Selecting and weighting features using a genetic algorithm in a case-based reasoning approach to personnel rostering

Personnel rostering problems are highly constrained resource allocation problems. Human rostering experts have many years of experience in making rostering decisions which reflect their individual goals and objectives. We present a novel method for capturing nurse rostering decisions and adapting them to solve new problems using the Case-Based Reasoning (CBR) paradigm. This method stores examples of previously encountered constraint violations and the operations that were used to repair them. The violations are represented as vectors of feature values. We investigate the problem of selecting and weighting features so as to improve the performance of the case-based reasoning approach. A genetic algorithm is developed for off-line feature selection and weighting using the complex data types needed to represent real-world nurse rostering problems. This approach significantly improves the accuracy of the CBR method and reduces the number of features that need to be stored for each problem. The relative importance of different features is also determined, providing an insight into the nature of expert decision making in personnel rostering.     

The roster quality staffing problem – A methodology for improving the roster quality by modifying the personnel structure

Quantitative decision support on personnel planning is often restricted to either rostering or staffing. There exist some approaches in which aspects at the staffing level and the rostering level are treated in a sequential way. Obviously, such practice risks producing suboptimal solutions at both decision levels. These arguments justify an integrated approach towards improving the overall quality of personnel planning. This contribution constitutes (1) the introduction of the roster quality staffing problem and (2) a three-step methodology that enables assessing the appropriateness of a personnel structure for achieving high quality rosters, while relying on an existing rostering algorithm. Based on the rostering assessment result, specific modifications to the personnel structure can be suggested at the staffing level. The approach is demonstrated by means of two different hospital cases, which have it that they are subject to complex rostering constraints. Experimental results show that the three-step methodology indeed points out alternative personnel structures that better comply with the rostering requirements. The roster analysis approach and the corresponding staffing recommendations integrate personnel planning needs at operational and tactical levels.     

Near-optimal MIP solutions for preference based self-scheduling

Making a high quality staff schedule is both difficult and time consuming for any company that has employees working on irregular schedules. We formulate a mixed integer program (MIP) to find a feasible schedule that satisfies all hard constraints while minimizing the soft constraint violations as well as satisfying as many of the employees’ requests as possible. We present the MIP model and show the result from four real world companies and institutions. We also compare the results with those of a local search based algorithm that is designed to emulate the solution strategies when the schedules are created manually. The results show that using near-optimal solutions from the MIP model, with a relative MIP gap of around 0.01–0.1, instead of finding the optimal solution, allows us to find very good solutions in a reasonable amount of time that compare favorably with both the manual solutions and the solutions found by the local search based algorithm.     

A hybrid model of integer programming and variable neighbourhood search for highly-constrained nurse rostering problems

This paper presents a hybrid multi-objective model that combines integer programming (IP) and variable neighbourhood search (VNS) to deal with highly-constrained nurse rostering problems in modern hospital environments. An IP is first used to solve the subproblem which includes the full set of hard constraints and a subset of soft constrains. A basic VNS then follows as a postprocessing procedure to further improve the IP’s resulting solutions. The satisfaction of the excluded constraints from the preceding IP model is the major focus of the VNS. Very promising results are reported compared with a commercial genetic algorithm and a hybrid VNS approach on real instances arising in a Dutch hospital. The comparison results demonstrate that our hybrid approach combines the advantages of both the IP and the VNS to beat other approaches in solving this type of problems. We also believe that the proposed methodology can be applied to other resource allocation problems with a large number of constraints.     

Elastic Constraint Branching, the Wedelin/Carmen Lagrangian Heuristic and Integer Programming for Personnel Scheduling

The Wedelin algorithm is a Lagrangian based heuristic that is being successfully used by Carmen Systems to solve large crew pairing problems within the airline industry. We extend the Wedelin approach by developing an implementation for personnel scheduling problems (also termed staff rostering problems) that exploits the special structure of these problems. We also introduce elastic constraint branching with the twin aims of improving the performance of our new approach and making it more column generation friendly. Numerical results show that our approach can outperform the commercial solver CPLEX on difficult commercial rostering problems.     

