
Eaton, M., S. Yurek, Z. Haider^{*}, M. Julien, F. Johnson, B. Udell, H. Charkhgard, C. Kwon. Spatial Conservation Planning under Uncertainty: Adapting to Climate Change Risks using Modern Portfolio Theory.
Ecological Applications, Accepted. [DOI] [DATA] Reserve design, spatial conservation planning, modern portfolio theory, multicriteria decision analysis, risk management, sealevel rise, urbanization, climate uncertainty [show abstract]
Climate change and urban growth impact habitats, species, and ecosystem services. To buffer against global change, an established adaptation strategy is designing protected areas to increase representation and complementarity of biodiversity features. Uncertainty regarding the scale and magnitude of landscape change complicates reserve planning and exposes decision makers to risk of failing to meet conservation goals. Conservation planning tends to treat risk as an absolute measure, ignoring the context of the management problem and risk preferences of stakeholders. Application to conservation of risk management theory emphasizes diversification of portfolio of assets, with the goal of reducing the impact of system volatility on investment return. We use principles of Modern Portfolio Theory (MPT), which quantifies risk as the variance and correlation among assets, to formalize diversification as an explicit strategy for managing risk in climatedriven reserve design. We extend MPT to specify a framework that evaluates multiple conservation objectives, allows decision makers to balance management benefits and risk when preferences are contested or unknown, and includes additional decision options such as parcel divestment when evaluating candidate reserve designs. We apply an efficient search algorithm that optimizes portfolio design for large conservation problems and a game theoretic approach to evaluate portfolio tradeoffs that satisfy decision makers with divergent benefit and risk tolerances, or when a single decision maker cannot resolve their own preferences. Evaluating several risk profiles for a case study in South Carolina, our results suggest that a reserve design may be somewhat robust to differences in risk attitude but that budgets will likely be important determinants of conservation planning strategies, particularly when divestment is considered a viable alternative. We identify a possible fiscal threshold where adequate resources allow protecting a sufficiently diverse portfolio of habitats such that the risk of failing to achieve conservation objectives is considerably lower. For a range of sealevel rise projections, conversion of habitat to open water (14180%) and wetland loss (17%) are unable to be compensated under the current protected network. In contrast, optimal reserve design outcomes are predicted to ameliorate expected losses relative to current and future habitat protected under the existing conservation estate.

Su. L.^{*}, C. Kwon. RiskAverse Network Design with Behavioral Conditional ValueatRisk for Hazardous Materials Transportation. Transportation Science, Accepted. [PDF] transportation; hazardous materials; network design; conditional valueatrisk; Benders decomposition [show abstract]
We consider a roadban problem in hazardous materials (hazmat) transportation. We formulate the problem as a network design problem to select a set of closed road segments for hazmat traffic and obtain a bilevel optimization problem. While modeling probabilistic routechoices of hazmat carriers by the random utility model (RUM) in the lower level, we consider a riskaverse measure called conditional valueatrisk (CVaR) in the upper level, instead of the widely used expected risk measure. Using RUM and CVaR, we quantify the risk of having hazmat accidents and large consequences, and design the network policy for roadbans accordingly. While CVaR has been used in hazmat routing problems, this paper is the first attempt to apply CVaR in risk averse hazmat network design problems considering stochastic routechoices of hazmat carriers. The resulting problem is a mixed integer nonlinear programming problem, for which we devise a line search approach combined with Benders decomposition. We demonstrate the efficiency of the proposed computational method with case studies. The average computation time for a network with 105 nodes and 268 arcs is 3 hours. Commercial solvers are inadequate to solve this problem, because the optimality gap is 99.9% after 24 hours just for a linear subproblem. By applying CVaR to the routechoice behavior of hazmat carriers, we protect the road network from undesirable routechoices that may lead to severe consequences. We define the Value of RUMCVaR Solutions (VRCS) over the deterministic model based on shortestpath problems and the expected risk measure. Our case study shows that VRCS can range from 4.9% to 64.1% depending on the probability threshold used in the CVaR measure.

Subramanian, V. T. K. Das, C. Kwon, A. Gosavi (2019). A DataDriven Methodology for Dynamic Pricing and Demand Response in Electric Power Networks. Electric Power Systems Research, 174,
105869. [DOI] [PDF] dynamic pricing; aggregated demand response; electric power network; Bayesian demand prediction [show abstract]
The practice of disclosing price of electricity before consumption (dynamic pricing) is essential to promote aggregatorbased demand response in smart and connected communities. However, both practitioners and researchers have expressed fear that wild fluctuations in demand response resulting from dynamic pricing may adversely affect the stability of both the network and the market. This paper presents a comprehensive methodology guided by a datadriven learning model to develop stable and coordinated strategies for both dynamic pricing as well as demand response. The methodology is designed to learn offline without interfering with network operations. Application of the methodology is demonstrated using simulation results from a sample 5bus PJM network. Results show that it is possible to arrive at stable dynamic pricing and demand response strategies that can reduce cost to the consumers as well as improve network load balance.

