Browsing by Subject "Operations research"

Across multiple industries (e.g., railroads, airlines, on-demand air taxi services), there are growing investments in future automated transportation systems. Even with these investments, there are still significant human-systems engineering challenges that require deeper investigation and planning. Specifically, fleets that include new levels of automation may require new concepts of how to design and staff network operations centers. Network operations centers have existed for over a century in the railroad and airline industries, where dispatchers have played a central role in safely and efficiently managing networks of railroads and flights. With operators in such safety-critical and time-sensitive positions, workload is the key indicator of their performance in terms of accuracy and efficiency. Yet, there are few tools available for decision-makers in these industries to explore how increasing levels of automation in fleets and operations centers may ultimately affect dispatcher workload.

Thus, this thesis presents a model of dispatcher workload. While automation may be the most pressing change in transportation industries, 10 variables related to configurations of the fleet and the operations center and how those variables interact to influence dispatcher workload were defined. These ten variables come from fleet conditions, strategic design factors, tactical staffing factors, and operational factors. A discrete event simulation was developed to computationally model dispatcher workload with over 10^18 possible configurations of these variables. Additionally, using time-based metrics and integrating results from a prior human reliability assessment, the simulation predicts human error on tasks.

A multi-level validation strategy was developed to build internal, external, and general confidence in using the dispatcher workload model across different domains with data from freight railroad, commuter railroad, and airline operations. In the process of developing and validating the workload model, several other research contributions were made to the field. Eighty-five probability density functions of dispatcher task inter-arrival and service time distributions were generated in the three domains. A data collection tool, Dispatcher’s Rough Assessment of Workload-Over Usual Times (DRAW-OUT), was designed to gather empirical dispatcher-generated estimates of utilization, the proxy for workload, throughout their shifts.

Using the model, experiments were conducted to analyze the sensitivity of dispatcher workload and performance to changes in different parameters. The size of the fleet a dispatcher managed was found to be the most significant factor out of all the other internal parameters. On the other hand, shift schedule, environmental conditions, and operator strategy were the parameters found to have the smallest influence on dispatcher performance. The model was also used to investigate future scenarios that managers could not previously explore due to limitations of time and resources. Results show that the general model is applicable for use in simulating dispatcher workload in both freight and commuter railroad operations as well as airline operations, including short- and long-haul flights, in present-day and future cases.

General confidence was built in the workload model and the Simulator of Humans & Automation in Dispatch Operations (SHADO) was developed as an online platform to provide open access to the underlying discrete event simulation. SHADO is a novel tool that allows stakeholders, including operational managers, to rapidly prototype dispatch operations and investigate human performance in any transportation system. With several theoretical and practical contributions, this work establishes the foundation for future research in the growing field of advanced transportation network operations.

This dissertation explores the development and analysis of new algorithms for sequential decision-making under uncertainty, with a focus on optimizing operations and resource allocations within online marketplaces such as e-commerce and rental platforms. The research initially revisits and expands upon the multi-item order fulfillment model, introducing dynamic policies that combine randomized fulfillment strategies, prophet inequalities, and subgradient methods. Our approaches not only achieve asymptotic optimality and strong approximation guarantees in the multi-item fulfillment setting, but also provide insights on how to construct robust policies in scenarios where you have limited resources. The findings in this dissertation introduce a novel approach to the management of resources in complex environments, presenting a nearly optimal framework for developing policies tailored to the complexities of multi-item order fulfillment. Moreover, our analysis can be extended into the domain of rental operations, showcasing the flexibility and broad applicability of our proposed solutions.

In addition, the dissertation addresses the complexities of online recommendation systems through a contextual bandit framework, examining both full-feedback and bandit-feedback settings. By formulating the problem to accommodate arbitrary mappings from user contexts to product feature values, this research provides new online algorithms that effectively minimize regret. The analysis extends to general policy classes, revealing an inherent trade-off between approximation accuracy and statistical error for a given policy class.

Collectively, this work advances theoretical knowledge in sequential decision-making and algorithm design, providing actionable strategies for improving decision-making processes such as fulfillment and recommendations in online marketplaces.

Many types of services are provided using some equipment or machines, e.g. transportation systems using vehicles. Designs of these systems require capacity decisions, e.g., the number of vehicles. In my dissertation, I use many-server and conventional heavy-traffic limit theory to derive asymptotically optimal capacity decisions, giving the desired level of delay and availability performance with minimum investment. The results provide near-optimal solutions and insights to otherwise analytically intractable problems.

The dissertation will comprise two essays. In the first essay, &ldquoAsymptotic Analysis of Delay-based Performance Metrics and Optimal Capacity Decisions for the Machine Repair Problem with Spares,&rdquo I study the M/M/R machine repair problem with spares. This system can be represented by a closed queuing network. Applications include fleet vehicles' repair and backup capacity, warranty services' staffing and spare items investment decisions. For these types of systems, customer satisfaction is essential; thus, the delays until replacements of broken units are even more important than delays until the repair initiations of the units. Moreover, the service contract may include conditions on not only the fill rate but also the probability of acceptable delay (delay being less than a specified threshold value).

