'A Bayesian Optimisation Algorithm for the Nurse Scheduling Problem'

Abstract- A Bayesian optimization algorithm for the nurse scheduling problem is presented, which involves choosing a suitable scheduling rule from a set for each nurse's assignment. Unlike our previous work that used GAs to implement implicit learning, the learning in the proposed algorithm is explicit, i.e. eventually, we will be able to identify and mix building blocks directly. The Bayesian optimization algorithm is applied to implement such explicit learning by building a Bayesian network of the joint distribution of solutions. The conditional probability of each variable in the network is computed according to an initial set of promising solutions. Subsequently, each new instance for each variable is generated by using the corresponding conditional probabilities, until all variables have been generated, i.e. in our case, a new rule string has been obtained. Another set of rule strings will be generated in this way, some of which will replace previous strings based on fitness selection. If stopping conditions are not met, the conditional probabilities for all nodes in the Bayesian network are updated again using the current set of promising rule strings. Computational results from 52 real data instances demonstrate the success of this approach. It is also suggested that the learning mechanism in the proposed approach might be suitable for other scheduling problems.

A Hybrid Genetic Algorithm to Solve a Logt-Sizing and Scheduling Problem

Abstract: This paper reports a lot-sizing and scheduling problem, which minimizes inventory and backlog costs on m parallel machines with sequence-dependent set-up times over t periods. Problem solutions are represented as product subsets ordered and/or unordered for each machine m at each period t. The optimal lot sizes are determined applying a linear program. A genetic algorithm searches either over ordered or over unordered subsets (which are implicitly ordered using a fast ATSP-type heuristic) to identify an overall optimal solution. Initial computational results are presented, comparing the speed and solution quality of the ordered and unordered genetic algorithm approaches.

'A Bayesian Optimisation Algorithm for the Nurse Scheduling Problem'

Abstract- A Bayesian optimization algorithm for the nurse scheduling problem is presented, which involves choosing a suitable scheduling rule from a set for each nurse's assignment. Unlike our previous work that used GAs to implement implicit learning, the learning in the proposed algorithm is explicit, i.e. eventually, we will be able to identify and mix building blocks directly. The Bayesian optimization algorithm is applied to implement such explicit learning by building a Bayesian network of the joint distribution of solutions. The conditional probability of each variable in the network is computed according to an initial set of promising solutions. Subsequently, each new instance for each variable is generated by using the corresponding conditional probabilities, until all variables have been generated, i.e. in our case, a new rule string has been obtained. Another set of rule strings will be generated in this way, some of which will replace previous strings based on fitness selection. If stopping conditions are not met, the conditional probabilities for all nodes in the Bayesian network are updated again using the current set of promising rule strings. Computational results from 52 real data instances demonstrate the success of this approach. It is also suggested that the learning mechanism in the proposed approach might be suitable for other scheduling problems.

An Indirect Genetic Algorithm for a Nurse Scheduling Problem

This paper describes a Genetic Algorithms approach to a manpower-scheduling problem arising at a major UK hospital. Although Genetic Algorithms have been successfully used for similar problems in the past, they always had to overcome the limitations of the classical Genetic Algorithms paradigm in handling the conflict between objectives and constraints. The approach taken here is to use an indirect coding based on permutations of the nurses, and a heuristic decoder that builds schedules from these permutations. Computational experiments based on 52 weeks of live data are used to evaluate three different decoders with varying levels of intelligence, and four well-known crossover operators. Results are further enhanced by introducing a hybrid crossover operator and by making use of simple bounds to reduce the size of the solution space. The results reveal that the proposed algorithm is able to find high quality solutions and is both faster and more flexible than a recently published Tabu Search approach.

A Bayesian optimization algorithm for the nurse scheduling problem

A Bayesian optimization algorithm for the nurse scheduling problem is presented, which involves choosing a suitable scheduling rule from a set for each nurse’s assignment. Unlike our previous work that used GAs to implement implicit learning, the learning in the proposed algorithm is explicit, i.e. eventually, we will be able to identify and mix building blocks directly. The Bayesian optimization algorithm is applied to implement such explicit learning by building a Bayesian network of the joint distribution of solutions. The conditional probability of each variable in the network is computed according to an initial set of promising solutions. Subsequently, each new instance for each variable is generated by using the corresponding conditional probabilities, until all variables have been generated, i.e. in our case, a new rule string has been obtained. Another set of rule strings will be generated in this way, some of which will replace previous strings based on fitness selection. If stopping conditions are not met, the conditional probabilities for all nodes in the Bayesian network are updated again using the current set of promising rule strings. Computational results from 52 real data instances demonstrate the success of this approach. It is also suggested that the learning mechanism in the proposed approach might be suitable for other scheduling problems.

