Dynamic online resource allocation problems

Online resource allocation problems consider assigning a limited number of available resources to sequentially arriving requests with the objective to maximize rewards. With the emergence of e-business, applications such as online order fulfillment and customer service require real-time resource allocation decisions to guarantee high service quality and customer satisfaction. Other typical applications include operation room scheduling, organ transplant, and passenger screening in aviation security. This dissertation approaches the dynamic online resource allocation problem by considering two models: multi-objective sequential stochastic assignment problems and online interval scheduling problems. Multi-objective sequential stochastic assignment problems are a class of matching problems. A fixed number of jobs arrive sequentially to be assigned to one of the available workers, with an n-dimensional value vector revealed upon each arrival. The objective is to maximize the reward vector given by the product of the job value vector and worker's success rate. We conduct a complete asymptotic analysis for three classes of Pareto optimal policies, with convergence rates and asymptotic objective values provided. Online interval scheduling problems consider reusable resources, where an adversarial sequence of jobs with fixed lengths are to be assigned on available machines. The objective is to maximize the total reward for completed jobs given by the product of the job value and the machine weight. For homogeneous machines, we propose a Pairing-m algorithm, which is 2-competitive for even m and (2+2/m)-competitive for odd m. For heterogeneous machines, two classes of approximation algorithms, Cooperative Greedy algorithms and Prioritized Greedy algorithms, are compared using competitive ratios with respect to varying machine weight ratios. We also provide lower bounds for competitive ratios of deterministic online scheduling algorithms in various scenarios. Stochastic online interval scheduling problems consider a sequence of jobs drawn from a given distribution. For identically and independently distributed jobs with a known distribution, we propose 2-competitive online algorithms for both equal-length and memoryless-length jobs. For job sequences with a random order of arrivals, we propose e-competitive and e^2/(e-1)-competitive online algorithms for both equal-length and memoryless-length jobs. We further extend these results to jobs with a random order of arrivals and geometric arrivals with parameter p. We propose a primal-dual analysis framework for online interval scheduling algorithms for both adversarial and stochastic job sequences. We formulate the online interval scheduling as a linear program with a corresponding dual program. For stochastic job sequences, we use complementary slackness conditions and weak duality to derive optimal algorithms and upper bounds for the optimal reward, respectively. For adversarial sequences, we use weak duality to compute the competitive ratios of scheduling algorithms

Any-Order Online Interval Selection

We consider the problem of online interval scheduling on a single machine, where intervals arrive online in an order chosen by an adversary, and the algorithm must output a set of non-conflicting intervals. Traditionally in scheduling theory, it is assumed that intervals arrive in order of increasing start times. We drop that assumption and allow for intervals to arrive in any possible order. We call this variant any-order interval selection (AOIS). We assume that some online acceptances can be revoked, but a feasible solution must always be maintained. For unweighted intervals and deterministic algorithms, this problem is unbounded. Under the assumption that there are at most $k$ different interval lengths, we give a simple algorithm that achieves a competitive ratio of $2k$ and show that it is optimal amongst deterministic algorithms, and a restricted class of randomized algorithms we call memoryless, contributing to an open question by Adler and Azar 2003; namely whether a randomized algorithm without access to history can achieve a constant competitive ratio. We connect our model to the problem of call control on the line, and show how the algorithms of Garay et al. 1997 can be applied to our setting, resulting in an optimal algorithm for the case of proportional weights. We also discuss the case of intervals with arbitrary weights, and show how to convert the single-length algorithm of Fung et al. 2014 into a classify and randomly select algorithm that achieves a competitive ratio of 2k. Finally, we consider the case of intervals arriving in a random order, and show that for single-lengthed instances, a one-directional algorithm (i.e. replacing intervals in one direction), is the only deterministic memoryless algorithm that can possibly benefit from random arrivals. Finally, we briefly discuss the case of intervals with arbitrary weights.Comment: 19 pages, 11 figure