Two-level decomposition algorithm for crew rostering problems with fair working condition

A typical railway crew scheduling problem consists of two phases: a crew pairing problem to determine a set of crew duties and a crew rostering problem. The crew rostering problem aims to find a set of rosters that forms workforce assignment of crew duties and rest periods satisfying several working regulations. In this paper, we present a two-level decomposition approach to solve railway crew rostering problem with the objective of fair working condition. To reduce computational efforts, the original problem is decomposed into the upper-level master problem and the lower-level subproblem. The subproblem can be further decomposed into several subproblems for each roster. These problems are iteratively solved by incorporating cuts into the master problem. We show that the relaxed problem of the master problem can be formulated as a uniform parallel machine scheduling problem to minimize makespan, which is NP-hard. An efficient branch-and-bound algorithm is applied to solve the master problem. Effective valid cuts are developed to reduce feasible search space to tighten the duality gap. Using data provided by the railway company, we demonstrate the effectiveness of the proposed method compared with that of constraint programming techniques for large-scale problems through computational experiments.     

A hybrid scatter search heuristic for personalized crew rostering in the airline industry

The crew scheduling problem in the airline industry is extensively investigated in the operations research literature since efficient crew employment can drastically reduce operational costs of airline companies. Given the flight schedule of an airline company, crew scheduling is the process of assigning all necessary crew members in such a way that the airline is able to operate all its flights and constructing a roster line for each employee minimizing the corresponding overall cost for personnel. In this paper, we present a scatter search algorithm for the airline crew rostering problem. The objective is to assign a personalized roster to each crew member minimizing the overall operational costs while ensuring the social quality of the schedule. We combine different complementary meta-heuristic crew scheduling combination and improvement principles. Detailed computational experiments in a real-life problem environment are presented investigating all characteristics of the procedure. Moreover, we compare the proposed scatter search algorithm with optimal solutions obtained by an exact branch-and-price procedure and a steepest descent variable neighbourhood search.     

A shift sequence based approach for nurse scheduling and a new benchmark dataset

This paper investigates an adaptive constructive method for solving nurse rostering problems. The constraints considered in the problems are categorised into three classes: those that are sequence related, those that are nurse schedule related and those that are roster related. We propose a decomposition approach (to construct solutions) that consists of two stages: (1) to construct high quality sequences for nurses by only considering the sequence constraints, and (2) to iteratively construct schedules for nurses and the overall rosters, based on the sequences built and considering the schedule and roster constraints. In the second stage of the schedule construction, nurses are ordered and selected adaptively according to the quality of the schedules they were assigned to in the last iteration. Greedy local search is carried out during and after the roster construction, in order to improve the (partial) rosters built. We show that the local search heuristic during the roster construction can further improve the constructed solutions for the benchmark problems tested.     

Multi-Skilled Workforce Optimisation

This paper describes a problem faced by CS Energy's Swanbank Power Station in the Australian state of Queensland. It involved the personnel scheduling (rostering) of staff with multiple skill levels at the power station. Such a problem can be classified using the six stage construction process proposed by Ernst et al. We assume that the three processes of ‘demand modelling,’ ‘shift starting times’ and ‘task scheduling’ are specified. We are concerned with the essential processes of ‘day off scheduling,’ ‘line of work construction’ and ‘shift assignment to staff’ with requirements to maintain multiple skills. Several other authors have reported results for staff with hierarchical skills while the methods proposed in this paper are for non-hierarchical skill sets. The paper describes a set covering approach to the multi-skilled rostering problem. We propose a number of solution strategies for the set covering approach and give a comparison of the results.     

The Solution of Massive Generalized Set Partitioning Problems in Aircrew Rostering

The scheduling and rostering of personnel is a problem that occurs in many organizations. Aircrew scheduling has attracted considerable attention with many heuristic methods being proposed, but in recent times set partitioning optimization methods have become more popular. The aircrew rostering problem is discussed and formulated as a generalized set partitioning model. Because of the extremely large optimization models that are generated in practical situations, some special computational techniques have been developed to produce solutions efficiently. These techniques are used to solve problems arising from an airline application in which set partitioning models with more than 650 constraints and 200 000 binary variables are generated. The solutions are produced on a Motorola 68020 microprocessor in little more than three hours.     