I address these concerns by expressing delays in terms of the broken-machines process; scaling this process by the number of required operating machines (or the number of customers in the system); and using many-server limit theorems (limits taken as the number of customers goes to infinity) to obtain the limiting expected delay and probability of acceptable delay for both delay until replacement and repair initiation. These results lead to an approximate optimization problem to decide on the repair and backup-capacity investment giving the minimum expected cost rate, subject to a constraint on the acceptable delay probability. Using the characteristics of the scaled broken-machines process, we obtain insights about the relationship between quality of service and capacity decisions. Inspired by the call-center literature, we categorize capacity level choice as efficiency-driven, quality-driven, or quality- and efficiency-driven. Hence, our study extends the conventional call center staffing problem to joint staffing and backup provisioning. Moreover, to our knowledge, the machine-repair problem literature has focused mainly on mean and fill rate measures of performance for steady-state cost analysis. This approach provides complex, nonlinear expressions not possible to solve analytically. The contribution of this essay to the machine-repair literature is the construction of delay-distribution approximations and a near-optimal analytical solution. Among the interesting results, we find that for capacity levels leading to very high utilization of both spares and repair capacity, the limiting distribution of delay until replacement depends on one type of resource only, the repair capacity investment.

In the second essay, &ldquoDiffusion Approximations and Near-Optimal Design of a Make-to-Stock Queue with Perishable Goods and Impatient Customers,&rdquo I study a make-to-stock system with perishable inventory and impatient customers as a two-sided queue with abandonment from both sides. This model describes many consumer goods, where not only spoilage but also theft and damage can occur. We will refer to positive jobs as individual products on the shelf and negative jobs as backlogged customers. In this sense, an arriving negative job provides the service to a waiting positive job, and vice versa. Jobs that must wait in queue before potential matching are subject to abandonment. Under certain assumptions on the magnitude of the abandonment rates and the scaled difference between the two arrival rates (products and customers), we suggest approximations to the system dynamics such as average inventory, backorders, and fill rate via conventional heavy traffic limit theory.

We find that the approximate limiting queue length distribution is a normalized weighted average of two truncated normal distributions and then extend our results to analyze make-to-stock queues with/without perishability and limiting inventory space by inducing thresholds on the production (positive) side of the queue. Finally, we develop conjectures for the queue-length distribution for a non-Markovian system with general arrival streams. We take production rate as the decision variable and suggest near-optimal solutions.

This dissertation studies coordination mechanism design for sustainable supply networks in a globalized environment, with the goal of achieving long-term profitability, environmental friendliness and social responsibility. We examine three different types of supply networks in detail.

The first network consists of one supplier and multiple retailers. The main issue is how to efficiently share a scarce resource, such as capacities for green technology, among all members with private information under dynamically changing environment. We design a shared surplus supply agreement among the members which can lead to both efficient private investments and efficient capacity allocation under unpredictable and unverifiable market conditions.

The second network is a serial supply chain. The source node provides critical raw material (like coffee cherries) for the entire chain and is typically located in an underdeveloped economy, the end node is a retailer serving consumer at a developed economy (like Starbucks Co.). We construct a dynamic supply agreement that takes into account the changing market and production conditions to ensure fair compensations so that the partners have the right incentives to work together to develop sustainable quality supply.

The third network is a stylized global production network of a multinational company consisting of a home plant and a foreign branch. The branch serves the foreign market but receives a key component from the home plant. The distinctive feature is that both facilities belong to the same company, governed by the headquarters, yet they each also have their own autonomies. We analyze the role of the headquarters in designing coordination mechanism to improve efficiency. We show the headquarters can delegate the coordination effort to the home plant, as long as it keeps veto power.

Digital transformation is changing the landscape of business and sparking waves of innovation, calling for advanced big data analytics and artificial intelligence techniques. To survive from intensified and rapidly changing market conditions in the big data era, it is crucial for companies to hone up their competitive advantages by wielding the great power of data. This thesis provides data-driven solutions to facilitate informed decision making under various forms of uncertainties, making contributions to both theory and applications.

Chapter 1 presents a study motivated by a real-life data set from a leading Chinese supermarket chain. The grocery retailer sells a perishable product, making joint pricing and inventory ordering decisions over a finite time horizon with lost sales. However, she does not have perfect information on (1) the demand-price relationship, (2) the demand noise distribution, (3) the inventory perishability rate, and (4) how the demand-price relationship changes over time. Moreover, the demand noise distribution is nonparametric for some products but parametric for others. To help the retailer tackle these challenges, we design two versions of data-driven pricing and ordering (DDPO) policies, for the settings of nonparametric and parametric noise distributions, respectively. Measuring performance by regret, i.e., the profit loss relative to a clairvoyant policy with perfect information, we show that both versions of our DDPO policies achieve the best possible rates of regret in their respective settings. Through a case study on the real-life data, we also demonstrate that both of our policies significantly outperform the historical decisions of the supermarket, establishing the practical value of our approach. In the end, we extend our model and policy to account for age-dependent product perishability and demand censoring.