Melendez, K. A. ^{*}, V. Subramanian, T. K. Das, C. Kwon (2019). Empowering enduse consumers of electricity to aggregate for demandside participation. Applied Energy, 248, 372–382.
[DOI] Demandside participation; Aggregation of enduse consumers; Fairness; Peertopeer trading; Energy sharing using EVs; Optimization of power systems [show abstract]
Enduse consumers (peers) are being empowered to aggregate for direct demandside participation through load scheduling and energy sharing. This is the result of the growth of Internet of Things (IoT) enabled loads, availability of advanced metering infrastructure, and the move towards realtime (RT) pricing of electricity. Peertopeer (P2P) cooperation has received significant interest in recent years, though the focus of this growing body of research is on modeling prosumer behavior in microgrids. Hence, there is a need for new methodologies to examine empowerment of all enduse consumers (not limited to prosumers) to form aggregations and develop fair rules of cooperation to reduce cost. This paper offers an optimization based methodology to address the above need for power systems. It minimizes the total cost and considers fairness using a Nash bargaining approach. Since cost and fairness are often in conflict, tradeoff strategies are also presented. The model to asses fairness is nonlinear. Hence, it is transformed into a second order cone program (SOCP) and solved using GUROBI software version 7.5.2. The methodology is implemented on a sample 5bus network, built using price and demand data from one of the load zones of Pennsylvania, New Jersey, and Maryland (PJM) power network in the United States. It is shown that two aggregations of peers participating in the sample network can reduce their total cost by 14.17% and 22.7%, while maintaining fairness. Concluding remarks highlight some of the limitations of the methodology.

Sun, L.^{*}, M. Karwan, C. Kwon. PathBased Approaches to Robust Network Design Problems Considering Boundedly Rational Network Users. Transportation Research Record, accepted. [DOI] [PDF] networks and graphs; satisficing; network design; hazardous materials; bilevel optimization [show abstract]
Network users may choose nonshortest paths, when (1) they satisfice with suboptimal routes, or (2) they have perception errors of the decision environment. The notion of generalized bounded rationality has been recently proposed to create a unified framework for these two sources of behavioral uncertainty in route choices. When the notion of generalized bounded rationality is used in robust network design problems, we obtain a bilevel optimization problem with the minmax objective function at the upper level, with three layers of optimization in total. In this paper, we derive equivalent singlelevel pathbased formulations that are readily solvable by available optimization libraries. We show how to incorporate them into robust multicommodity network design problems in hazardous materials transportation.

Su, L.^{*}, L. Sun^{*}, M. Karwan, C. Kwon (2019). Spectral Risk Measure Minimization in Hazardous Materials Transportation. IISE Transactions, 59(6), 638–652. [DOI] [PDF] hazardous materials transportation; risk management; spectral risk; coherent risk measures [show abstract]
Due to catastrophic consequences of potential accidents in hazardous materials (hazmat) transportation, a riskaverse approach for routing is necessary. In this paper, we consider spectral risk measures, for riskaverse hazmat routing, which overcome challenges posed in the existing approaches such as conditional valueatrisk. In spectral risk measures, one can define the spectrum function precisely to reflect the decision maker's risk preference. We show that spectral risk measures can provide a unified routing framework for popular existing hazmat routing methods based on expected risk, maximum risk, and conditional valueatrisk. We first consider a special class of spectral risk measures, for which the spectrum function is represented as a step function. We develop a mixed integer linear programming model in hazmat routing to minimize these special spectral risk measures and propose an efficient search algorithm to solve the problem. For general classes of spectral risk measures, we suggest approximation methods and pathbased approaches. We propose an optimization procedure to approximate general spectrum functions using a step function. We illustrate the usage of spectral risk measures and the proposed computational approaches using data from real road networks.

