Decentralized task allocation for dynamic, time-sensitive tasks

Thesis: S.M., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2018.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (pages 103-110).In time-sensitive and dynamic missions, autonomous vehicles must respond quickly to new information and objectives. In the case of dynamic task allocation, a team of agents are presented with a new, unknown task that must be allocated with their original allocations. This is exacerbated further in decentralized settings where agents are limited to utilizing local information during the allocation process. This thesis presents a fully decentralized, dynamic task allocation algorithm that extends the Consensus-Based Bundle Algorithm (CBBA) to allow for allocating new tasks. Whereas static CBBA requires a full resetting of previous allocations, CBBA with Partial Replanning (CBBA-PR) enables the agents to only partially reset their allocations to efficiently and quickly allocate a new task. By varying the number of existing tasks that are reset during replan, the team can trade-off convergence speed with amount of coordination. By specifically choosing the lowest bid tasks for resetting, CBBA-PR is shown to converge linearly with the number of tasks reset and the network diameter of the team. In addition, limited replanning methods are presented for scenarios without sufficient replanning time. These include a single reset bidding procedure for agents at capacity, a no-replanning heuristic that can identify scenarios that does not require replanning, and a subteam formation algorithm for reducing the network diameter. Finally, this thesis describes hardware and simulation experiments used to explore the effects of ad-hoc, decentralized communication on consensus algorithms and to validate the performance of CBBA-PR.by Noam Buckman.S.M

Scheduled service network design for integrated planning of rail freight transportation