Serial Dictatorship Mechanism for Project Scheduling with Non-Renewable Resources

This paper considers a resource-constrained project scheduling problem with self-interested agents. A novel resource allocation model is presented and studied in a mechanism design setting without money. The novelties and specialties of our contribution include that the nonrenewable resources are supplied at different dates, the jobs requiring the resources are related with precedence relations, and the utilities of the agents are based on the tardiness values of their jobs. We modify a classical scheduling algorithm for implementing the Serial Dictatorship Mechanism, which is then proven to be truthful and Pareto-optimal. Furthermore, the properties of the social welfare are studied

On optimality of exact and approximation algorithms for scheduling problems

We consider the classical scheduling problem on parallel identical machines to minimize the makespan. Under the exponential time hypothesis (ETH), lower bounds on the running times of exact and approximation algorithms are characterized

Traffic management and control of automated guided vehicles using artificial neural networks

An industrial traffic management and control system based on Automated Guided Vehicles faces several combined problems. Decisions must be made concerning which vehicles will respond, or are allocated to each of the transport orders. Once a vehicle is allocated a transport order, a route has to be selected that allows it to reach its target location. In order for the vehicle to move efficiently along the selected route it must be provided with the means to recognise and adapt to the changing characteristics of the path it must follow. When several vehicles are involved these decisions are interrelated and must take into account the coordination of the movements of the vehicles in order to avoid collisions and maximise the performance of the transport system. This research concentrates on the problem of routing the vehicles that have already been assigned destinations associated with transport orders. In nearly all existing AGV systems this problem is simplified by considering there to be a fixed route between source and destination workstations. However if the system is to be used more efficiently, and particularly if it must support the requirements of modern manufacturing strategies, such as Justin- Time and Flexible Manufacturing Systems, of moving very small batches more frequently, then there is a need for a system capable of dealing with the increased complexity of the routing problem. The consideration of alternative paths between any two workstations together with the possibility of other vehicles blocking routes while waiting at a particular location, increases enormously the number of alternatives that must be considered in order to identify the routes for each vehicle leading to an optimum solution. Current methods used to solve this type of problem do not provide satisfactory solutions for all cases, which leaves scope for improvement. The approach proposed in this work takes advantage of the use of Backpropagation Artificial Neural Networks to develop a solution for the routing problem. A novel aspect of the approach implemented is the use of a solution derived for routing a single vehicle in a physical layout when some pieces of track are set as unavailable, as the basis for the solution when several vehicles are involved. Another original aspect is the method developed to deal with the problem of selecting a route between two locations based on an analysis of the conditions of the traffic system, when each movement decision has to be made. This lead to the implementation of a step-by-step search of the available routes for each vehicle. Two distinct phases can be identified in the approach proposed. First the design of a solution based on an ANN to solve the single vehicle case, and subsequently the development and testing of a solution for a multi-vehicle case. To test and implement these phases a specific layout was selected, and an algorithm was implemented to generate the data required for the design of the ANN solution. During the development of alternative solutions it was found that the addition of simple rules provided a useful means to overcome some of the limitations of the ANN solution, and a "hybrid" solution was originated. Numerous computer simulations were performed to test the solutions developed against alternatives based on the best published heuristic rules. The results showed that while it was not possible to generate a globally optimal solution, near optimal solutions could be obtained and the best hybrid solution was marginally better than the best of the currently available heuristic rules

Preliminary specification and design documentation for software components to achieve catallaxy in computational systems

This Report is about the preliminary specifications and design documentation for software components to achieve Catallaxy in computational systems. -- Die Arbeit beschreibt die Spezifikation und das Design von Softwarekomponenten, um das Konzept der Katallaxie in Grid Systemen umzusetzen. Eine Einführung ordnet das Konzept der Katallaxie in bestehende Grid Taxonomien ein und stellt grundlegende Komponenten vor. Anschließend werden diese Komponenten auf ihre Anwendbarkeit in bestehenden Application Layer Netzwerken untersucht.Grid Computing