Operations Research - Ph.D. / Sc.D.
http://hdl.handle.net/1721.1/7903
2014-09-30T09:24:24ZData-driven optimization and analytics for operations management applications
http://hdl.handle.net/1721.1/85695
Data-driven optimization and analytics for operations management applications
Uichanco, Joline Ann Villaranda
In this thesis, we study data-driven decision making in operation management contexts, with a focus on both theoretical and practical aspects. The first part of the thesis analyzes the well-known newsvendor model but under the assumption that, even though demand is stochastic, its probability distribution is not part of the input. Instead, the only information available is a set of independent samples drawn from the demand distribution. We analyze the well-known sample average approximation (SAA) approach, and obtain new tight analytical bounds on the accuracy of the SAA solution. Unlike previous work, these bounds match the empirical performance of SAA observed in extensive computational experiments. Our analysis reveals that a distribution's weighted mean spread (WMS) impacts SAA accuracy. Furthermore, we are able to derive distribution parametric free bound on SAA accuracy for log-concave distributions through an innovative optimization-based analysis which minimizes WMS over the distribution family. In the second part of the thesis, we use spread information to introduce new families of demand distributions under the minimax regret framework. We propose order policies that require only a distribution's mean and spread information. These policies have several attractive properties. First, they take the form of simple closed-form expressions. Second, we can quantify an upper bound on the resulting regret. Third, under an environment of high profit margins, they are provably near-optimal under mild technical assumptions on the failure rate of the demand distribution. And finally, the information that they require is easy to estimate with data. We show in extensive numerical simulations that when profit margins are high, even if the information in our policy is estimated from (sometimes few) samples, they often manage to capture at least 99% of the optimal expected profit. The third part of the thesis describes both applied and analytical work in collaboration with a large multi-state gas utility. We address a major operational resource allocation problem in which some of the jobs are scheduled and known in advance, and some are unpredictable and have to be addressed as they appear. We employ a novel decomposition approach that solves the problem in two phases. The first is a job scheduling phase, where regular jobs are scheduled over a time horizon. The second is a crew assignment phase, which assigns jobs to maintenance crews under a stochastic number of future emergencies. We propose heuristics for both phases using linear programming relaxation and list scheduling. Using our models, we develop a decision support tool for the utility which is currently being piloted in one of the company's sites. Based on the utility's data, we project that the tool will result in 55% reduction in overtime hours.
Thesis: Ph. D., Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2013.; 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 163-166).
2013-01-01T00:00:00ZEmission regulations in the electricity market : an analysis from consumers, producers and central planner perspectives
http://hdl.handle.net/1721.1/84716
Emission regulations in the electricity market : an analysis from consumers, producers and central planner perspectives
Figueroa Rodriguez, Cristian Ricardo
In the first part of this thesis, the objective is to identify optimal bidding strategies in the wholesale electricity market. We consider asymmetric producers submitting bids to a system operator. The system operator allocates demand via a single clearing price auction. The highest accepted bid sets the per unit market price payed by consumers. We find a pure Nash equilibrium to the bidding strategies of asymmetric producers unattainable in a symmetric model. Our results show that producers with relatively large capacities are able to exercise market power. However, the market may seem competitive due to the large number of producers serving demand. The objective of the second part of the thesis, is to compare two regulation policies: a fixed transfer price, such as tax regulation, and a permit system, such as cap-and-trade. For this purpose, we analyze an economy where risk neutral manufacturers satisfy price sensitive demand. The objective of the regulation established by the central planner is to achieve an external objective, e.g. reduce pollution or limit consumption of scarce resource. When demand is uncertain, designing these regulations to achieve the same expected level of the external objective results in the same expected consumer price but very different manufacturers' expected profit and central planner revenue. For instance, our results show that when the firms are price takers, the manufacturers with the worst technology always prefer a tax policy. Interestingly, we identify conditions under which the manufacturers with the cleanest technology benefit from higher expected profit as tax rate increases. In the third part of the thesis, we investigate the impact labeling decisions have on the supply chain. We consider a two stage supply chain consisting of a supplier and a retailer. Demand is considered stochastic, decreasing in price and increasing in a quality parameter, e.g. carbon emissions. The unit production cost for the supplier is increasing in the quality level chosen. We identify two different contracts that maximize the efficiency of the supply chain while allowing the different parties to achieve their objectives individually.
Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2013.; 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 119-122).
2013-01-01T00:00:00ZOptimal routes for electric vehicles facing uncertainty, congestion, and energy constraints
http://hdl.handle.net/1721.1/84715
Optimal routes for electric vehicles facing uncertainty, congestion, and energy constraints
Fontana, Matthew William
There are many benefits of owning a battery electric vehicle, including zero tailpipe emissions, potential independence from oil, lower fuel costs, and the option to recharge the battery at home. However, a significant concern about owning a battery electric vehicle is range anxiety: the fear that the battery will run out of charge before the driver reaches his or her destination. We address range anxiety by providing a robust optimization framework to give drivers confidence that they can reach their destinations in a reasonable amount of time with enough energy in the battery, even when there is uncertainty in travel time and energy consumption on the roads. The robust optimization appropriately incorporates uncertainty without significantly increasing the complexity of the problem. This thesis describes that optimization framework and how to use it on real-world examples to find appropriate routes, with a central part being the application of robust optimization to the problem. We develop an energy model, an optimization-based formulation using robust optimization, and algorithms to quickly find good routes for battery electric vehicles. The combination of using robust optimization, the A-Star algorithm to find shortest paths, and Lagrangian relaxation allows us to solve the problem in seconds or less. For one example start and destination, our algorithms required less than 2 seconds for each instance (energy consumption limit). In addition, for example trips, we compute a Pareto frontier to illustrate the time-energy tradeoff from driving different routes. We use Lagrangian relaxation to provide lower bounds and estimates that suggest that our algorithms produce near-optimal solutions. We apply our methodology to example trips in Massachusetts and Michigan to demonstrate its practicality and its potential for real-world use. Future work could continue to improve the modeling accuracy and include algorithmic enhancements to further improve running time, especially for larger networks.
Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2013.; 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 165-170).
2013-01-01T00:00:00ZTractable multi-product pricing under discrete choice models
http://hdl.handle.net/1721.1/82871
Tractable multi-product pricing under discrete choice models
Keller, Philipp W. (Philipp Wilhelm), 1982-
We consider a retailer offering an assortment of differentiated substitutable products to price-sensitive customers. Prices are chosen to maximize profit, subject to inventory/ capacity constraints, as well as more general constraints. The profit is not even a quasi-concave function of the prices under the basic multinomial logit (MNL) demand model. Linear constraints can induce a non-convex feasible region. Nevertheless, we show how to efficiently solve the pricing problem under three important, more general families of demand models. Generalized attraction (GA) models broaden the range of nonlinear responses to changes in price. We propose a reformulation of the pricing problem over demands (instead of prices) which is convex. We show that the constrained problem under MNL models can be solved in a polynomial number of Newton iterations. In experiments, our reformulation is solved in seconds rather than days by commercial software. For nested-logit (NL) demand models, we show that the profit is concave in the demands (market shares) when all the price-sensitivity parameters are sufficiently close. The closed-form expressions for the Hessian of the profit that we derive can be used with general-purpose nonlinear solvers. For the special (unconstrained) case already considered in the literature, we devise an algorithm that requires no assumptions on the problem parameters. The class of generalized extreme value (GEV) models includes the NL as well as the cross-nested logit (CNL) model. There is generally no closed form expression for the profit in terms of the demands. We nevertheless how the gradient and Hessian can be computed for use with general-purpose solvers. We show that the objective of a transformed problem is nearly concave when all the price sensitivities are close. For the unconstrained case, we develop a simple and surprisingly efficient first-order method. Our experiments suggest that it always finds a global optimum, for any model parameters. We apply the method to mixed logit (MMNL) models, by showing that they can be approximated with CNL models. With an appropriate sequence of parameter scalings, we conjecture that the solution found is also globally optimal.
Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2013.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 199-204).
2013-01-01T00:00:00Z