Cette thèse étudie une approche intégrant la gestion de l’horaire et la conception de réseaux de services pour le transport ferroviaire de marchandises. Le transport par rail s’articule autour d’une structure à deux niveaux de consolidation où l’affectation des wagons aux blocs ainsi que des blocs aux services représentent des décisions qui complexifient grandement la gestion des opérations. Dans cette thèse, les deux processus de consolidation ainsi que l’horaire d’exploitation sont étudiés simultanément. La résolution de ce problème permet d’identifier un plan d’exploitation rentable comprenant les politiques de blocage, le routage et l’horaire des trains, de même que l’habillage ainsi que l’affectation du traffic. Afin de décrire les différentes activités ferroviaires au niveau tactique, nous étendons le réseau physique et construisons une structure de réseau espace-temps comprenant trois couches dans lequel la dimension liée au temps prend en considération les impacts temporels sur les opérations. De plus, les opérations relatives aux trains, blocs et wagons sont décrites par différentes couches. Sur la base de cette structure de réseau, nous modélisons ce problème de planification ferroviaire comme un problème de conception de réseaux de services. Le modèle proposé se formule comme un programme mathématique en variables mixtes. Ce dernie r s’avère très difficile à résoudre en raison de la grande taille des instances traitées et de sa complexité intrinsèque. Trois versions sont étudiées : le modèle simplifié (comprenant des services directs uniquement), le modèle complet (comprenant des services directs et multi-arrêts), ainsi qu’un modèle complet à très grande échelle. Plusieurs heuristiques sont développées afin d’obtenir de bonnes solutions en des temps de calcul raisonnables. Premièrement, un cas particulier avec services directs est analysé. En considérant une cara ctéristique spécifique du problème de conception de réseaux de services directs nous développons un nouvel algorithme de recherche avec tabous. Un voisinage par cycles est privilégié à cet effet. Celui-ci est basé sur la distribution du flot circulant sur les blocs selon les cycles issus du réseau résiduel. Un algorithme basé sur l’ajustement de pente est développé pour le modèle complet, et nous proposons une nouvelle méthode, appelée recherche ellipsoidale, permettant d’améliorer davantage la qualité de la solution. La recherche ellipsoidale combine les bonnes solutions admissibles générées par l’algorithme d’ajustement de pente, et regroupe les caractéristiques des bonnes solutions afin de créer un problème élite qui est résolu de facon exacte à l’aide d’un logiciel commercial. L’heuristique tire donc avantage de la vitesse de convergence de l’algorithme d’ajustement de pente et de la qualité de solution de la recherche ellipsoidale. Les tests numériques illustrent l’efficacité de l’heuristique proposée. En outre, l’algorithme représente une alternative intéressante afin de résoudre le problème simplifié. Enfin, nous étudions le modèle complet à très grande échelle. Une heuristique hybride est développée en intégrant les idées de l’algorithme précédemment décrit et la génération de colonnes. Nous proposons une nouvelle procédure d’ajustement de pente où, par rapport à l’ancienne, seule l’approximation des couts liés aux services est considérée. La nouvelle approche d’ajustement de pente sépare ainsi les décisions associées aux blocs et aux services afin de fournir une décomposition naturelle du problème. Les résultats numériques obtenus montrent que l’algorithme est en mesure d’identifier des solutions de qualité dans un contexte visant la résolution d’instances réelles.This thesis studies a scheduled service network design problem for rail freight transportation planning. Rails follow a special two level consolidation organization, and the car-to-block, block-to-service handling procedure complicates daily operations. In this research, the two consolidation processes as well as the operation schedule are considered simultaneously, and by solving this problem, we provide an overall cost-effective operating plan, including blocking policy, train routing, scheduling, make-up policy and traffic distribution. In order to describe various rail operations at the tactical level, we extend the physical network and construct a 3-layer time-space structure, in which the time dimension takes into consideration the temporal impacts on operations. Furthermore, operations on trains, blocks, and cars are described in different layers. Based on this network structure, we model the rail planning problem to a service network design formulation. The proposed model relies on a complex mixed-integer programming formulation. The problem is very hard to solve due to the computational difficulty as well as the tremendous size of the application instances. Three versions of the problem are studied, which are the simplified model (with only non-stop services), complete model (with both non-stop and multi-stop services) and very-large-scale complete model. Heuristic algorithms are developed to provide good feasible solutions in reasonable computing efforts. A special case with non-stop services is first studied. According to a specific characteristic of the direct service network design problem, we develop a tabu search algorithm. The tabu search moves in a cycle-based neighborhood, where flows on blocks are re-distributed according to the cycles in a conceptual residual network. A slope scaling based algorithm is developed for the complete model, and we propose a new method, called ellipsoidal search, to further improve the solution quality. Ellipsoidal search combines the good feasible solutions generated from the slope scaling, and collects the features of good solutions into an elite problem, and solves it with exact solvers. The algorithm thus takes advantage of the convergence speed of slope scaling and solution quality of ellipsoidal search, and is proven effective. The algorithm also presents an alternative for solving the simplified problem. Finally, we work on the very-large-size complete model. A hybrid heuristic is developed by integrating the ideas of previous research with column generation. We propose a new slope scaling scheme where, compared with the previous scheme, only approximate service costs instead of both service and block costs are considered. The new slope scaling scheme thus separates the block decisions and service decisions, and provide a natural decomposition of the problem. Experiments show the algorithm is good to solve real-life size instances

Resource Allocation Models in Healthcare Decision Making

We present models for allocating limited healthcare resources efficiently among target populations in order to maximize society's welfare and/or minimize the expected costs. In general, this thesis is composed of two major parts. Firstly, we formulate a novel uncapacitated fixed-charge location problem which considers the preferences of customers and the reliability of facilities simultaneously. A central planner selects facility locations from a set of candidate sites to minimize the total cost of opening facilities and providing service. Each customer has a strict preference order over a subset of the candidate sites, and uses her most preferred available facility. If that facility fails due to a disruptive event, the customer attends her next preferred available facility. This model bridges the gap between the location models that consider the preferences of customers and the ones that consider the reliability of facilities. It applies to many healthcare settings, such as preventive care clinics, senior centers, and disaster response centers. In such situations, patient (or customer) preferences vary significantly. Therefore, there could be a large number of subgroups within the population depending on their preferences of potential facility sites. In practice, solving problems with large numbers of population subgroups is very important to increase granularity when considering diverse preferences of several different customer types. We develop a Lagrangian branch-and-bound algorithm and a branch-and-cut algorithm. We also propose valid inequalities to tighten the LP relaxation of the model. Our numerical experiments show that the proposed solution algorithms are efficient, and can be applied to problems with extremely large numbers of customers. Secondly, we study the allocation of colorectal cancer (CRC) screening resources among individuals in a population. CRC can be early-detected, and even prevented, by undergoing periodic cancer screenings via colonoscopy. Current guidelines are based on existing medical evidence, and do not explicitly consider (i) all possible alternative screening policies, and (ii) the effect of limited capacity of colonoscopy screening on the economic feasibility of the screening program. We consider the problem of allocating limited colonoscopy capacity for CRC screening and surveillance to a population composed of patients of different risk groups based on risk factors including age, CRC history, etc. We develop a mixed integer program that maximizes the quality-adjusted life years for a given patient population considering the population's demographics, CRC progression dynamics, and relevant constraints on the system capacity and the screening program effectiveness. We show that the current guidelines are not always optimal. In general, when screening capacity is high, the optimal screening programs recommend higher screening rates than the current guidelines, and the optimal screening policies change with age and gender. This shows the significance of incorporating screening capacity into the decisions of optimal screening policies