Hard and soft constraints for reasoning about qualitative conditional preferences

Many real life optimization problems are defined in terms of both hard and soft constraints, and qualitative conditional preferences. However, there is as yet no single framework for combined reasoning about these three kinds of information. In this paper we study how to exploit classical and soft constraint solvers for handling qualitative preference statements such as those captured by the CP-nets model. In particular, we show how hard constraints are sufficient to model the optimal outcomes of a possibly cyclic CP-net, and how soft constraints can faithfully approximate the semantics of acyclic conditional preference statements whilst improving the computational efficiency of reasoning about these statements. This material is based in part upon works supported by the Science Foundation Ireland under Grant No. 00/PI.1/C075     

Comparison and hybridization of crossover operators for the nurse scheduling problem

In this paper, we present a hybrid genetic algorithm for the well-known nurse scheduling problem (NSP). The NSP involves the construction of roster schedules for nursing staff in order to maximize the quality of the roster schedule subject to various hard constraints. In the literature, several genetic algorithms have been proposed to solve the NSP under various assumptions. The contribution of this paper is twofold. First, we extensively compare the various crossover operators and test them on a standard dataset in a solitary approach. Second, we propose several options to hybridize the various crossover operators.     

Branch-and-price for staff rostering: An efficient implementation using generic programming and nested column generation

We present a novel generic programming implementation of a column-generation algorithm for the generalized staff rostering problem. The problem is represented as a generalized set partitioning model, which is able to capture commonly occurring problem characteristics given in the literature. Columns of the set partitioning problem are generated dynamically by solving a pricing subproblem, and constraint branching in a branch-and-bound framework is used to enforce integrality. The pricing problem is formulated as a novel three-stage nested shortest path problem with resource constraints that exploits the inherent problem structure. A very efficient implementation of this pricing problem is achieved by using generic programming principles in which careful use of the C++ pre-processor allows the generator to be customized for the target problem at compile-time. As well as decreasing run times, this new approach creates a more flexible modeling framework that is well suited to handling the variety of problems found in staff rostering. Comparison with a more-standard run-time customization approach shows that speedups of around a factor of 20 are achieved using our new approach. The adaption to a new problem is simple and the implementation is automatically adjusted internally according to the new definition. We present results for three practical rostering problems. The approach captures all features of each problem and is able to provide high-quality solutions in less than 15 minutes. In two of the three instances, the optimal solution is found within this time frame.     

Towards a practical engineering tool for rostering

The profitability and morale of many organizations (such as factories, hospitals and airlines) are affected by their ability to schedule their personnel properly. Sophisticated and powerful constraint solvers such as ILOG, CHIP, ECLiPSe, etc. have been demonstrated to be extremely effective on scheduling. Unfortunately, they require non-trivial expertise to use. This paper describes ZDC-rostering, a constraint-based tool for personnel scheduling that addresses the software crisis and fills a void in the space of solvers. ZDC-rostering is easier to use than the above constraint-based solvers and more effective than Microsoft’s Excel Solver. ZDC-rostering is based on an open-source computer-aided constraint programming package called ZDC, which decouples problem formulation (or modelling) from solution generation in constraint satisfaction. ZDC is equipped with a set of constraint algorithms, including Extended Guided Local Search, whose efficiency and effectiveness have been demonstrated in a wide range of applications. Our experiments show that ZDC-rostering is capable of solving realistic-sized and very tightly-constrained problems efficiently. ZDC-rostering demonstrates the feasibility of applying constraint satisfaction techniques to solving rostering problems, without having to acquire deep knowledge in constraint technology.     

