Routing and scheduling optimisation under uncertainty for engineering applications

The thesis aims to develop a viable computational approach suitable for solving large vehicle routing and scheduling optimisation problems affected by uncertainty. The modelling framework is built upon recent advances in Stochastic Optimisation, Robust Optimisation and Distributionally Robust Optimization. The utility of the methodology is presented on two classes of discrete optimisation problems: scheduling satellite communication, which is a variant of Machine Scheduling, and the Vehicle Routing Problem with Time Windows and Synchronised Visits. For each problem class, a practical engineering application is formulated using data coming from the real world. The significant size of the problem instances reinforced the need to apply a different computational approach for each problem class. Satellite communication is scheduled using a Mixed-Integer Programming solver. In contrast, the vehicle routing problem with synchronised visits is solved using a hybrid method that combines Iterated Local Search, Constraint Programming and the Guided Local Search metaheuristic. The featured application of scheduling satellite communication is the Satellite Quantum Key Distribution for a system that consists of one spacecraft placed in the Lower Earth Orbit and a network of optical ground stations located in the United Kingdom. The satellite generates cryptographic keys and transmits them to individual ground stations. Each ground station should receive the number of keys in proportion to the importance of the ground station in the network. As clouds containing water attenuate the signal, reliable scheduling needs to account for cloud cover predictions, which are naturally affected by uncertainty. A new uncertainty sets tailored for modelling uncertainty in predictions of atmospheric phenomena is the main contribution to the methodology. The uncertainty set models the evolution of uncertain parameters using a Multivariate Vector Auto-Regressive Time Series, which preserves correlations over time and space. The problem formulation employing the new uncertainty set compares favourably to a suite of alternative models adapted from the literature considering both the computational time and the cost-effectiveness of the schedule evaluated in the cloud cover conditions observed in the real world. The other contribution of the thesis in the satellite scheduling domain is the formulation of the Satellite Quantum Key Distribution problem. The proof of computational complexity and thorough performance analysis of an example Satellite Quantum Key Distribution system accompany the formulation. The Home Care Scheduling and Routing Problem, which instances are solved for the largest provider of such services in Scotland, is the application of the Vehicle Routing Problem with Time Windows and Synchronised Visits. The problem instances contain over 500 visits. Around 20% of them require two carers simultaneously. Such problem instances are well beyond the scalability limitations of the exact method and considerably larger than instances of similar problems considered in the literature. The optimisation approach proposed in the thesis found effective solutions in attractive computational time (i.e., less than 30 minutes) and the solutions reduced the total travel time threefold compared to alternative schedules computed by human planners. The Essential Riskiness Index Optimisation was incorporated into the Constraint Programming model to address uncertainty in visits' duration. Besides solving large problem instances from the real world, the solution method reproduced the majority of the best results reported in the literature and strictly improved the solutions for several instances of a well-known benchmark for the Vehicle Routing Problem with Time Windows and Synchronised Visits.The thesis aims to develop a viable computational approach suitable for solving large vehicle routing and scheduling optimisation problems affected by uncertainty. The modelling framework is built upon recent advances in Stochastic Optimisation, Robust Optimisation and Distributionally Robust Optimization. The utility of the methodology is presented on two classes of discrete optimisation problems: scheduling satellite communication, which is a variant of Machine Scheduling, and the Vehicle Routing Problem with Time Windows and Synchronised Visits. For each problem class, a practical engineering application is formulated using data coming from the real world. The significant size of the problem instances reinforced the need to apply a different computational approach for each problem class. Satellite communication is scheduled using a Mixed-Integer Programming solver. In contrast, the vehicle routing problem with synchronised visits is solved using a hybrid method that combines Iterated Local Search, Constraint Programming and the Guided Local Search metaheuristic. The featured application of scheduling satellite communication is the Satellite Quantum Key Distribution for a system that consists of one spacecraft placed in the Lower Earth Orbit and a network of optical ground stations located in the United Kingdom. The satellite generates cryptographic keys and transmits them to individual ground stations. Each ground station should receive the number of keys in proportion to the importance of the ground station in the network. As clouds containing water attenuate the signal, reliable scheduling needs to account for cloud cover predictions, which are naturally affected by uncertainty. A new uncertainty sets tailored for modelling uncertainty in predictions of atmospheric phenomena is the main contribution to the methodology. The uncertainty set models the evolution of uncertain parameters using a Multivariate Vector Auto-Regressive Time Series, which preserves correlations over time and space. The problem formulation employing the new uncertainty set compares favourably to a suite of alternative models adapted from the literature considering both the computational time and the cost-effectiveness of the schedule evaluated in the cloud cover conditions observed in the real world. The other contribution of the thesis in the satellite scheduling domain is the formulation of the Satellite Quantum Key Distribution problem. The proof of computational complexity and thorough performance analysis of an example Satellite Quantum Key Distribution system accompany the formulation. The Home Care Scheduling and Routing Problem, which instances are solved for the largest provider of such services in Scotland, is the application of the Vehicle Routing Problem with Time Windows and Synchronised Visits. The problem instances contain over 500 visits. Around 20% of them require two carers simultaneously. Such problem instances are well beyond the scalability limitations of the exact method and considerably larger than instances of similar problems considered in the literature. The optimisation approach proposed in the thesis found effective solutions in attractive computational time (i.e., less than 30 minutes) and the solutions reduced the total travel time threefold compared to alternative schedules computed by human planners. The Essential Riskiness Index Optimisation was incorporated into the Constraint Programming model to address uncertainty in visits' duration. Besides solving large problem instances from the real world, the solution method reproduced the majority of the best results reported in the literature and strictly improved the solutions for several instances of a well-known benchmark for the Vehicle Routing Problem with Time Windows and Synchronised Visits