Combinatorial exchange models for a user-driven air traffic flow management in Europe

2008/2009Air Traffic Flow Management (ATFM) is the service responsible to guarantee that the available capacity of the air transportation system is efficiently used and never exceeded. It guarantees safety of air transportation by adopting a series of measures which range from strategic long-term ones to the imposition of ground delays to flights at a tactical level. These ATFM delays are imposed to individual flights at the departure airport prior to their take-off, since it is safer and less costly to anticipate on the ground any delay predicted somewhere in the system. They are assigned by a central authority according to a First-Planned-First-Served principle, without taking into account individual Airlines' preferences. This criteria of assignment can cause an aggregated cost of delay experienced by users, higher than the minimal one, due to the fact that the cost of delay is a non-linear function of the duration and it depends on many variables such as the type of aircraft, the specific origin-destination pair, ecc. This thesis tackles the issue of formalizing and analyzing alternative models for the assignment of ATFM resources which take into account individual airlines preferences. In particular mathematical programming models are analyzed, that extend the concept of ATFM slot currently adopted to the one of Target Window, as proposed in the CATS European project. Such a concept is in line with the SESAR program, recently adopted in Europe to develop the new generation system of Air Traffic Management, which imposes a direct involvement of Airspace users whenever external constraints need to be enforced that modify their original requests. The first Chapter provides a general introduction to the context of Air Traffic Management and Air Traffic Control. In the second Chapter the principles, methods and performances of the ATFM system are described according to the current situation as well as to the SESAR target concept. The problem of optimally assign ATFM resources is then described mathematically and then analyzed to uncover two fundamental structures that determine its tractability: one corresponds to the case in which there is a unique capacity constrained resource while in the second there is an unrestricted number of constrained resources. In Chapter three a number of properties are proved that give insight into the applicability of different mechanisms for a central calculation of the optimal solution by the ATFM authority. Since such mechanisms involve cost minimization for several agents they are formulated as exchanges, i.e. particular types of auctions in which each participant may buy and/or sell several indivisible goods. The last part of the thesis included in Chapter four deals with the design of iterative exchange mechanisms, whose application in real world presents several advantages with respect to centralized models, from the distribution of computational complexity among participants to the preservation of disclosure of private information by Aircraft Operators. In this case an optimal model based on the Lagrangian relaxation of the separable central problem is first formulated and analyzed. To overcome practical issues possibly deriving from its application in real operations, an heuristic iterative Market-based mechanism is finally formalized. This algorithm exploits some of the underlying characteristics specific to the problem to derive near-optimal solutions in an acceptable time. Computational results are obtained by simulating its implementation on real traffic data and they show that considerable cost savings are possible with respect to a First-Planned-First-Served central allocation. The contribute of this thesis is twofold. The first is to provide a mathematical description, modeling and analysis of the ATFM resource exchange problem faced by Airspace users when network capacity needs to be rationed among them. The second consists in the methodological innovation represented by the formulation of the Market Mechanism which is compliant with several requirements represented by legislative and practical constraints and whose simulation provided encouraging results.XXII Cicl

Optimization based methods for solving some problems in telecommunications and the internet