Saghand, P.G., H. Charkhgard, C. Kwon (2019). A BranchandBound Algorithm for a Class of Mixed Integer Linear Maximum Multiplicative Programs: A Multiobjective Optimization Approach. Computers & Operations Research, 101, 263–274.
[DOI] Multiplicative programming; Multiobjective optimization; Optimization over the efficient set; Linear programming; Branchandbound algorithm [show abstract]
We present a linear programming based branchandbound algorithm for a class of mixed integer optimization problems with a bilinear objective function and linear constraints. This class of optimization problems can be viewed as a special case of the problem of optimization over the set of efficient solutions in multiobjective optimization. It is known that when there exists no integer decision variable, such a problem can be solved in polynomial time. In fact, in such a case, the problem can be transformed into a SecondOrder Cone Program (SOCP) and so it can be solved efficiently by a commercial solver such as CPLEX SOCP solver. However, in a recent study, it is shown that such a problem can be solved even faster in practice by using a biobjective linear programming based algorithm. So, in this study, we embed that algorithm in an effective branchandbound framework to solve mixed integer instances. We also develop several enhancement techniques including preprocessing and cuts. An extensive computational study demonstrate that the proposed branchandbound algorithm outperforms a commercial mixed integer SOCP solver. Moreover, the effect of different branching and node selecting strategies is explored.

Haider, Z.^{*}, A. Nikolaev, J. E. Kang, C. Kwon (2018). Inventory Rebalancing through Pricing in Public Bike Sharing Systems. European Journal of Operational Research,
270(1), 103–117. [DOI] [PDF] transportation; bikesharing; sharedmobility; rebalancing; pricing; heuristics [show abstract]
This paper presents a new conceptual approach to improve the operational performance of public bike sharing systems using pricing schemes. Its methodological developments are accompanied by experimental analyses with bike demand data from Capital Bikeshare program of Washington, DC. An optimized price vector determines the incentive levels that can persuade system customers to take bicycles from, or park them at, neighboring stations so as to strategically minimize the number of imbalanced stations. This strategy intentionally makes some imbalanced stations even more imbalanced, creating hub stations. This reduces the need for trucks and dedicated staff to carry out inventory repositioning. For smaller networks, a bilevel optimization model is introduced to minimize the number of imbalanced stations optimally. The results are compared with a heuristic approach that adjusts route prices by segregating the stations into different categories based on their current inventory profile, projected future demand, and maximum and minimum inventory values calculated to fulfill certain desired service level requirements. We use a routing model for repositioning trucks to show that the proposed optimization model and the latter heuristic approach, called the iterative price adjustment scheme (IPAS), reduce the overall operating cost while partially or fully obviating the need for a manual repositioning operation.

Zhang, A.^{*}, J. E. Kang, K. Axhausen, C. Kwon (2018). Multiday ActivityTravel Pattern Sampling Based on SingleDay Data. Transportation Research Part C: Emerging
Technologies, 89, 96–112. [DOI] [PDF] ActivityTravel Patterns; Daytoday variability; Interpersonal variability; Sampling Multiday ActivityTravel Patterns [show abstract]
Although it is important to consider multiday activities in transportation planning, multiday activitytravel data are expensive to acquire and therefore rarely available. In this study, we propose to generate multiday activitytravel data through sampling from readily available singleday household travel survey data. A key observation we make is that the distribution of interpersonal variability in singleday travel activity datasets is similar to the distribution of intrapersonal variability in multiday. Thus, interpersonal variability observed in crosssectional singleday data of a group of people can be used to generate the daytoday intrapersonal variability. The proposed sampling method is based on activitytravel pattern type clustering, travel distance and variability distribution to extract such information from singleday data. Validation and stability tests of the proposed sampling methods are presented.

Haider, Z.^{*}, H. Charkhgard, C. Kwon (2018). A Robust Optimization Approach for Solving Problems in Conservation Planning. Ecological Modelling, 368, 288–297. [DOI] [PDF] conservation planning; robust optimization; invasion control; reserve selection; biobjective mixed integer linear programming [show abstract]
In conservation planning, the data related to size, growth and diffusion of populations is sparse, hard to collect and unreliable at best. If and when the data is readily available, it is not of sufficient quantity to construct a probability distribution. In such a scenario, applying deterministic or stochastic approaches to the problems in conservation planning either ignores the uncertainty completely or assumes a distribution that does not accurately describe the nature of uncertainty. To overcome these drawbacks, we propose a robust optimization approach to problems in conservation planning that considers the uncertainty in data without making any assumption about its probability distribution. We explore two of the basic formulations in conservation planning related to reserve selection and invasive species control to show the value of the proposed robust optimization. Several novel techniques are developed to compare the results produced by the proposed robust optimization approach and the existing deterministic approach. For the case when the robust optimization approach fails to find a feasible solution, a novel biobjective optimization technique is developed to handle infeasibility by modifying the level of uncertainty. Some numerical experiments are conducted to demonstrate the efficacy of our proposed approach in finding more applicable conservation planning strategies.