Real-Life Optimum Shift Scheduling Design

In many industries, manpower shift scheduling poses problems that require immediate solutions. The fundamental need in this domain is to ensure that all shifts are assigned to cover all or as many jobs as possible. The shifts should additionally be planned with minimum manpower utilization, minimum manpower idleness and enhanced adaptability of employee schedules. The approach used in this study was to utilize an existing manpower prediction method to decide the minimum manpower required to complete all jobs. Based on the minimum manpower number and shift criteria, the shifts were assigned to form schedules using random pick and criteria-based selection methods. The potential schedules were then optimized and the best ones selected. Based on several realistic test instances, the proposed heuristic approach appears to offer promising solutions for shift scheduling as it improves shift idle time, complies with better shift starting time and significantly reduces the manpower needed and the time spent on creating schedules, regardless of data size

Nurse Rostering: A Tabu Search Technique With Embedded Nurse Preferences

The decision making in assigning all nursing staffs to shift duties in a hospital unit must be done appropriately because it is a crucial task due to various requirements and constraints that need to be fulfilled. The shift assignment or also known as roster has a great impact on the nurses’ operational circumstances which are strongly related to the intensity of quality of health care. The head nurse usually spends a substantial amount of time developing manual rosters, especially when there are many staff requests. Yet, sometimes she could not ensure that all constraints are met. Therefore, this research identified the relevant constraints being imposed in solving the nurse rostering problem (NRP) and examined the efficient method to generate the nurse roster based on constraints involved. Subsequently, as part of this research, we develop a Tabu Search (TS) model to solve a particular NRP. There are two aspects of enhancement in the proposed TS model. The first aspect is in the initialization phase of the TS model, where we introduced a semi-random initialization method to produce an initial solution. The advantage of using this initialization method is that it avoids the violation of hard constraints at any time in the TS process. The second aspect is in the neighbourhood generation phase, where several neighbours need to be generated as part of the TS approach. In this phase, we introduced two different neighbourhood generation methods, which are specific to the NRP. The proposed TS model is evaluated for its efficiency, where 30 samples of rosters generated were taken for analysis. The feasible solutions (i.e. the roster) were evaluated based on their minimum penalty values. The penalty values were given based on different violations of hard and soft constraints. The TS model is able to produce efficient rosters which do not violate any hard constraints and at the same time, fulfill the soft constraints as much as possible. The performance of the model is certainly better than the manually generated model and also comparable to the existing similar nurse rostering model