Chapter 2 discusses a work inspired by a real-life smart meter data set from a major U.S. electric utility company. The company serves retail electricity customers over a finite time horizon. Besides granular data of customers' consumptions, the company has access to high-dimensional features on customer characteristics and exogenous factors. What is unique in this context is that these features exhibit three types of heterogeneity---over time, customers, or both. They induce an underlying cluster structure and influence consumptions differently in each cluster. The company knows neither the underlying cluster structure nor the corresponding consumption models. To tackle this challenge, we design a novel data-driven policy of joint spectral clustering and feature-based dynamic pricing that efficiently learns the underlying cluster structure and the consumption behavior in each cluster, and maximizes profits on the fly. Measuring performance by average regret, i.e., the profit loss relative to a clairvoyant policy with perfect information per customer per period, we derive distinct theoretical performance guarantees by showing that our policy achieves the best possible rate of regret. Our case study based on the real-life smart meter data indicates that our policy significantly increases the company profits by 146\% over a three-month period relative to the company policy. Our policy performance is also robust to various forms of model misspecification. Finally, we extend our model and method to allow for temporal shifts in feature means, general cost functions, and potential effect of strategic customer behavior on consumptions.

Chapter 3 investigates an image cropping problem faced by a large Chinese digital platform. The platform aims to crop and display a large number of images to maximize customer conversions in an automated fashion, but it does not know how cropped images influence conversions, referred to as the reward function. What the platform knows is that good cropping should capture salient objects and texts, collectively referred to as salient features, as much as possible. Due to the high dimensionality of digital images and the unknown reward function, finding the optimal cropping for a given image is a highly unstructured learning problem. To overcome this challenge, we leverage the more advanced deep learning techniques to design a neural network policy with two types of neural networks, one for detecting salient features and the other for learning the reward function. We then show that our policy achieves the best possible theoretical performance guarantee by deriving matching upper and lower bounds on regret. To the best of our knowledge, these results are the first of their kind in deep learning applications in revenue management. Through case studies on the real-life data set and a field experiment, we demonstrate that our policy achieves statistically significant improvement on conversions over the platform's incumbent policy, translating into an annual revenue increase of 2.85 million U.S. dollars. Moreover, our neural network policy significantly outperforms the traditional machine learning methods and exhibits good performance even if the reward function is misspecified.

This dissertation explores decision problems faced by organizations willing to address or support the incorporation of sustainability aspects on their "business as usual" activities. We study to specific problems. First, we analyze the decision problem of a forest manager who, in addition to selling timber, has the option of selling carbon offsets for the carbon sequestered by the forest. We study both the single-rotation and the multiple-rotations harvesting problems, and develop stochastic dynamic programming models to find the optimal harvesting and offset-selling policy, the expected optimal harvesting time, and the expected optimal reward under different offset-trading schemes. Then, we study the case in which an organization (sustainability buyer) outsources sustainability efforts to another organization (sustainability seller). While buyers cannot directly exert sustainability efforts, they can provide economic or technical support to their sellers in order to incentivize these efforts. We investigate how the effort and support decisions change according to characteristics of stakeholders, buyers, and sellers. Considering that buyers can compete on the sustainability effort exerted by their sellers, we extend our analysis to the case of competing buyers, and we determine conditions under which sharing sellers is preferred by the buyers to having separate sellers for each buyer.

This dissertation studies the optimal design and performance evaluation of large-scale supply chain systems with graphical structures such as assemble-to-order (ATO) systems and e-commerce fulfillment networks. It consists of three essays.

The first essay studies the design of effective operational policies in the assemble-to-order (ATO) systems. We consider continuous-review ATO systems with general bills of materials (BOM) and general leadtimes. First, we characterize the asymptotically optimal policy for the M-system. The policy consists of a periodic review priority (PRP) allocation rule and a coordinated base-stock (CBS) replenishment policy. We then construct heuristic policies using insights from the asymptotically optimal policy. In particular, we adopt the PRP allocation rule and develop a decomposition approach for inventory replenishment. This approach decomposes a general system into a set of assembly subsystems and constructs a linear program to compute the optimal policy parameters. However, both the CBS and the assembly decomposition approach are limited to simple systems. We then consider a second approach, which decomposes a system into a set of distribution subsystems and each subsystem has a straightforward optimal solution, which is similar to the newsvendor problem. Finally, in a numeral test, we find that the assembly decomposition is very effective but computationally expensive and thus only good for small-scale systems; the distribution decomposition performs as effective as the optimal independent base-stock (IBS) policy, but is highly scalable than finding the optimal IBS policy for large-scale systems.