Toumazis, I.^{*}, M. Kurt, A. Toumazi, L. Karakosta, C. Kwon. Comparative Effectiveness of UptoThree Lines of Chemotherapy Treatment Plans for Metastatic Colorectal Cancer. Medical Decision Making, Accepted.
[DOI] [PDF] [show abstract]
Modern chemotherapy agents transformed standard care for metastatic colorectal cancer (mCRC) but raised concerns about the financial burden of the disease. We studied comparative effectiveness of treatment plans that involve up to three lines of therapies and impact of treatment sequencing on health and cost outcomes. We employed a Markov model to represent the dynamically changing health status of mCRC patients and used MonteCarlo simulation to evaluate various treatment plans consistent with existing guidelines. We calibrated our model by a metaanalysis of published data from an extensive list of clinical trials and measured the effectiveness of each plan in terms of cost per qualityadjusted lifeyear (QALY). We examined the sensitivity of our model and results with respect to key parameters in two scenarios serving as base and worstcases for patients\T1\textquoteright overall and progression free survivals. The derived efficient frontiers included 7 and 5 treatment plans in base and worstcases, respectively. The incremental costeffectiveness ratio (ICER) ranged between \protect \T1\textdollar 26,260 and \protect \T1\textdollar 152,530 when the treatment plans on the efficient frontiers were compared against the least costly efficient plan in basecase, and between \protect \T1\textdollar 21,256 to \protect \T1\textdollar 60,040 in worstcase. All efficient plans were expected to lead to fewer than 2.5 AEs and on average successive AEs were spaced more than 9 weeks apart from each other in basecase. Based on ICER, all efficient treatment plans exhibit at least 87% chance of being efficient. Sensitivity analyses show that the ICERs were most dependent on drug acquisition cost, distributions of progression free and overall survivals, and health utilities. We conclude that improvements in health outcomes may come at high incremental costs and are highly dependent in the order treatments are administered.

Chung, B.D., S. Park, C. Kwon (2018). Equitable Distribution of Recharging Stations for Electric Vehicles. SocioEconomic Planning Science, 63, 1–11. [DOI] [PDF] electric vehicles; flow refueling location problem; demand equity; flow equity [show abstract]
Given the limited driving range of battery electric vehicles and lack of sufficient charging infrastructure, locating charging stations is an important decision problem to enable longdistance travels by battery electric vehicles. This paper considers an important political factor in such location problems: the equitable access to charging stations among geographical regions. We propose three types of equity constraints to the flow refueling location model: two constraints based on travel demand and the other based on flow. For solving the problem with flow equity constraints, we propose a multiphase heuristic method. We test the proposed models and computational method in a real expressway network in Korea.

Zhang, A.^{*}, J.E. Kang, C. Kwon (2017). Incorporating Demand Dynamics in MultiPeriod Capacitated Fastcharging Location Planning for Electric Vehicles. Transportation Research Part B: Methodological, 103,
5–29. [DOI] [PDF] [DATA] electric vehicles; facility location; flow refueling location problem; multiperiod planning; vehicle market demand dynamics; alternative fuel vehicles [show abstract]
We develop a multiperiod capacitated flow refueling location problem for electric vehicles (EVs) as EV market responds to the charging infrastructure. The optimization model will help us determine the optimal location of chargers as well as the number of charging modules at each station over multiple time periods. We define a number of demand dynamics, including flow demand growth varying with charging opportunities on path as well as demand growing naturally with less affect from charging infrastructure, with two objective functions (one maximizing flow coverage and the other maximizing electric vehicle demand). A case study based on a road network around Washington, D.C., New York City, and Boston is presented to provide numerical experiments related to demand dynamics, showing the potential problems in multiperiod planning.