Analysis of mathematical programming problems prior to applying the simplex algorithm

Large practical linear and integer programming problems are not always presented in a form which is the most compact representation of the problem. Such problems are likely to posses generalized upper bound(GUB) and related structures which may be exploited by algorithms designed to solve them efficiently. The steps of an algorithm which by repeated application reduces the rows, columns, and bounds in a problem matrix and leads to the freeing of some variables are first presented. The ‘unbounded solution’ and ‘no feasible solution’ conditions may also be detected by this. Computational results of applying this algorithm are presented and discussed. An algorithm to detect structure is then described. This algorithm identifies sets of variables and the corresponding constraint relationships so that the total number of GUB-type constraints is maximized. Comparisons of computational results of applying different heuristics in this algorithm are presented and discussed.     

Scheduling a triple round robin tournament with minitournaments for the Finnish national youth ice hockey league

This paper presents a method to schedule a triple round robin tournament, which involves minitournaments, each hosted by one team. A key issue is that at the end of the season the number of home games should be balanced over the teams, despite the fact that in minitournament matches only the host team plays at home. This format is played in the Finnish national ice hockey league for players under the age of 20 years, where the problem is further complicated by many other constraints, for example, preassigned matches resulting from away tours that should limit the distances travelled by the teams. To obtain a schedule for this league, we sequentially solve four distinct combinatorial problems. This method allows us to construct a schedule for the 2009–2010 season, which is superior to the official schedule: it has no hard constraint violations, and outperforms the official schedule on three of five soft constraints.     

Bounded knapsack sharing

A bounded knapsack sharing problem is a maximin or minimax mathematical programming problem with one or more linear inequality constraints, an objective function composed of single variable continuous functions called tradeoff functions, and lower and upper bounds on the variables. A single constraint problem which can have negative or positive constraint coefficients and any type of continuous tradeoff functions (including multi-modal, multiple-valued and staircase functions) is considered first. Limiting conditions where the optimal value of a variable may be plus or minus infinity are explicitly considered. A preprocessor procedure to transform any single constraint problem to a finite form problem (an optimal feasible solution exists with finite variable values) is developed. Optimality conditions and three algorithms are then developed for the finite form problem. For piecewise linear tradeoff functions, the preprocessor and algorithms are polynomially bounded. The preprocessor is then modified to handle bounded knapsack sharing problems with multiple constraints. An optimality condition and algorithm is developed for the multiple constraint finite form problem. For multiple constraints, the time needed for the multiple constraint finite form algorithm is the time needed to solve a single constraint finite form problem multiplied by the number of constraints. Some multiple constraint problems cannot be transformed to multiple constraint finite form problems.     

A Neural Network Application in Personnel Scheduling

In this paper, we present and evaluate a neural network model for solving a typical personnel-scheduling problem, i.e. an airport ground staff rostering problem. Personnel scheduling problems are widely found in servicing and manufacturing industries. The inherent complexity of personnel scheduling problems has normally resulted in the development of integer programming-based models and various heuristic solution procedures. The neural network approach has been admitted as a promising alternative to solving a variety of combinatorial optimization problems. While few works relate neural network to applications of personnel scheduling problems, there is great theoretical and practical value in exploring the potential of this area. In this paper, we introduce a neural network model following a relatively new modeling approach to solve a real rostering case. We show how to convert a mixed integer programming formulation to a neural network model. We also provide the experiment results comparing the neural network method with three popular heuristics, i.e. simulated annealing, Tabu search and genetic algorithm. The computational study reveals some potential of neural networks in solving personnel scheduling problems.     

Ship maintenance scheduling by genetic algorithm and constraint-based reasoning

Ship maintenance scheduling is a process to decide start times of maintenance activities that satisfy all precedence and resource constraints and optimize the ship availability. In this paper, ship maintenance scheduling is modelled as a constraint satisfaction problem (CSP). The variables of CSP are the start times and its domain values are the start and horizon of the schedule. To solve the ship maintenance scheduling problem in the Royal Malaysian Navy, we have adopted a constraint-based reasoning (CBR) which requires start times of the first activities of maintenance cycles to solve the problem by the CBR. Thus, we adopt a genetic algorithm (GA) to find the start times of the first activities. The simulation results showed the effectiveness of the present hybrid algorithm.