The purpose of this thesis is to develop some new algorithms based on optimization techniques for solving some problems in some areas of telecommunications and the Internet. There are two main parts to this thesis. In the first part we discuss optimization based stochastic and queueing models in telecommunications network corrective maintenance. In the second part we develop optimization based clustering (OBC) algorithms for network evolution and multicast routing. The most typical scenario encountered during mathematical optimization modelling in telecommunications, for example, is to minimize the cost of establishment and maintenance of the networks subject to the performance constraints of the networks and the reliability constraints of the networks as well. Most of these optimization problems are global optimization, that is, they have many local minima and most of these local minima do not provide any useful information for solving these problems. Therefore, the development of effective methods for solving such global optimization problems is important. To run the telecommunications networks with cost-effective network maintenance,we need to establish a practical maintenance model and optimize it. In the first part of the thesis, we solve a known stochastic programming maintenance optimization model with a direct method and then develop some new models. After that we introduce queue programming models in telecommunications network maintenance optimization. The ideas of profit, loss, and penalty will help telecommunications companies have a good view of their maintenance policies and help them improve their service. In the second part of this thesis we propose the use of optimization based clustering (OBC) algorithms to determine level-constrained hierarchical trees for network evolution and multicast routing. This problem is formulated as an optimization problem with a non-smooth, non-convex objective function. Different algorithms are examined for solving this problem. Results of numerical experiments using some artifiicial and real-world databases are reported.Doctor of Philosoph

Auction algorithms for generalized nonlinear network flow problems

Thesis (Ph.D.)--Boston UniversityNetwork flow is an area of optimization theory concerned with optimization over networks with a range of applicability in fields such as computer networks, manufacturing, finance, scheduling and routing, telecommunications, and transportation. In both linear and nonlinear networks, a family of primal-dual algorithms based on "approximate" Complementary Slackness (ε-CS) is among the fastest in centralized and distributed environments. These include the auction algorithm for the linear assignment/transportation problems, ε-relaxation and Auction/Sequential Shortest Path (ASSP) for the min-cost flow and max-flow problems. Within this family, the auction algorithm is particularly fast, as it uses "second best" information, as compared to using the more generic ε-relaxation for linear assignment/transportation. Inspired by the success of auction algorithms, we extend them to two important classes of nonlinear network flow problems. We start with the nonlinear Resource Allocation Problem (RAP). This problem consists of optimally assigning N divisible resources to M competing missions/tasks each with its own utility function. This simple yet powerful framework has found applications in diverse fields such as finance, economics, logistics, sensor and wireless networks. RAP is an instance of generalized network (networks with arc gains) flow problem but it has significant special structure analogous to the assignment/transportation problem. We develop a class of auction algorithms for RAP: a finite-time auction algorithm for both synchronous and asynchronous environments followed by a combination of forward and reverse auction with ε-scaling to achieve pseudo polynomial complexity for any non-increasing generalized convex utilities including non-continuous and/ or non-differentiable functions. These techniques are then generalized to handle shipping costs on allocations. Lastly, we demonstrate how these techniques can be used for solving a dynamic RAP where nodes may appear or disappear over time. In later part of the thesis, we consider the convex nonlinear min-cost flow problem. Although E-relaxation and ASSP are among the fastest available techniques here, we illustrate how nonlinear costs, as opposed to linear, introduce a significant bottleneck on the progress that these algorithms make per iteration. We then extend the core idea of the auction algorithm, use of second best to make aggressive steps, to overcome this bottleneck and hence develop a faster version of ε-relaxation. This new algorithm shares the same theoretical complexity as the original but outperforms it in our numerical experiments based on random test problem suites