Ahmed, M.T.^{*}, J. Zhuang and C. Kwon (2017). Understanding Conflicting Interests of a Government and a Tobacco Manufacturer: A GameTheoretic Approach. Group Decision and Negotiation, 26(6), 1209–1230.
[DOI] [PDF] Farming; Subsidy; Food security; Rice; Tobacco; Nash Equilibrium [show abstract]
Rice is the staple food of nearly half of the population of the world, most of whom live in developing countries. Ensuring a domestic supply of rice from outside sources is difficult for developing countries as less than 5% of the total world\T1\textquoteright s production is available for international trade. Hence, in order to ensure domestic food security, e.g., food availability and access, governments provide subsidies in agriculture. In many occasions, public money used for the subsidy goes toward promoting undesirable crops like tobacco. Although the strategic interaction between governments and manufacturers is critical, it has not been studied in the literature. This study fills this gap by considering a game between a government (of a developing country) and a tobacco manufacturer in which the government decides on a mix of subsidies and the tobacco manufacturer decides on declaring a purchasing price of tobacco. We provide a numerical study to show that controlling the output harvest price is more effective in reaching the desired end result for both the government and the tobacco manufacturer. A subsidy in fertilizer results in the measurable increase in the government spending but does not have significant effect in reaching the production target. The fertilizer subsidy should be provided only when the output price is too high to be affordable for the population.

Sun, L.^{*}, M. Karwan, C. Kwon (2018). Generalized Bounded Rationality and Robust Multicommodity Network Design. Operations Research, 66(1), 42–57. [DOI] [PDF] bounded rationality; satisficing; perception; network design; robust optimization; inverse optimization [show abstract]
Often network users are not perfectly rational, especially when they are satisficingrather than optimizingdecision makers and each individual's perception of the decision environment reflects personal preferences or perception errors due to lack of information. While the assumption of satisficing drivers has been used in modeling route choice behavior, this research uses a linkbased perception error model to describe driver's uncertain behavior, without assuming stochasticity. In congestionfree networks, we show that the perception error model is more general than the existing bounded rationality models with satisficing drivers with special cases when the two approaches yield the same results; that is, satisficing under accurate perception is equivalent to optimizing under inaccurate perception. This motivates us to define generalized bounded rationality in route choice behavior modeling. The proposed modeling framework is general enough to capture linkspecific costperception of drivers. We use a Monte Carlo method to estimate modeling parameter values to guarantee a certain coverage probability in comparison with the random utility model. We demonstrate how the notion of generalized bounded rationality can be used in robust multicommodity network design problems and devise a cutting plane algorithm. We illustrate our approaches in the context of hazardous materials transportation.

Taslimi, M.^{*}, R. Batta, C. Kwon (2017). A Comprehensive Modeling Framework for Hazmat Network Design, Hazmat Response Team Location, and Equity of Risk. Computers and Operations Research, 79, 119–130. [DOI]
[PDF] Hazmat emergency response team; Bilevel network design; Greedy heuristic algorithm; Equity of risk; Robust solution [show abstract]
This paper considers a bilevel hazmat transportation network design problem in which hazmat shipments have to be transported over a road network between specified origindestination points. The bilevel framework involves a regulatory authority and hazmat carriers. The control variables for the regulatory authority are locations of hazmat response teams and which additional links to include for hazmat travel. The regulatory authority (upper level) aims to minimize the maximum transport risk incurred by a transportation zone, which is related to risk equity. Our measure of risk incorporates the average response time to the hazmat incidents. Hazmat carriers (lower level) seek to minimize their travel cost. Using optimality conditions, we reformulate the nonlinear bilevel model into a singlelevel mixed integer linear program, which is computationally solvable for medium size problems using a commercial solver. For large size problems, we propose a greedy heuristic approach, which we empirically demonstrate to find good solutions with reasonable computational effort. We also seek a robust solution to capture stochastic characteristics of the model. Experimental results are based on popular test networks from the Sioux Falls and Albany areas.

Li, X., R. Batta, C. Kwon (2017). Effective and Equitable Supply of Gasoline to Impacted Areas in the Aftermath of a Natural Disaster. SocioEconomic Planning Sciences, 57, 25–34. [DOI] [PDF] humanitarian logistics, disaster operations management, location, allocation [show abstract]
The focus of this research is on supplying gasoline after a natural disaster. There are two aspects for this work: determination of which gas stations should be provided with generators (among those that do not have electric power) and determination of a delivery scheme that accounts for increased demand due to lack of public transportation and considerations such as equity. We develop an MIP for this situation. Two case studies based on Hurricane Sandy in New Jersey are developed and solved in CPLEX.

Chung, S. H. and C. Kwon (2016). Integrated Supply Chain Management for Perishable Products: Dynamics and Oligopolistic Competition Perspectives with Application to Pharmaceuticals. International Journal of Production Economics, 179, 117–129.
[DOI] [PDF] pharmaceutical supply chain, perishable inventory dynamics, oligopolistic competition, variational inequality, interior point methods [show abstract]
We propose an integrated supply chain management framework that allows us to explicitly consider the impact of product perishability on a broad scale that includes manufacturers, distribution centers, wholesalers, and demand markets. The framework proposed herein also makes it possible to consider the oligopolistic competition across wholesalers that drives price and demand fluctuations. Furthermore, the supply chain decision rules are derived from necessary conditions in the framework. The inclusion of such salient features allows the framework to generate outcomes that suggest realistic managerial insights. We provide a numerical example in which two multinational pharmaceutical firms producing a homogeneous medicinal drug and four oligopolistic wholesalers are considered.