Aging based maintenance and reinvestment scheduling of electric distribution

The maintenance of electric distribution network is a topical question for distribution system operators because of increasing significance of failure costs. In this dissertation the maintenance practices of the distribution system operators are analyzed and a theory for scheduling maintenance activities and reinvestment of distribution components is created. The scheduling is based on the deterioration of components and the increasing failure rates due to aging. The dynamic programming algorithm is used as a solving method to maintenance problem which is caused by the increasing failure rates of the network. The other impacts of network maintenance like environmental and regulation reasons are not included to the scope of this thesis. Further the tree trimming of the corridors and the major disturbance of the network are not included to the problem optimized in this thesis. For optimizing, four dynamic programming models are presented and the models are tested. Programming is made in VBA-language to the computer. For testing two different kinds of test networks are used. Because electric distribution system operators want to operate with bigger component groups, optimal timing for component groups is also analyzed. A maintenance software package is created to apply the presented theories in practice. An overview of the program is presented.

Scheduling of track inspection and maintenance activities in railroad networks

The U.S. railroad companies spend billions of dollars every year on railroad track maintenance in order to ensure safety and operational efficiency of their railroad networks. Besides maintenance costs, other costs such as train accident costs, train and shipment delay costs and rolling stock maintenance costs are also closely related to track maintenance activities. Optimizing the track maintenance process on the extensive railroad networks is a very complex problem with major cost implications. Currently, the decision making process for track maintenance planning is largely manual and primarily relies on the knowledge and judgment of experts. There is considerable potential to improve the process by using operations research techniques to develop solutions to the optimization problems on track maintenance. In this dissertation study, we propose a range of mathematical models and solution algorithms for three network-level scheduling problems on track maintenance: track inspection scheduling problem (TISP), production team scheduling problem (PTSP) and job-to-project clustering problem (JTPCP). TISP involves a set of inspection teams which travel over the railroad network to identify track defects. It is a large-scale routing and scheduling problem where thousands of tasks are to be scheduled subject to many difficult side constraints such as periodicity constraints and discrete working time constraints. A vehicle routing problem formulation was proposed for TISP, and a customized heuristic algorithm was developed to solve the model. The algorithm iteratively applies a constructive heuristic and a local search algorithm in an incremental scheduling horizon framework. The proposed model and algorithm have been adopted by a Class I railroad in its decision making process. Real-world case studies show the proposed approach outperforms the manual approach in short-term scheduling and can be used to conduct long-term what-if analyses to yield managerial insights. PTSP schedules capital track maintenance projects, which are the largest track maintenance activities and account for the majority of railroad capital spending. A time-space network model was proposed to formulate PTSP. More than ten types of side constraints were considered in the model, including very complex constraints such as mutual exclusion constraints and consecution constraints. A multiple neighborhood search algorithm, including a decomposition and restriction search and a block-interchange search, was developed to solve the model. Various performance enhancement techniques, such as data reduction, augmented cost function and subproblem prioritization, were developed to improve the algorithm. The proposed approach has been adopted by a Class I railroad for two years. Our numerical results show the model solutions are able to satisfy all hard constraints and most soft constraints. Compared with the existing manual procedure, the proposed approach is able to bring significant cost savings and operational efficiency improvement. JTPCP is an intermediate problem between TISP and PTSP. It focuses on clustering thousands of capital track maintenance jobs (based on the defects identified in track inspection) into projects so that the projects can be scheduled in PTSP. A vehicle routing problem based model and a multiple-step heuristic algorithm were developed to solve this problem. Various side constraints such as mutual exclusion constraints and rounding constraints were considered. The proposed approach has been applied in practice and has shown good performance in both solution quality and efficiency.

Multi-criteria short-term maintenance outage scheduling in smart distribution systems

Effective legislation and standards for the coordination procedures between consumers, producers and the system operator supports the advances in the technologies that lead to smart distribution systems. In short-term (ST) maintenance scheduling procedure, the energy producers in a distribution system access to the long-term (LT) outage plan that is released by the distribution system operator (DSO). The impact of this additional information on the decision-making procedure of producers in ST maintenance scheduling is studied in this paper. The final ST maintenance plan requires the approval of the DSO that has the responsibility to secure the network reliability and quality, and other players have to follow the finalized schedule. Maintenance scheduling in the producers’ layer and the coordination procedure between them and the DSO is modelled in this paper. The proposed method is applied to a 33-bus distribution system.