The second essay focuses on optimizing the operational decision at one layer of the supply chain network when some operational decisions at another layer are unknown to the decision-maker. More specifically, we consider the transportation network design problem for the e-commerce marketplace. A salient feature in this problem is decentralized decision-making. While the middle-mile manager decides the network configuration on a weekly or bi-weekly basis, the real-time flows of millions of packages on any given network configuration (which we call the flow response) are controlled by a fulfillment policy employed by a different decision entity. Thus, we face a fixed-cost network design problem with unknown flow response. To meet this challenge, we first develop a predictive model for the unknown response leveraging observed shipment data and machine learning techniques. Apart from the most natural network-level predictive model, we find that the more parsimonious destination-level and arc-level predictive models are more effective. We then embed the predictive model to the original network design problem and characterize this transformed problem as a c-supermodular minimization problem. We develop a linear-time algorithm with an approximation guarantee that depends on c. We demonstrate that this algorithm is scalable and effective in a numerical study.

The third essay investigates how to use the Graph Neural Network (GNN) model to predict the operational performances of supply chain networks. GNN is a newly developed machine learning tool to leverage the graphical structure information. It has demonstrated good prediction accuracy in various contexts, including social, bioinformatics and citation networks. Surprisingly, GNNs have not received much attention in supply chain systems despite the fact that many systems exhibit a graphical structure, such as assemble-to-order systems and process flexibility networks. To the best of our knowledge, we are the first to explore the application of GNN to supply chain problems. As operational performances of the entire network can often be decomposed into node-level or edge-level performances, we study both node-level and edge-level predictions. We find that while the existing GNN model can generate reasonable node-level predictions, special tailoring is needed for edge-level predictions of supply chain networks. A key contribution of our research is to develop a novel graph transformation approach, which allows an edge to learn from its neighborhood edges. Tested on different synthetic datasets from two different supply chain systems, we implement the GNN model with our proposed graph transformation and several benchmark methods, including an existing GNN model and the traditional machine learning methods, such as the convolutional neural network and random forest. The results indicate that our approach significantly outperforms the benchmarks in edge-level prediction. We also observe the importance of utilizing the graphical structure and edge directions. Our comparison reveals that it is beneficial to start with node-level or edge-level predictions and then aggregate them together for the graph-level prediction, instead of the direct graph-level prediction commonly used in other applications.

This dissertation studies how a subscription service provider offers contracts to customers without full information on their preferences. The first essay studies a mechanism design problem for business interruption (BI) insurance. More specifically, we study how an insurer deals with adverse selection and moral hazard when offering BI insurance to a firm. The firm makes demand forecasts and can make a recovery effort if a disruption occurs; both are unobservable to the insurer. We first find that because of the joint effect of limited production capacity and self-impelled recovery effort, the firm with a lower demand forecast benefits more from the BI insurance than that with a higher demand forecast. Anticipating a higher premium, the low-demand firm has an incentive to pretend to have the higher demand forecast to obtain more profit. We then characterize the optimal insurance contracts to deal with information asymmetry and show how the firm's operational and informational characteristics affect the optimal insurance contracts. We also analyze the case where the firm can choose its initial capacity and find that from the firm's perspective, capacity and BI insurance could be either substitutes or complements.The second essay focuses on the learning-and-earning trade-off in subscription service offerings. We consider a service provider offering a subscription service to customers over a multi-period planning horizon. The customers decide whether to subscribe according to a utility model representing their preferences for the subscription service. The provider has a prior belief about the customer utility model. Adjusting the price and subscription period over time, the provider updates its belief based on the transaction data of new customers and the usage data of existing subscribers. The provider aims to minimize its regret, namely the expected profit loss relative to a clairvoyant with full information on the customer utility model. To analyze regret, we first study the clairvoyant's full-information problem. The resulting dynamic program, however, suffers from the curse of dimensionality. We develop a customer-centric approach to resolve this issue and obtain the optimal policy for the full-information problem. This approach strikes an optimal balance between immediate and future profits from an individual customer. When the provider does not have full information, we find that a simple and commonly used certainty-equivalence policy, which learns only passively, exhibits poor performance. We illustrate that this can be due to incomplete or slow learning, but it can also occur because of offering a suboptimal contract with a long subscription period in the beginning. We propose a two-phase learning policy that first focuses on information accumulation and then profit maximization. We show that our policy achieves asymptotically optimal performance with its regret growing logarithmically in the planning horizon. Our results indicate that the provider should be cautious about offering a long subscription period when it is uncertain about customer preferences.

Distributed optimization methods allow us to decompose an optimization problem

into smaller, more manageable subproblems that are solved in parallel. For this

reason, they are widely used to solve large-scale problems arising in areas as diverse

as wireless communications, optimal control, machine learning, artificial intelligence,

computational biology, finance and statistics, to name a few. Moreover, distributed

algorithms avoid the cost and fragility associated with centralized coordination, and

provide better privacy for the autonomous decision makers. These are desirable

properties, especially in applications involving networked robotics, communication

or sensor networks, and power distribution systems.

In this thesis we propose the Accelerated Distributed Augmented Lagrangians

(ADAL) algorithm, a novel decomposition method for convex optimization prob-

lems with certain separability structure. The method is based on the augmented

Lagrangian framework and addresses problems that involve multiple agents optimiz-

ing a separable convex objective function subject to convex local constraints and

linear coupling constraints. We establish the convergence of ADAL and also show

that it has a worst-case O(1/k) convergence rate, where k denotes the number of

iterations.