Esfandeh, T.^{*}, R. Batta, and C. Kwon (2018). TimeDependent Hazardousmaterials Network Design Problem. Transportation Science, 52(2), 454–473. [DOI] [PDF]
[DATA] hazardous materials transportation; network design; column generation; label setting [show abstract]
We extend the hazardousmaterials (hazmat) network design problem to account for the timedependent road closure as a policy tool in order to reduce hazmat transport risk by altering carriers' departure times and route choices. We formulate the timedependent network design problem using an alternativebased model with each alternative representing a combined path and departuretime choice. We also present an extended model that can not only account for consecutive timebased road closure policies, but also allow stopping at the intermediate nodes of the network in the routing/scheduling decisions of the carriers. Heuristic algorithms based on columngeneration and labelsetting are presented. To illustrate the advantages that can be gained through the use of our methodology, we present results from numerical experiments based on a transportation network from Buffalo, NY. To investigate the impact of the extensions, we consider three versions of the problem by gradually refining the model. We show that under consideration of extensions, the design policies are more applicable and effective.

Kumar, A. A., J. E. Kang, C. Kwon, and A. Nikolaev (2016). Inferring OriginDestination Pairs and UtilityBased Travel Preferences for Shared Mobility Systems Users in a MultiModal Environment. Transportation Research Part B:
Methodological, 91, 270–291. [DOI] [PDF] OriginDestination estimation, Traveler preferences, Expectation Maximization, Probabilistic inference, Multimodal route choice, Bike Sharing Systems, Shared Mobility Systems [show abstract]
This paper presents a methodological framework to identify populationwide traveler type distribution and simultaneously infer individual travelers' OriginDestination (OD) pairs, based on the individual records of a shared mobility (bike) system use in a multimodal travel environment. Given the information about the travelers' outbound and inbound bike stations under varied price settings, the developed Selective Set Expectation Maximization (SSEM) algorithm infers an underlying distribution of travelers over the given traveler ``types. or ``classes. treating each traveler's OD pair as a latent variable; the inferred most likely traveler type for each traveler then informs their most likely OD pair. The experimental results based on simulated data demonstrate high SSEM learning accuracy both on the aggregate and dissagregate levels.

Sun, L.^{*}, M. H. Karwan, C. Kwon (2016). Implications of Cost Equity Consideration in Hazmat Network Design. Transportation Research Record: Journal of the
Transportation Research Board, No. 2567, Transportation Research Board, Washington, D.C.,
2016, pp. 67–77. [DOI] [PDF] [show abstract]
The hazmat network design problem (HNDP) aims to reduce the risk of transporting hazmat in the network by enforcing regulation policies. The goal of reducing risk can increase cost for different hazmat carriers. Since HNDP involves multiple parties, it is essential to take the cost increase of all carriers into consideration for the implementation of the regulation policy. While we can consider cost by placing upper bounds on the total increase, the actual cost increase for various OD pairs can differ, which results in unfairness among carriers. Thus we propose to consider the cost equity issue as well in HNDP. Additionally, due to the existence of multiple solutions in current HNDP models and the possibility of unnecessarily closing road segments, we introduce a new objective considering the length of all the closed links. Our computational experience is based on a real network and we show results under different cost consideration cases.

Esfandeh, T.^{*}, C. Kwon, R. Batta (2016). Regulating Hazardous Materials Transportation by Dual Toll Pricing. Transportation Research Part B: Methodological, 83,
20–35. [DOI] [PDF] hazardous material transportation; toll setting; nonconvex optimization; bilevel programming [show abstract]
We investigate dualtoll setting as a policy tool to mitigate the risk of hazardous material (hazmat) shipment in road networks. We formulate the dualtoll problem as a bilevel program wherein the upper level aims at minimizing the risk, and the lower level explores the user equilibrium decision of the regular vehicles and hazmat carriers given the toll. When the upper level objective is to minimize the risk and all links are tollable, we decompose the formulation into firststage and secondstage, and suggest a computational method to solve each stage. Our twostage solution methodology guarantees nonnegative valid dual tolls regardless of the solution accuracy of the firststage problem. We also consider a general dualtoll setting problem where the regulator rather wishes to minimize a combination of risk and the paid tolls and/or some links are untollable. To solve this truly bilevel problem, we provide heuristic algorithms that decompose the problem into subproblems each being solved by a line search. Case studies based on the Sioux Falls network illustrate the insights on the dualtoll policies.