Congestion removal in the next generation internet

The ongoing development of new and demanding Internet applications requires the Internet to deliver better service levels that are significantly better than the best effort service that the Internet currently provides and was built for. These improved service levels include guaranteed delays, jitter and bandwidth. Through extensive research into Quality of Service and Differentiated Service (DiffServ) it has become possible to provide guaranteed services, however this turns out to be inadequate without the application of Traffic Engineering methodologies and principles. Traffic Engineering is an integral part of network operation. Its major goal is to deliver the best performance from an existing service provider's network resources and, at the same time, to enhance a customers' view of network performance. In this thesis, several different traffic engineering methods for optimising the operation of native IP and IP networks employing MPLS are proposed. A feature of these new methods is their fast run times and this opens the way to making them suitable for application in an online traffic engineering environment. For native IP networks running shortest path based routing protocols, we show that an LP-based optimisation based on the well known multi-commodity flow problem can be effective in removing network congestion. Having realised that Internet service providers are now moving towards migrating their networks to the use of MPLS, we have also formulated optimisation methods to traffic engineer MPLS networks by selecting suitable routing paths and utilising the feature of explicit routing contained in MPLS. Although MPLS is capable of delivering traffic engineering across different classes of traffic, network operators still prefer to rely on the proven and simple IP based routing protocols for best effort traffic and only use MPLS to route traffic requiring special forwarding treatment. Based on this fact, we propose a method that optimises the routing patterns applicable to different classes of traffic based on their bandwidth requirements. A traffic engineering comparison study that evaluates the performance of a neural network-based method for MPLS networks and LP-based weight setting approach for shortest path based networks has been performed using a well-known open source network simulator, called ns2. The comparative evaluation is based upon the packet loss probability. The final chapter of the thesis describes the software development of a network management application called OptiFlow which integrates techniques described in earlier chapters including the LP-based weight setting optimisation methodology; it also uses traffic matrix estimation techniques that are required as input to the weight setting models that have been devised. The motivation for developing OptiFlow was to provide a prototype set of tools that meet the congestion management needs of networking industries (ISPs and telecommunications companies - telcos)

