http://hdl.handle.net/1721.1/7903 2013-05-25T11:27:59Z http://hdl.handle.net/1721.1/77828 Resource allocation in stochastic processing networks : performance and scaling Zhong, Yuan, Ph.D. Massachusetts Institute of Technology. Operations Research Center This thesis addresses the design and analysis of resource allocation policies in largescale stochastic systems, motivated by examples such as the Internet, cloud facilities, wireless networks, etc. A canonical framework for modeling many such systems is provided by "stochastic processing networks" (SPN) (Harrison [28, 29]). In this context, the key operational challenge is efficient and timely resource allocation. We consider two important classes of SPNs: switched networks and bandwidth-sharing networks. Switched networks are constrained queueing models that have been used successfully to describe the detailed packet-level dynamics in systems such as input-queued switches and wireless networks. Bandwidth-sharing networks have primarily been used to capture the long-term behavior of the flow-level dynamics in the Internet. In this thesis, we develop novel methods to analyze the performance of existing resource allocation policies, and we design new policies that achieve provably good performance. First, we study performance properties of so-called Maximum-Weight-[alpha] (MW-[alpha]) policies in switched networks, and of a-fair policies in bandwidth-sharing networks, both of which are well-known families of resource allocation policies, parametrized by a positive parameter [alpha] > 0. We study both their transient properties as well as their steady-state behavior. In switched networks, under a MW-a policy with a 2 1, we obtain bounds on the maximum queue size over a given time horizon, by means of a maximal inequality derived from the standard Lyapunov drift condition. As a corollary, we establish the full state space collapse property when [alpha] > 1. In the steady-state regime, for any [alpha] >/= 0, we obtain explicit exponential tail bounds on the queue sizes, by relying on a norm-like Lyapunov function, different from the standard Lyapunov function used in the literature. Methods and results are largely parallel for bandwidth-sharing networks. Under an a-fair policy with [alpha] >/= 1, we obtain bounds on the maximum number of flows in the network over a given time horizon, and hence establish the full state space collapse property when [alpha] >/= 1. In the steady-state regime, using again a norm-like Lyapunov function, we obtain explicit exponential tail bounds on the number of flows, for any a > 0. As a corollary, we establish the validity of the diffusion approximation developed by Kang et al. [32], in steady state, for the case [alpha] = 1. Second, we consider the design of resource allocation policies in switched networks. At a high level, the central performance questions of interest are: what is the optimal scaling behavior of policies in large-scale systems, and how can we achieve it? More specifically, in the context of general switched networks, we provide a new class of online policies, inspired by the classical insensitivity theory for product-form queueing networks, which admits explicit performance bounds. These policies achieve optimal queue-size scaling, in the conventional heavy-traffic regime, for a class of switched networks, thus settling a conjecture (documented in [51]) on queue-size scaling in input-queued switches. In the particular context of input-queued switches, we consider the scaling behavior of queue sizes, as a function of the port number n and the load factor [rho]. In particular, we consider the special case of uniform arrival rates, and we focus on the regime where [rho] = 1 - 1/f(n), with f(n) >/= n. We provide a new class of policies under which the long-run average total queue size scales as O(n1.5 -f(n) log f(n)). As a corollary, when f(n) = n, the long-run average total queue size scales as O(n2.5 log n). This is a substantial improvement upon prior works [44], [52], [48], [39], where the same quantity scales as O(n3 ) (ignoring logarithmic dependence on n). Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2012.; Cataloged from PDF version of thesis.; Includes bibliographical references (p. 189-193). 2012-01-01T00:00:00Z http://hdl.handle.net/1721.1/77827 Provably near-optimal algorithms for multi-stage stochastic optimization models in operations management Shi, Cong, Ph.D. Massachusetts Institute of Technology Many if not most of the core problems studied in operations management fall into the category of multi-stage stochastic optimization models, whereby one considers multiple, often correlated decisions to optimize a particular objective function under uncertainty on the system evolution over the future horizon. Unfortunately, computing the optimal policies is usually computationally intractable due to curse of dimensionality. This thesis is focused on providing provably near-optimal and tractable policies for some of these challenging models arising in the context of inventory control, capacity planning and revenue management; specifically, on the design of approximation algorithms that admit worst-case performance guarantees. In the first chapter, we develop new algorithmic approaches to compute provably near-optimal policies for multi-period stochastic lot-sizing inventory models with positive lead times, general demand distributions and dynamic forecast updates. The proposed policies have worst-case performance guarantees of 3 and typically perform very close to optimal in extensive computational experiments. We also describe a 6-approximation algorithm for the counterpart model under uniform capacity constraints. In the second chapter, we study a class of revenue management problems in systems with reusable resources and advanced reservations. A simple control policy called the class selection policy (CSP) is proposed based on solving a knapsack-type linear program (LP). We show that the CSP and its variants perform provably near-optimal in the Halfin- Whitt regime. The analysis is based on modeling the problem as loss network systems with advanced reservations. In particular, asymptotic upper bounds on the blocking probabilities are derived. In the third chapter, we examine the problem of capacity planning in joint ventures to meet stochastic demand in a newsvendor-type setting. When resources are heterogeneous, there exists a unique revenue-sharing contract such that the corresponding Nash Bargaining Solution, the Strong Nash Equilibrium, and the system optimal solution coincide. The optimal scheme rewards every participant proportionally to her marginal cost. When resources are homogeneous, there does not exist a revenue-sharing scheme which induces the system optimum. Nonetheless, we propose provably good revenue-sharing contracts which suggests that the reward should be inversely proportional to the marginal cost of each participant. Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2012.; Cataloged from PDF version of thesis.; Includes bibliographical references (p. 157-165). 2012-01-01T00:00:00Z http://hdl.handle.net/1721.1/77826 Air traffic flow management at airports : a unified optimization approach Frankovich, Michael Joseph The cost of air traffic delays is well documented, and furthermore, it is known that the significant proportion of delays is incurred at airports. Much of the air traffic flow management literature focuses on traffic flows between airports in a network, and when studies have focused on optimizing airport operations, they have focused largely on a single aspect at a time. In this thesis, we fill an important gap in the literature by proposing unified approaches, on both strategic and tactical levels, to optimizing the traffic flowing through an airport. In particular, we consider the entirety of key problems faced at an airport: a) selecting a runway configuration sequence; b) determining the balance of arrivals and departures to be served; c) assigning flights to runways and determining their sequence; d) determining the gate-holding duration of departures and speedcontrol of arrivals; and e) routing flights to their assigned runway and onwards within the terminal area. In the first part, we propose an optimization approach to solve in a unified manner the strategic problems (a) and (b) above, which are addressed manually today, despite their importance. We extend the model to consider a group of neighboring airports where operations at different airports impact each other due to shared airspace. We then consider a more tactical, flight-by-flight, level of optimization, and present a novel approach to optimizing the entire Airport Operations Optimization Problem, made up of subproblems (a) - (e) above. Until present, these have been studied mainly in isolation, but we present a framework which is both unified and tractable, allowing the possibility of system-optimal solutions in a practical amount of time. Finally, we extend the models to consider the key uncertainties in a practical implementation of our methodologies, using robust and stochastic optimization. Notable uncertainties are the availability of runways for use, and flights' earliest possible touchdown/takeoff times. We then analyze the inherent trade-off between robustness and optimality. Computational experience using historic and manufactured datasets demonstrates that our approaches are computationally tractable in a practical sense, and could result in cost benefits of at least 10% over current practice. Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2012.; Cataloged from PDF version of thesis.; Includes bibliographical references (p. 137-140). 2012-01-01T00:00:00Z http://hdl.handle.net/1721.1/77825 Lowering outbound shipping costs in an online retail environment by making better fulfillment and replenishment decisions Acimovic, Jason Andrew As online retailing - or e-tailing - continues to grow as more and more customers buy physical goods on the internet, finding ways to reduce the cost and environmental impact of outbound shipping in this sector will become increasingly important. We investigate the impact of making poor fulfillment and replenishment decisions using data obtained from a large American online retailer. Then, we propose implementable - i.e., computationally tractable and relatively intuitive - solutions for both the fulfillment and replenishment problems, both tested either on actual data from our industrial partner or on small but realistic models. We first focus on the fulfillment problem, namely, deciding from which warehouse(s) to fulfill a customer's order when several options exist. We propose a heuristic that utilizes the dual values of a transportation linear program to estimate the opportunity cost of depleting inventory from a warehouse. This linear program values inventory at a warehouse due to both its geography and the size of its catalogue. After showing that this linear program is asymptotically optimal - using concepts developed in airline network revenue management - we then test the heuristic on industry data, showing a 1% reduction in outbound shipping costs as compared to a myopic fulfillment policy. The last part of the thesis focuses on replenishment. Every period, for each item, the network places an order to restock all the warehouses. Complicating this decision are two factors. First, the orders will not arrive immediately, but rather require a lead time to be delivered. During this time a random number of customers will place orders with the network. Second, any customer's order may be filled from any warehouse, which becomes important when warehouses stock out of an item. Therefore, it is not trivial to calculate the optimal inventory to order to each warehouse. We show that using a standard replenishment policy - popular in practice - can lead to dynamics that result in increased outbound shipping costs. We propose a replenishment policy heuristic that is intuitive and performs well on examples. This heuristic has two variants: a simpler one that assumes deterministic demand, and a more complicated one that accounts for stochasticity. Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2012.; Cataloged from PDF version of thesis.; Includes bibliographical references (p. 181-185). 2012-01-01T00:00:00Z