Sun, L.^{*}, M. Karwan, and C. Kwon (2016). Incorporating Driver Behaviors in Network Design Problems: Challenges and Opportunities. Transport Reviews, 36(4), 454–478. [DOI] [PDF] network design; behavior route choice; random utility; random regret; bounded rationality; cumulative prospect theory; fuzzy logic; dynamic learning; SILK theory [show abstract]
The goal of network design problem (NDP) is to make optimal decisions to achieve a certain objective such as minimizing total travel time or maximizing tolls collected in the network. A critical component to NDP is how travelers make their route choices. Researchers in transportation have adopted human decision theories to describe more accurate route choice behaviors. In this paper, we review the NDP with various route choice models: the random utility model (RUM), Random RegretMinimization (RRM) model, bounded rationality (BR), cumulative prospect theory (CPT), the fuzzy logic model (FLM) and dynamic learning models (DLM). Moreover, we identify challenges in applying behavioral route choice models to NDP and opportunities for future research.

Hwang, H., J. Park, S. H. Chang, N. Attard, S. Wells, C. Kwon, K. Friedman (2015). The Ties that Bind: Economic and Freight Transportation Implications of U.S.Canada Border Bridges Using a Binational Transportation NetworkCombined Economic Model. Research
in Transportation Business & Management, 16, 32–49. [DOI] [PDF] Crossborder freight; trade network analysis; border wait time; Binational TransNIEMO [show abstract]
This study combines USCanada binational highway network data with a freight flow dataset using ports of entry (POE) via highway border crossings. Through several subprocedures, the US and Canada highway systems are integrated into a single network dataset. In addition, border wait time dataset was monitored and analyzed to set the border delay baseline. This dataset enables us to explore the freight traffic pattern between the US and Canada. Weighted Eigenvector Score is computed using a Social Network Analysis tool. The results demonstrate that major regional bodies are the primary users of major POE between the US and Canada. This study not only offers an improved understanding of the economic implications of USCanada border crossings, but also contributes to developing a simulation tool, a binational Transportationcombined National Interstate Economic Model. Such a tool is expected to extend and apply to other contexts, such as transportation and national and binational security, among other applications. Additionally, this study suggests several important considerations for US and Canadian officials charged with devising policy to protect against security threats while facilitating legitimate flows of goods, services and people across the border.

Sun, L.^{*}, M. Karwan, and C. Kwon (2016). Robust Hazmat Network Design Problems Considering Risk Uncertainty. Transportation Science, 50(4), 1188–1203. [DOI] [PDF]
hazardous materials transportation; network design; robust optimization [show abstract]
We study robust network design problems for hazardous materials transportation considering risk uncertainty. Risk uncertainty is considered in two ways: (1) uncertainty on each link across all shipments, and (2) uncertainty on each link for each shipment. We extend an existing heuristic framework to solve these two robust network design problems and propose a Lagrangian relaxation heuristic to solve subproblems within the framework. We present our computational experiences and illustrate general insights based on real networks.

Toumazis, I^{*}. and C. Kwon (2016). Worstcase Conditional ValueatRisk Minimization for Hazardous Materials Transportation. Transportation Science, 50(4), 1174–1187. [DOI] [PDF] [DATA] hazardous materials transportation; conditional valueatrisk; robust optimization
[show abstract]
Despite significant advances in risk management, routing hazardous materials (hazmat) has relied on relatively simpler methods. In this paper, we formally introduce an advanced risk measure, called conditional valueatrisk (CVaR), applied to truck routing problems for hazmat transportation. We find that CVaR offers a flexible, riskaverse, and computationally tractable routing method that is adequate to mitigate hazmat accidents. We further extend CVaR to consider the worstcase CVaR (WCVaR) under data uncertainty. The two important data types in hazmat transportation are accident probabilities and accident consequences, both of which are subject to many ambiguous factors. In addition, historical data are usually insufficient to construct probability distribution of accident probabilities and consequences. This motivates a new robust optimization approach to consider and compute WCVaR. Important axioms are studied for both CVaR and WCVaR risk measures to be coherent and appropriate in the context of hazmat transportation, and computational methods are proposed. We demonstrate the proposed notions of CVaR and WCVaR through a case study in a realistic road network.