An Algorithmic approach to shift structure optimization

Workforce scheduling in organizations often consists of three major phases: workload prediction, shift generation, and staff rostering. Workload prediction involves using historical behaviour of e.g. customers to predict future demand for work. Shift generation is the process of transforming the determined workload into shifts as accurately as possible. In staff rostering, the generated shifts are assigned to employees. In general the problem and even its subproblems are NP-hard, which makes them highly challenging for organizations to solve. Heuristic optimization methods can be used to solve practical instances within reasonable running times, which in turn can result in e.g. improved revenue, improved service, or more satisfied employees for the organizations. This thesis presents some specific subproblems along with practical solution methods--- Työvoiman aikataulutusprosessi koostuu kolmesta päävaiheesta: työtarpeen ennustaminen, työvuorojen muodostus ja työvuorojen miehitys. Tulevaa työtarvetta ennustetaan pääasiassa menneisyyden asiakaskäytöksen perusteella käyttäen esimerkiksi tilastollisia malleja tai koneoppimiseen perustuvia menetelmiä. Työvuorojen muodostuksessa tehdään työvuororakenne, joka noudattaa ennustettua ja ennalta tiedettyä työtarvetta mahdollisimman tarkasti. Työvuorojen miehityksessä määritetään työvuoroille tekijät. Jokainen vaihe itsessään on haasteellinen ratkaistava. Erityisesti työvuorojen miehitys on yleensä NP-kova ongelma. On kuitenkin mahdollista tuottaa käytännöllisiä ratkaisuja järkevässä ajassa käyttäen heuristisia optimointimenetelmiä. Näin on saavutettavissa mitattavia hyötyjä mm. tuottoon, asiakkaiden palvelutasoon sekä työntekijöiden työtyyväisyyteen. Tässä väitöskirjassa esitellään eräitä työvoiman aikataulutuksen aliongelmia sekä niihin sopivia ratkaisumenetelmiä

Effective integrations of constraint programming, integer programming and local search for two combinatorial optimisation problems

This thesis focuses on the construction of effective and efficient hybrid methods based on the integrations of Constraint Programming (CP), Integer Programming (IP) and local search (LS) to tackle two combinatorial optimisation problems from different application areas: the nurse rostering problems and the portfolio selection problems. The principle of designing hybrid methods in this thesis can be described as: for the combinatorial problems to be solved, the properties of the problems are investigated firstly and the problems are decomposed accordingly in certain ways; then the suitable solution techniques are integrated to solve the problem based on the properties of substructures/subproblems by taking the advantage of each technique. For the over-constrained nurse rostering problems with a large set of complex constraints, the problems are first decomposed by constraint. That is, only certain selected set of constraints is considered to generate feasible solutions at the first stage. Then the rest of constraints are tackled by a second stage local search method. Therefore, the hybrid methods based on this constraint decomposition can be represented by a two-stage framework “feasible solution + improvement”. Two integration methods are proposed and investigated under this framework. In the first integration method, namely a hybrid CP with Variable Neighourhood Search (VNS) approach, the generation of feasible initial solutions relies on the CP while the improvement of initial solutions is gained by a simple VNS in the second stage. In the second integration method, namely a constraint-directed local search, the local search is enhanced by using the information of constraints. The experimental results demonstrate the effectiveness of these hybrid approaches. Based on another decomposition method, Dantzig-Wolfe decomposition, in the third integration method, a CP based column generation, integrates the feasibility reasoning of CP with the relaxation and optimality reasoning of Linear Programming. The experimental results demonstrate the effectiveness of the methods as well as the knowledge of the quality of the solution. For the portfolio selection problems, two integration methods, which integrate Branch-and-Bound algorithm with heuristic search, are proposed and investigated. In layered Branch-and-Bound algorithm, the problem is decomposed into the subsets of variables which are considered at certain layers in the search tree according to their different features. Node selection heuristics, and branching rules, etc. are tailored to the individual layers, which speed up the search to the optimal solution in a given time limit. In local search branching Branch-and-Bound algorithm, the idea of local search is applied as the branching rule of Branch-and-Bound. The local search branching is applied to generate a sequence of subproblems. The procedure for solving these subproblems is accelerated by means of the solution information reusing. This close integration between local search and Branch-and-Bound improves the efficiency of the Branch-and-Bound algorithm according to the experimental results. The hybrid approaches benefit from each component which is selected according to the properties of the decomposed problems. The effectiveness and efficiency of all the hybrid approaches to the two application problems developed in this thesis are demonstrated. The idea of designing appropriate components in hybrid approach concerning properties of subproblems is a promising methodology with extensive potential applications in other real-world combinatorial optimisation problems