Moreover, we show that ADAL converges to a local minimum of the problem

for cases with non-convex objective functions. This is the first published work that

formally establishes the convergence of a distributed augmented Lagrangian method

ivfor non-convex optimization problems. An alternative way to select the stepsizes

used in the algorithm is also discussed. These two contributions are independent

from each other, meaning that convergence of the non-convex ADAL method can

still be shown using the stepsizes from the convex case, and, similarly, convergence

of the convex ADAL method can be shown using the stepsizes proposed in the non-

convex proof.

Furthermore, we consider cases where the distributed algorithm needs to operate

in the presence of uncertainty and noise and show that the generated sequences of

primal and dual variables converge to their respective optimal sets almost surely. In

particular, we are concerned with scenarios where: i) the local computation steps

are inexact or are performed in the presence of uncertainty, and ii) the message

exchanges between agents are corrupted by noise. In this case, the proposed scheme

can be classified as a distributed stochastic approximation method. Compared to

existing literature in this area, our work is the first that utilizes the augmented

Lagrangian framework. Moreover, the method allows us to solve a richer class of

problems as compared to existing methods on distributed stochastic approximation

that consider only consensus constraints.

Extensive numerical experiments have been carried out in an effort to validate

the novelty and effectiveness of the proposed method in all the areas of the afore-

mentioned theoretical contributions. We examine problems in convex, non-convex,

and stochastic settings where uncertainties and noise affect the execution of the al-

gorithm. For the convex cases, we present applications of ADAL to certain popular

network optimization problems, as well as to a two-stage stochastic optimization

problem. The simulation results suggest that the proposed method outperforms

the state-of-the-art distributed augmented Lagrangian methods that are known in

the literature. For the non-convex cases, we perform simulations on certain simple

non-convex problems to establish that ADAL indeed converges to non-trivial local

vsolutions of the problems; in comparison, the straightforward implementation of the

other distributed augmented Lagrangian methods on the same problems does not

lead to convergence. For the stochastic setting, we present simulation results of

ADAL applied on network optimization problems and examine the effect that noise

and uncertainties have in the convergence behavior of the method.

As an extended and more involved application, we also consider the problem

of relay cooperative beamforming in wireless communications systems. Specifically,

we study the scenario of a multi-cluster network, in which each cluster contains

multiple single-antenna source destination pairs that communicate simultaneously

over the same channel. The communications are supported by cooperating amplify-

and-forward relays, which perform beamforming. Since the emerging problem is non-

convex, we propose an approximate convex reformulation. Based on ADAL, we also

discuss two different ways to obtain a distributed solution that allows for autonomous

computation of the optimal beamforming decisions by each cluster, while taking into

account intra- and inter-cluster interference effects.

Our goal in this thesis is to advance the state-of-the-art in distributed optimization by proposing methods that combine fast convergence, wide applicability, ease

of implementation, low computational complexity, and are robust with respect to

delays, uncertainty in the problem parameters, noise corruption in the message ex-

changes, and inexact computations.

High-dimensional state spaces and/or decision spaces sometimes arise when sequential operational decisions need to be made dynamically in reflection of complex system information. To tackle the "curse of dimensionality," effective heuristics are needed that achieve both computational efficiency and satisfactory performance (e.g. high revenue or low cost).

This dissertation studies two such problems with three essays. The first two essays consider a dynamic pricing problem faced by a seller of a limited amount of inventory over a short time horizon. She faces an unknown demand which she must learn about during the selling season from observing customer purchase decisions. This problem can be formulated as a Bayesian dynamic program, with a high-dimensional state space representing the prior belief about the unknown demand. In the first essay, we develop insights, solution bounds, and heuristics for the problem. It is demonstrated that our derivative-based heuristics provide good revenue performance compared with two well-known algorithms in the literature. In the second essay, we apply open-loop policies to this dynamic pricing problem and reveal counter-intuitive observations. In particular, incorporating more information into a policy may actually hurt its revenue performance. This can be explained by the incomplete learning effect under limited inventory.

The third essay studies the hospital's problem to dynamically schedule elective surgeries in advance. Since after surgeries patients stay for a random number of days in an ICU with limited bed capacity, the schedule takes into account current and future ICU congestion and dynamically adjusts itself accordingly. This problem is formulated as a dynamic program where both the state space and the decision space are infinite-dimensional. We devise two schemes to relax the problem as an allocation scheduling problem and use the solution to the relaxed problems to construct heuristic solutions to the original problem. Numerical experiment confirms that our heuristics outperform benchmarks.

Increased use of wind energy in electricity systems can help reduce green house gas emissions and enhance energy security. However, the traditional scheduling and dispatching processes used to ensure the cost-effective and reliable supply of electricity in wholesale energy and ancillary service markets are not designed to deal with wind production uncertainty and variability. The growing variability and uncertainty of wind resources misinforms the scheduling and dispatching processes and ultimately causes economic and environmental inefficiencies. Various approaches have been proposed to integrate the wind uncertainty and variability into the electricity market clearing processes and enhance their economic and environmental efficiency. This dissertation develops a framework that enables quantifying the inefficiencies caused by the wind uncertainty and assessing the economic and environmental efficiency that could be gained by integrating the uncertainty into the market clearing design.