Essays On Perioperative Services Problems In Healthcare

One of the critical challenges in healthcare operations management is to efficiently utilize the expensive resources needed while maintaining the quality of care provided. Simulation and optimization methods can be effectively used to provide better healthcare services. This can be achieved by developing models to minimize patient waiting times, minimize healthcare supply chain and logistics costs, and maximize access. In this proposal, we study some of the important problems in healthcare operations management. More specifically, we focus on perioperative services and study scheduling of operating rooms (ORs) and management of necessary resources such as staff, equipment, and surgical instruments. We develop optimization and simulation methods to coordinate material handling decisions, inventory management, and OR scheduling. In Chapter 1 of this dissertation, we investigate material handling services to improve the flow of surgical materials in hospitals. The ORs require timely supply of surgical materials such as surgical instruments, linen, and other additional equipment required to perform the surgeries. The availability of surgical instruments at the right location is crucial to both patient safety and cost reduction in hospitals. Similarly, soiled material must also be disposed of appropriately and quickly. Hospitals use automated material handling systems to perform these daily tasks, minimize workforce requirements, reduce risk of contamination, and reduce workplace injuries. Most of the literature related to AGV systems focuses on improving their performance in manufacturing settings. In the last 20 years, several articles have addressed issues relevant to healthcare systems. This literature mainly focuses on improving the design and management of AGV systems to handle the specific challenges faced in hospitals, such as interactions with patients, staff, and elevators; adhering to safety standards and hygiene, etc. In Chapter 1, we focus on optimizing the delivery of surgical instrument case carts from material departments to ORs through automated guided vehicles (AGV). We propose a framework that integrates data analysis with system simulation and optimization. We test the performance of the proposed framework through a case study developed using data from a partnering hospital, Greenville Memorial Hospital (GMH) in South Carolina. Through an extensive set of simulation experiments, we investigate whether performance measures, such as travel time and task completion time, improve after a redesign of AGV pathways. We also study the impact of fleet size on these performance measures and use simulation-optimization to evaluate the performance of the system for different fleet sizes. A pilot study was conducted at GMH to validate the results of our analysis. We further evaluated different policies for scheduling the material handling activities to assess their impact on delays and the level of inventory required. Reducing the inventory level of an instrument may negatively impact the flexibility in scheduling surgeries, cause delays, and therefore, reduce the service level provided. On the other hand, increasing inventory levels may not necessarily eliminate the delays since some delays occur because of inefficiencies in the material handling processes. Hospitals tend to maintain large inventories to ensure that the required instruments are available for scheduled surgery. Typically, the inventory level of surgical instruments is determined by the total number of surgeries scheduled in a day, the daily schedule of surgeries that use the same instrument, the processing capacity of the central sterile storage division (CSSD), and the schedule of material handling activities. Using simulation-optimization tools, we demonstrate that integrating decisions of material handling activities with inventory management has the potential to reduce the cost of the system. In Chapter 2 we focus on coordinating OR scheduling decisions with efficient management of surgical instruments. Hospitals pay more attention to OR scheduling. This is because a large portion of hospitals\u27 income is due to surgical procedures. Inventory management of decisions follows the OR schedules. Previous work points to the cost savings and benefits of optimizing the OR scheduling process. However, based on our review of the literature, only a few articles discuss the inclusion of instrument inventory-related decisions in OR schedules. Surgical instruments are classified as (1) owned by the hospital and (2) borrowed from other hospitals or vendors. Borrowed instruments incur rental costs that can be up to 12-25\% of the listed price of the surgical instrument. A daily schedule of ORs determines how many rental instruments would be required to perform all surgeries in a timely manner. A simple strategy used in most hospitals is to first schedule the ORs, followed by determining the instrument assignments. However, such a strategy may result in low utilization of surgical instruments owned by hospitals. Furthermore, creating an OR schedule that efficiently uses available surgical instruments is a challenging problem. The problem becomes even more challenging in the presence of material handling delays, stochastic demand, and uncertain surgery duration. In this study, we propose an alternative scheduling strategy in which the OR scheduling and inventory management decisions are coordinated. More specifically, we propose a mixed-integer programming model that integrates instrument assignment decisions with OR scheduling to minimize costs. This model determines how many ORs to open, determines the schedule of ORs, and also identifies the instrument assignments for each surgery. If the level of instrument inventory cannot meet the surgical requirements, our model allows instruments to be rented at a higher cost. We introduce and evaluate the solution methods for this problem. We propose a Lagrangean decomposition-based heuristic, which is an iterative procedure. This heuristic separates the scheduling problem from the inventory assignment problem. These subproblems are computationally easier to solve and provide a lower bound on the optimal cost of the integrated OR scheduling problem. The solution of the scheduling subproblem is used to generate feasible solutions in every iteration. We propose two alternatives to find feasible solutions to our problem. These alternatives provide an upper bound on the cost of the integrated scheduling problem. We conducted a thorough sensitivity analysis to evaluate the impact of different parameters, such as the length of the scheduling horizon, the number of ORs that can be used in parallel, the number of surgeries, and various cost parameters on the running time and quality of the solution. Using a case study developed at GMH, we demonstrate that integrating OR scheduling decisions with inventory management has the potential to reduce the cost of the system. The objective of Chapter 3 is to develop quick and efficient algorithms to solve the integrated OR scheduling and inventory management problem, and generate optimal/near-optimal solutions that increase the efficiency of GMH operations. In Chapter 2, we introduced the integrated OR scheduling problem which is a combinatorial optimization problem. As such, the problem is challenging to solve. We faced these challenges when trying to solve the problem directly using the Gurobi solver. The solutions obtained via construction heuristics were much farther from optimality while the Lagrangean decomposition-based heuristics take several hours to find good solutions for large-sized problems. In addition, those methods are iterative procedures and computationally expensive. These challenges have motivated the development of metaheuristics to solve OR scheduling problems, which have been shown to be very effective in solving other combinatorial problems in general and scheduling problems in particular. In Chapter 3, we adopt a metaheuristic, Tabu search, which is a versatile heuristic that is used to solve many different types of scheduling problems. We propose an improved construction heuristic to generate an initial solution. This heuristic identifies the number if ORs to be used and then the assignment of surgeries to ORs. In the second step, this heuristic identifies instrument-surgery assignments based on a first-come, first-serve basis. The proposed Tabu search method improves upon this initial solution. To explore different areas of the feasible region, we propose three neighborhoods that are searched one after the other. For each neighborhood, we create a preferred attribute candidate list which contains solutions that have attributes of good solutions. The solutions on this list are evaluated first before examining other solutions in the neighborhood. The solutions obtained with Tabu search are compared with the lower and upper bounds obtained in Chapter \ref{Ch2}. Using a case study developed at GMH, we demonstrate that high-quality solutions can be obtained by using very little computational time

Multi-objective airline schedule recovery

Master'sMASTER OF ENGINEERIN