Resource constrained routing and scheduling: Review and research prospects

In the service industry, it is crucial to efficiently allocate scarce resources to perform tasks and meet particular service requirements. What considerably complicates matters is when these resources, for example skilled technicians, nurses, and home carers have to visit different customer locations. This paper provides a comprehensive survey on resource constrained routing and scheduling that unveils the problem characteristics with respect to resource qualifications, service requirements and problem objectives. It also identifies the most effective exact and heuristic algorithms for this class of problems. The paper closes with several research prospects

Applications of Mathematical Programming in Personnel Scheduling

In the few decades of its existence, mathematical programming has evolved into an important branch of operations research and management science. This thesis consists of four papers in which we apply mathematical programming to real-life personnel scheduling and project management problems. We develop exact mathematical programming formulations. Furthermore, we propose effective heuristic strategies to decompose the original problems into subproblems that can be solved effciently with tailored mathematical programming formulations. We opt for solution methods that are based on mathematical programming, because their advantages in practice are a) the exibility to easily accommodate changes in the problem setting, b) the possibility to evaluate the quality of the solutions obtained, and c) the possibility to use general-purpose solvers, which are often the only software available in practice

Effective integrations of constraint programming, integer programming and local search for two combinatorial optimisation problems

This thesis focuses on the construction of effective and efficient hybrid methods based on the integrations of Constraint Programming (CP), Integer Programming (IP) and local search (LS) to tackle two combinatorial optimisation problems from different application areas: the nurse rostering problems and the portfolio selection problems. The principle of designing hybrid methods in this thesis can be described as: for the combinatorial problems to be solved, the properties of the problems are investigated firstly and the problems are decomposed accordingly in certain ways; then the suitable solution techniques are integrated to solve the problem based on the properties of substructures/subproblems by taking the advantage of each technique. For the over-constrained nurse rostering problems with a large set of complex constraints, the problems are first decomposed by constraint. That is, only certain selected set of constraints is considered to generate feasible solutions at the first stage. Then the rest of constraints are tackled by a second stage local search method. Therefore, the hybrid methods based on this constraint decomposition can be represented by a two-stage framework “feasible solution + improvement”. Two integration methods are proposed and investigated under this framework. In the first integration method, namely a hybrid CP with Variable Neighourhood Search (VNS) approach, the generation of feasible initial solutions relies on the CP while the improvement of initial solutions is gained by a simple VNS in the second stage. In the second integration method, namely a constraint-directed local search, the local search is enhanced by using the information of constraints. The experimental results demonstrate the effectiveness of these hybrid approaches. Based on another decomposition method, Dantzig-Wolfe decomposition, in the third integration method, a CP based column generation, integrates the feasibility reasoning of CP with the relaxation and optimality reasoning of Linear Programming. The experimental results demonstrate the effectiveness of the methods as well as the knowledge of the quality of the solution. For the portfolio selection problems, two integration methods, which integrate Branch-and-Bound algorithm with heuristic search, are proposed and investigated. In layered Branch-and-Bound algorithm, the problem is decomposed into the subsets of variables which are considered at certain layers in the search tree according to their different features. Node selection heuristics, and branching rules, etc. are tailored to the individual layers, which speed up the search to the optimal solution in a given time limit. In local search branching Branch-and-Bound algorithm, the idea of local search is applied as the branching rule of Branch-and-Bound. The local search branching is applied to generate a sequence of subproblems. The procedure for solving these subproblems is accelerated by means of the solution information reusing. This close integration between local search and Branch-and-Bound improves the efficiency of the Branch-and-Bound algorithm according to the experimental results. The hybrid approaches benefit from each component which is selected according to the properties of the decomposed problems. The effectiveness and efficiency of all the hybrid approaches to the two application problems developed in this thesis are demonstrated. The idea of designing appropriate components in hybrid approach concerning properties of subproblems is a promising methodology with extensive potential applications in other real-world combinatorial optimisation problems