To assess the potential inefficiencies posed by wind uncertainty, three objectives are addressed. (1) Elucidate the incentives that wind uncertainty might create for electricity markets’ demand-side participants to develop market manipulation strategies and determine the factors that might contribute to or mitigate such market power. (2) Estimate the economic and environmental costs of wind uncertainty and the improvements that could be achieved by various approaches for integrating the wind uncertainty into the market clearing design. (3) Investigate how CO2 pricing policies that affect the priority order of generators in the supply curve and the grid’s overall flexibility impact the uncertainty costs and the improvements that could be achieved by integrating the uncertainty into the market clearing design.

First, in order to highlight the opportunities that wind uncertainty creates for the demand-side strategic behavior, this paper explores the effects of allowing large, price-responsive consumers to provide reserves in a power system with significant penetration of wind energy when the market is cleared using stochastic market clearing (SMC). The problem is formulated as a bilevel optimization problem representing a Stackelberg game between the large consumer and the other market participants. The study highlights how a large price-responsive consumer takes advantage of the wind uncertainty and leverages its ramp reserve deployment capability to understate its demand in the day-ahead market (DAM) and reduce the overall day-ahead (DA) and real-time (RT) prices to minimize the total daily cost of purchasing electricity in the DA and RT markets. The study also reveals how wind uncertainty, reserve deployment capacity, and transmission congestion contribute to the market power of large consumers that should be limited to mitigate their market power.

Next, to estimate the economic and environmental inefficiencies of the wind uncertainty, a framework is developed that replicates the operation of wholesale energy market clearing under the traditional design and adjusted designs that indirectly or directly integrate the uncertainty into the market clearing mechanisms. The indirect integration, referred to as augmented deterministic design, maintains the deterministic nature of market clearing mechanisms, i.e., DA unit commitment (DAUC) and economic dispatch (DAED), and deals with the uncertainty through scheduling ramp capability requirements, which are quantified exogenously to the market clearing processes based on the wind uncertainty characterization. The direct integration requires transition to the stochastic market clearing design in which stochastic optimization models are used for direct integration of the wind uncertainty characterization in the DAUC and DAED processes. The stochastic design allows endogenous quantification of the ramp capability requirements and optimizes energy and ramp capability reserve schedules by accounting for the expected cost of recourse actions taken to reconcile the RT balance mismatch caused by the deviation of wind energy producers from their DA production schedules.

The proposed framework resolves the differences of adjusted market clearing designs in terms of pricing, settlement, and reliability management to ensure a fair comparison of their dispatch, economic, and environmental outcomes. The comparative analysis reveals that the augmented deterministic and the stochastic designs enhance the economic and environmental outcomes, yet the stochastic design is superior as it offers more efficient and flexible energy and reserve schedules that are well coordinated with the anticipation of RT wind energy realizations. As a result, the stochastic design’s schedules can be adjusted more conveniently and cost-effectively to reconcile the deviations leading to greater operation and startup fuel cost savings; lower cycling of slow producers, higher wind integration and finally lower air emissions. Furthermore, stochastic design offers more efficient prices that reflect the system’s operation costs and wind uncertainty more effectively, provide greater remuneration of operational flexibility by producers, and reduce the revenue sufficiency guarantee payments that collectively improve the social surplus to a higher extent with respect to the augmented deterministic design.

Lastly, the developed market simulation framework is extended to include another adjusted deterministic design, referred to as hybrid deterministic design that uses stochastic optimization for direct integration of the wind uncertainty characterization to the residual unit commitment (RUC) stage. Then the economic and environmental outcomes of alternative market clearing designs are simulated under two carbon-pricing scenarios to evaluate their sensitivity to the introduction of a carbon price that alters the merit order of generation technologies in the supply curve.

The results imply that the stochastic market clearing design is superior to all adjusted deterministic designs. With introduction of a CO2 price, augmented and hybrid deterministic designs lose their effectiveness due to the shift in merit order of producers. However, stochastic market clearing maintains its superior performance that increases its superiority with respect to adjusted deterministic designs.

Decisions in health care must often be made under inherent uncertainty; from treating patients, to provisioning medical devices, to operational decisions at an outpatient clinic. The outcomes depend on the health of patients as well as the availability of health care professionals and resources. Complex models of clinic performance allow for experiments with new schedules and resource levels without the time, cost, unfeasibility, or risk of testing new policies in real clinics. Model-based methods quantify the effect of various uncertain factors such as the availability of personnel on health care quality indicators like patient wait times in a clinic.

