, + url = {https://doi.org/10.1080/02286203.2007.11442393}, + doi = {10.1080/02286203.2007.11442393}, + abstract = {This paper presents a simulation approach for employee days-off scheduling when the daily labour demands are random variables. A simulation model is constructed, and a case study application of the proposed approach is described. The model recognizes limited staff availability, stochastic workload variability, and policy restrictions on the choice of employee work schedules. The model has been successfully applied in the days-off scheduling of a multicraft maintenance workforce of an oil and gas pipelines department. Without increasing the number or cost of employees, the model recommended alternative days-off assignments that are expected to reduce throughput times for maintenance work orders by an average of 25\%.}, + number = {1}, + urldate = {2019-08-27}, + journal = {International Journal of Modelling and Simulation}, + author = {Alfares, H. K.}, + month = jan, + year = {2007}, + keywords = {days-off schedules, Employee scheduling, maintenance, simulation, stochastic optimization}, + pages = {9--15} +} + +@inproceedings{chapados_retail_2011, + series = {Lecture {Notes} in {Computer} {Science}}, + title = {Retail {Store} {Workforce} {Scheduling} by {Expected} {Operating} {Income} {Maximization}}, + isbn = {978-3-642-21311-3}, + abstract = {We address the problem of retail store sales personnel scheduling by casting it in terms of an expected operating income maximization. In this framework, salespeople are no longer only responsible for operating costs, but also contribute to operating revenue. We model the marginal impact of an additional staff by making use of historical sales and payroll data, conditioned on a store-, date- and time-dependent traffic forecast. The expected revenue and its uncertainty are then fed into a constraint program which builds an operational schedule maximizing the expected operating income. A case study with a medium-sized retailer suggests that revenue increases of 7\% and operating income increases of 3\% are possible with the approach.}, + language = {en}, + booktitle = {Integration of {AI} and {OR} {Techniques} in {Constraint} {Programming} for {Combinatorial} {Optimization} {Problems}}, + publisher = {Springer Berlin Heidelberg}, + author = {Chapados, Nicolas and Joliveau, Marc and Rousseau, Louis-Martin}, + editor = {Achterberg, Tobias and Beck, J. Christopher}, + year = {2011}, + keywords = {Constraint Programming, Retail, Shift Scheduling, Statistical Forecasting}, + pages = {53--58} +} + +@inproceedings{nissen_automatic_2010, + series = {Lecture {Notes} in {Computer} {Science}}, + title = {Automatic {Generation} of {Optimised} {Working} {Time} {Models} in {Personnel} {Planning}}, + isbn = {978-3-642-15461-4}, + abstract = {Retail is traditionally labour-intensive. Demand-oriented workforce management has great significance due to the amount of competition which enforces a strict cost management while keeping a good service level. Thus, highly flexible working time models are of particular importance. Our project addresses the question how to automatically and simultaneously assign staff to workstations and generate optimised working time models under constraints and on the basis of fluctuating personnel demand. The planning is completed for an entire year in order to assess adapted versions of the evolution strategy and particle swarm optimisation. A commercial constructive method is used as benchmark.}, + language = {en}, + booktitle = {Swarm {Intelligence}}, + publisher = {Springer Berlin Heidelberg}, + author = {Nissen, Volker and Günther, Maik}, + editor = {Dorigo, Marco and Birattari, Mauro and Di Caro, Gianni A. and Doursat, René and Engelbrecht, Andries P. and Floreano, Dario and Gambardella, Luca Maria and Groß, Roderich and Şahin, Erol and Sayama, Hiroki and Stützle, Thomas}, + year = {2010}, + keywords = {integrated personnel planning, metaheuristics}, + pages = {384--391} +} + +@article{horn_scheduling_2007, + title = {Scheduling patrol boats and crews for the {Royal} {Australian} {Navy}}, + volume = {58}, + issn = {0160-5682}, + url = {https://doi.org/10.1057/palgrave.jors.2602300}, + doi = {10.1057/palgrave.jors.2602300}, + abstract = {The Royal Australian Navy's Patrol Boat Force carries out essential tasks in the surveillance, policing and defence of Australia's coastal waters. To help the Navy make efficient use of a new generation of boats, the authors have developed optimization procedures to schedule the activities of the boats and their crews. The procedures—embodied in a software system called CBM (‘Crews, Boats, Missions’)—use simulated annealing and specialized heuristic techniques within a multi-stage problem-solving framework. Tests show that CBM is reliable in terms of solution quality, and flexible with respect to the range of scheduling conditions applied. CBM has proved valuable to the Navy as an investigatory tool, and it is planned that it should be adapted for operational use, as part of a decision support system to aid in the ongoing management of patrol boat operations.}, + number = {10}, + urldate = {2019-08-27}, + journal = {Journal of the Operational Research Society}, + author = {Horn, M. E. T. and Jiang, H. and Kilby, P.}, + month = oct, + year = {2007}, + keywords = {heuristics, metaheuristics, military, multi-objective, optimization, penalty methods, planning, scheduling, simulated annealing}, + pages = {1284--1293} +} + +@inproceedings{laguna_modeling_2005, + series = {Operations {Research}/{Computer} {Science} {Interfaces} {Series}}, + title = {Modeling and {Solving} a {Selection} and {Assignment} {Problem}}, + isbn = {978-0-387-23529-5}, + abstract = {In this paper, we first provide an MIP formulation of a selection/assignment problem and then we discuss a solution method based both on the use of a commercial general-purpose scatter-search and a simple implementation of tabu search. This optimization problem is related to a research project supported by the Office of Naval Research where sailors need to be selected to perform a set of jobs that require specific skill levels. The results of our computational experiments indicate the usefulness of the software system for workforce planning that we have developed.}, + language = {en}, + booktitle = {The {Next} {Wave} in {Computing}, {Optimization}, and {Decision} {Technologies}}, + publisher = {Springer US}, + author = {Laguna, Manuel and Wubbena, Terry}, + editor = {Golden, Bruce and Raghavan, S. and Wasil, Edward}, + year = {2005}, + keywords = {assignment/selection problem, bin packing, metaheuristic optimization}, + pages = {149--162} +} + +@incollection{goos_complexity_1996, + address = {Berlin, Heidelberg}, + title = {The complexity of timetable construction problems}, + volume = {1153}, + isbn = {978-3-540-61794-5 978-3-540-70682-3}, + url = {http://link.springer.com/10.1007/3-540-61794-9_66}, + abstract = {This paper shows that timetable construction is NP-complete in a number of quite different ways that arise in practice, and discusses the prospects of overcoming these problems. A formal specification of the problem based on TTL, a timetable specification language, is given.}, + language = {en}, + urldate = {2019-08-27}, + booktitle = {Practice and {Theory} of {Automated} {Timetabling}}, + publisher = {Springer Berlin Heidelberg}, + author = {Cooper, Tim B. and Kingston, Jeffrey H.}, + editor = {Goos, Gerhard and Hartmanis, Juris and Leeuwen, Jan and Burke, Edmund and Ross, Peter}, + year = {1996}, + doi = {10.1007/3-540-61794-9_66}, + pages = {281--295} +} \ No newline at end of file