Coordination between mid-term maintenance outage decisions and short-term security-constrained scheduling in smart distribution systems

Distribution systems are the first volunteers experiencing the benefits of smart grids. The smart grid concept impacts the internal legislation and standards in grid-connected and isolated distribution systems. Demand side management, the main feature of smart grids, acquires clear meaning in low voltage distribution systems. In these networks, various coordination procedures are required between domestic, commercial and industrial consumers, producers and the system operator. Obviously, the technical basis for bidirectional communication is the prerequisite of developing such a coordination procedure. The main coordination is required when the operator tries to dispatch the producers according to their own preferences without neglecting its inherent responsibility. Maintenance decisions are first determined by generating companies, and then the operator has to check and probably modify them for final approval. In this paper the generation scheduling from the viewpoint of a distribution system operator (DSO) is formulated. The traditional task of the DSO is securing network reliability and quality. The effectiveness of the proposed method is assessed by applying it to a 6-bus and 9-bus distribution system.

Optimal scheduling of aircrafts’ engines repair process

We address a real world scheduling problem concerning the repair process of aircrafts’ engines by TAP - Maintenance & Engineering (TAP-ME). TAP-ME is the maintenance, repair and overhaul organization of TAP Portugal, Portugal’s leading airline, which employs about 4000 persons to provide maintenance and engineering services in aircraft, engines and components. TAP-ME is aiming to optimize its maintenance services, focusing on the reduction of the engines repair turnaround time.

Scheduling aircraft’s engines repair process: a mathematical model

In this talk, we discuss a scheduling problem that originated at TAP - Maintenance & Engineering - the maintenance, repair and overhaul organization of Portugal’s leading airline. In the repair process of aircrafts’ engines, the operations to be scheduled may be executed on a certain workstation by any processor of a given set, and the objective is to minimize the total weighted tardiness. A mixed integer linear programming formulation, based on the flexible job shop scheduling, is presented here, along with computational experiment on a real instance, provided by TAP-ME, from a regular working week. The model was also tested using benchmarking instances available in literature.

Scheduling the repair of aircraft components - a case study

In aircraft components maintenance shops, components are distributed amongst repair groups and their respective technicians based on the type of repair, on the technicians skills and workload, and on the customer required dates. This distribution planning is typically done in an empirical manner based on the group leader’s past experience. Such a procedure does not provide any performance guarantees, leading frequently to undesirable delays on the delivery of the aircraft components. Among others, a fundamental challenge faced by the group leaders is to decide how to distribute the components that arrive without customer required dates. This paper addresses the problems of prioritizing the randomly arriving of aircraft components (with or without pre-assigned customer required dates) and of optimally distributing them amongst the technicians of the repair groups. We proposed a formula for prioritizing the list of repairs, pointing out the importance of selecting good estimators for the interarrival times between repair requests, the turn-around-times and the man hours for repair. In addition, a model for the assignment and scheduling problem is designed and a preliminary algorithm along with a numerical illustration is presented.

A Constructive Genetic Algorithm for permutation flowshop scheduling

The general flowshop scheduling problem is a production problem where a set of n jobs have to be processed with identical flow pattern on in machines. In permutation flowshops the sequence of jobs is the same on all machines. A significant research effort has been devoted for sequencing jobs in a flowshop minimizing the makespan. This paper describes the application of a Constructive Genetic Algorithm (CGA) to makespan minimization on flowshop scheduling. The CGA was proposed recently as an alternative to traditional GA approaches, particularly, for evaluating schemata directly. The population initially formed only by schemata, evolves controlled by recombination to a population of well-adapted structures (schemata instantiation). The CGA implemented is based on the NEH classic heuristic and a local search heuristic used to define the fitness functions. The parameters of the CGA are calibrated using a Design of Experiments (DOE) approach. The computational results are compared against some other successful algorithms from the literature on Taillard`s well-known standard benchmark. The computational experience shows that this innovative CGA approach provides competitive results for flowshop scheduling; problems. (C) 2007 Elsevier Ltd. All rights reserved.

Scheduling in a two-machine flowshop for the minimization of the mean absolute deviation from a common due date

This paper addresses the minimization of the mean absolute deviation from a common due date in a two-machine flowshop scheduling problem. We present heuristics that use an algorithm, based on proposed properties, which obtains an optimal schedule fora given job sequence. A new set of benchmark problems is presented with the purpose of evaluating the heuristics. Computational experiments show that the developed heuristics outperform results found in the literature for problems up to 500 jobs. (C) 2007 Elsevier Ltd. All rights reserved.

Short-term wind forecasting for energy resources scheduling

This paper proposes a wind power forecasting methodology based on two methods: direct wind power forecasting and wind speed forecasting in the first phase followed by wind power forecasting using turbines characteristics and the aforementioned wind speed forecast. The proposed forecasting methodology aims to support the operation in the scope of the intraday resources scheduling model, namely with a time horizon of 5 minutes. This intraday model supports distribution network operators in the short-term scheduling problem, in the smart grid context. A case study using a real database of 12 months recorded from a Portuguese wind power farm was used. The results show that the straightforward methodology can be applied in the intraday model with high wind speed and wind power accuracy. The wind power forecast direct method shows better performance than wind power forecast using turbine characteristics and wind speed forecast obtained in first phase.