Despite their purported value, few opportunities have existed to test models from data collection through optimization. This dissertation develops a clinic model from end-to-end, beginning with a description of the medical practice, to data collection, to model validation, to optimization. Specialty medical practice is abstracted into treatment steps, measured electronically, and verified through systematic observation. These data are anonymized and made available for researchers. A validation framework uses the data to develop and test candidate models, selecting one that maximizes predictive accuracy while retaining interpretability and reproducibility. The resulting model is used in improving schedules via heuristic optimization. Clustering the results reveals clinic performance groups that represent different goals in clinic quality.

This dissertation contributes to the rapidly growing empirical research area in the field of operations management. It contains two essays, tackling two different sets of operations management questions which are motivated by and built on field data sets from two very different industries --- air cargo logistics and retailing.

The first essay, based on the data set obtained from a world leading third-party logistics company, develops a novel and general Bayesian hierarchical learning framework for estimating customers' spillover learning, that is, customers' learning about the quality of a service (or product) from their previous experiences with similar yet not identical services. We then apply our model to the data set to study how customers' experiences from shipping on a particular route affect their future decisions about shipping not only on that route, but also on other routes serviced by the same logistics company. We find that customers indeed borrow experiences from similar but different services to update their quality beliefs that determine future purchase decisions. Also, service quality beliefs have a significant impact on their future purchasing decisions. Moreover, customers are risk averse; they are averse to not only experience variability but also belief uncertainty (i.e., customer's uncertainty about their beliefs). Finally, belief uncertainty affects customers' utilities more compared to experience variability.

The second essay is based on a data set obtained from a large Chinese supermarket chain, which contains sales as well as both wholesale and retail prices of un-packaged perishable vegetables. Recognizing the special characteristics of this particularly product category, we develop a structural estimation model in a discrete-continuous choice model framework. Building on this framework, we then study an optimization model for joint pricing and inventory management strategies of multiple products, which aims at improving the company's profit from direct sales and at the same time reducing food waste and thus improving social welfare.

Collectively, the studies in this dissertation provide useful modeling ideas, decision tools, insights, and guidance for firms to utilize vast sales and operations data to devise more effective business strategies.

This dissertation examines optimal solutions in complex decision problems with one or more of the following components: online decisions, model uncertainty and learning. The first model studies the problem of online selection of a monotone subsequence and provides distributional properties of the optimal objective function. The second model studies the robust optimization approach to the decision problem of an auction bidder who has imperfect information about rivals' bids and wants to maximize her worst-case payoff. The third model analyzes the performance of a myopic Bayesian policy and one of its variants in the dynamic pricing problem of a monopolistic insurer who sells a business interruption insurance product over a planning horizon.

This dissertation studies the optimal control of two different dynamic systems with learning: (i) diagnostic service systems, and (ii) green incentive policy design. In both cases, analytical models have been developed to improve our understanding of the system, and managerial insights are gained on its optimal management.

We first consider a diagnostic service system in a queueing framework, where the service is in the form of sequential hypothesis testing. The agent should dynamically weigh the benefit of performing an additional test on the current task to improve the accuracy of her judgment against the incurred delay cost for the accumulated workload. We analyze the accuracy/congestion tradeoff in this setting and fully characterize the structure of the optimal policy. Further, we allow for admission control (dismissing tasks from the queue without processing) in the system, and derive its implications on the structure of the optimal policy and system's performance.

We then study Feed-in-Tariff (FIT) policies, which are incentive mechanisms by governments to promote renewable energy technologies. We focus on two key network externalities that govern the evolution of a new technology in the market over time: (i) technological learning, and (ii) social learning. By developing an intertemporal model that captures these dynamics, we investigate how lawmakers should leverage on such effects to make FIT policies more efficient. We contrast our findings against the current practice of FIT-implementing jurisdictions, and also determine how the FIT regimes should depend on specific technology and market characteristics.

This dissertation studies operations management problems in service operations and supply chains, analyzing the impact of strategic customers and disruptive technologies. We investigate three problems, and insights from the study of each one illuminate the effect of information and/or strategic customer behavior on decision makers in operations management systems.

The first problem involves the strategic routing behavior of customers in a service network with multiple stations, when customers can choose the order of stations that they visit. We propose a two-station game with all customers present at the start of service and deterministic service times, and we find that strategic customers "herd," i.e., in equilibrium all customers choose the same route. For unobservable systems, we prove that the game is supermodular, and we then identify a broad class of learning rules---which includes both fictitious play and Cournot best-response---that converges to herding in finite time. By combining different theoretical and numerical analyses, we find that the herding behavior is prevalent in many other congested open-routing service networks, including those with arrivals over time, those with stochastic service times, and those with more than two stations. We also find that the system under herding performs very close to the first-best outcome in terms of cumulative system time.

The second problem relates to a disruptive, on-demand delivery platform who provides delivery from an independent sit-down restaurant. Food delivery platforms maintain a symbiotic relationship with the existing providers in their industry; rather than "stealing" demand from an established player, these platforms work with restaurants to connect customers with the restaurant's product by providing an additional purchase channel. We model the restaurant as a queueing system with customer waiting costs. First, we solve the revenue maximization problem faced by a monopolist who controls both the dine-in and delivery prices and receives all revenues from the system. These results are related to the priority queueing and pricing literature and are of independent interest. We also demonstrate that a coordination problem exists between the restaurant and platform. We then investigate means of coordinating this supply chain via different contracts between the restaurant and the platform. We find that a two-way revenue-sharing contract coordinates the supply chain.

Finally, our third problem is spawned from an industry collaboration aimed at improving the inventory planning decisions of a company that sells high-tech goods with short life cycles. We develop a novel heuristic based on a power approximation in the extant literature. The power approximation computes near-optimal (s,S) policies for infinite-horizon inventory problems. We propose a new form of this approximation, devised using real demand data from our industry partner, and a heuristic based on the approximation that updates the inventory policy as new demand forecasts are generated. We evaluate the performance of our heuristic---also on real demand data, though for a different time period and for different items than were used to fit our model---and find that it performs quite well.

Decision tree optimization is notoriously difficult from a computational perspective but essential for the field of interpretable machine learning. Despite efforts over the past 40 years, only recently have optimization breakthroughs been made that have allowed practical algorithms to find \textit{optimal} decision trees. These new techniques have the potential to trigger a paradigm shift where it is possible to construct sparse decision trees to efficiently optimize a variety of objective functions without relying on greedy splitting and pruning heuristics that often lead to suboptimal solutions. The contribution in this work is to provide a general framework for decision tree optimization that addresses the two significant open problems in the area: treatment of imbalanced data and fully optimizing over continuous variables. We present techniques that produce optimal decision trees over a variety of objectives including F-score, AUC, and partial area under the ROC convex hull. We also introduce a scalable algorithm that produces provably optimal results in the presence of continuous variables and speeds up decision tree construction by several orders of magnitude relative to the state-of-the art.

Advanced information and production technologies are transforming the ways products can be produced and delivered, and hence present tremendous opportunities to reshape the global supply chains. This dissertation examines the operational implications of these technologies on production sequencing, supply chain inventory positioning, and spare parts logistics. These studies result in the following three essays. The first essay studies the optimal sequencing of two consecutive production stages when the random demands for multiple end products are correlated. We provide conditions to determine when operations reversal is beneficial under the long run average cost measure. The second essay examines a multi-echelon supply chain under evolving demand distributions, which is due to the dynamic world state driven by external factors. We provide analytical bounds for the optimal solutions, and further obtain easy-to-compute heuristics with superior performance. The third essay investigates the impact of adopting 3D printing technology on the spare parts logistics design. We construct a general framework for identifying the optimal supply option for each type of part: which part should be stocked, which should be printed, and which should be sourced in a hybrid way. We also propose simple heuristic solutions that yield close to optimal performance and interesting managerial insights. Collectively, the studies in this dissertation provide useful modeling ideas, decision tools, and guidance for firms to improve the operational performance of their supply chains.

Modern machine learning methods have demonstrated remarkable success in many indus- tries. For instance, the famous ChatGPT relies on a machine learning model trained with a substantial volume of text and conversation data. To achieve optimal model performance, an efficient optimization algorithm is essential for learning the model parameters. Among optimization methods, gradient descent (GD) methods are the simplest ones. Traditionally, GD methods have shown excellent performance in conventional machine learning problems with nice objective functions and simple training paradigms where computation occurs on a single server storing all the data. However, the understanding of how GD methods perform in modern machine learning problems with non-convex and non-smooth objective functions or more complex training paradigm remains limited.This thesis is dedicated to providing a theoretical understanding of why gradient descent methods excel in modern machine learning problems. In the first half of the thesis, we study stochastic gradient descent(SGD) in training multi-layer fully connected feedforward neural networks with Rectified Linear Unit (ReLU) activation. Since the loss function in training deep neural networks is non-convex and non-smooth, the standard convergence guarantees of GD for convex loss functions cannot be applied. Instead, through a kernel perspective, we demonstrate that when fresh data arrives in a stream, SGD ensures the exponential convergence of the average prediction error. In the second half, we investigate the utilization of GD methods in a new training paradigm, featuring a central parameter server (PS) and numerous clients storing data locally. Privacy constraints prevent the local data from being revealed to the PS, making this distributed learning setting particularly relevant in the current big-data era where data is often sensitive and too large to be stored on a single device. In practical applications, this distributed setting presents two major challenges: data heterogeneity and adversarial attacks. To overcome these challenges and achieve accurate estimates of model parameters, we propose a GD-based algorithm and provide convergence guarantees for both strongly convex and non-convex loss functions.

We propose an approximation scheme for single-product periodic-review inventory systems with L-natural-convex structure. We lay out three well-studied inventory models, namely the lost-sales system, the perishable inventory system, and the joint inventory-pricing problem. We approximate the value functions for these models by the class of L-natural-convex quadratic functions, through the technique of linear programming approach to approximate dynamic programming. A series of heuristics are derived based on the quadratic approximation, and their performances are evaluated by comparison with existing heuristics. We present the numerical results and show that our heuristics outperform the benchmarks for majority of cases and scale well with long lead times. In this dissertation we also discuss the alternative strategies we have tried but with unsatisfactory result.