Hariharan, V.G., D. Talukdar, and C. Kwon (2015). Optimal Targeting of Advertisement for New Products with Multiple Consumer Segments. International Journal of Research in
Marketing, 32(3), 263–271. [DOI] [PDF] [PDF] new product diffusion; advertisement; targeting; social contagion; dynamic optimization [show abstract]
Armed with improved targeting technology, firms are increasingly interested to optimize their advertising dollars through consumer segmentspecific targeting, particularly while introducing new products. That task becomes especially important in markets with distinct consumer segments \T1\textendash the early market and the main market \T1\textendash that affect each other\T1\textquoteright s adoption behavior. In this study, in contrast to prior normative studies that assume a singlesegment market structure, we derive dynamic optimal advertising and segmentspecific targeting strategies for firms facing a twosegment market structure. We allow for mutual demand interactions between the two segments, and for the diffusion parameters, advertising sensitivity, and cost of targeting to differ across the segments. We model the effect of advertising as a logarithmic function that accounts for diminishing marginal returns. Among our key findings: From profit optimization perspective, our twosegment model outperforms the singlesegment model under multiple diffusion dynamics contexts \T1\textendash especially for the \T1\textquoteleft bimodal chasm\T1\textquoteright and the \T1\textquoteleft early dip followed by bellshaped\T1\textquoteright type diffusion patterns \T1\textendash even when the cost of targeting the early market is relatively high. Our numerical analyses indicate that the optimal share of advertisement targeted to the early market segment at launch needs to be much higher than the share of the early market segment in the population. Advertising sensitivity, relative cost of targeting the early market, and the proportion of early market consumers in the population have the greatest effects on the optimal time to transition the targeted advertising spending from the early to the main market segment.

Chung, S. H. and C. Kwon (2015). MultiPeriod Planning for ElectricCar Charging Station Locations: a Case of Korean Expressways. European Journal of Operational Research. 242(2), 677–687.
[DOI] [PDF] [DATA] flowrefueling location; electric vehicles; multiperiod planning; Korean Expressways [show abstract]
One of the most critical barriers to widespread adoption of electric cars is the lack of charging station infrastructure. Although it is expected that a sufficient number of charging stations will be constructed eventually, due to various practical reasons they may have to be introduced gradually over time. In this paper, we formulate a multiperiod optimization model based on a flowrefueling location model for strategic charging station location planning. We also propose two myopic methods and develop a case study based on the real traffic flow data of the Korean Expressway network in 2011. We discuss the performance of the three proposed methods.

Lee, T. and C. Kwon (2014). A Short Note on the Robust Combinatorial Optimization Problems with Cardinality Constrained Uncertainty. 4OR, 12(4), 373–378. [DOI] [PDF] [CODE] robust combinatorial optimization; discrete optimization [show abstract]
Robust combinatorial optimization problems with cardinality constrained uncertainty may be solved by a finite number of nominal problems. In this paper, we show that the number of nominal problems to be solved can be reduced significantly.

Park, J., C. Kwon, and M. Son (2014). Economic Implications of the CanadaU.S. Border Bridges: Applying a Binational Economic Model for Canada and the U.S.. Research in Transportation Business and Management,
11, 123–133. [DOI] [PDF] Border bridges; congestion; freight transportation; economic costs [show abstract]
This study provides an approach to measure the economic costs stemming from delays on the bridges connecting the U.S. and Canada. We selected the busiest bridges in the U.S. and Canada that connects the BuffaloNiagara Metropolitan region and the Ontario province. Separated by the Great Lakes and waterways, Ontario has a significant portion of its trade activities with the U.S. by way of freight transportation crossing border bridges connecting the two countries. Using binational economic models, we found that the economic implications of the CanadaU.S. border bridges are in the range of $120,000 to $400,000 per day in total. Furthermore, the binational economic models we developed have provided which industries are most impacted from the freight delays on the bridges based on diverse scenarios. Our modeling approach and scenario development process provide diverse simulation tests with the changes of freight transportation costs and patterns for key sectors.

Kang, Y.^{*}, R. Batta and C. Kwon (2014). ValueatRisk Model for Hazardous Material Transportation. Annals of Operations Research, 222(1), 361–387. [DOI]
[PDF] [DATA] hazardous materials transportation; valueatrisk; social risk mitigation [show abstract]
This paper introduces a ValueatRisk (VaR) model to generate route choices for a hazmat shipment based on a specified risk confidence level. VaR is a threshold value such that the probability of the loss exceeding the VaR value is less than a given probability level. The objective is to determine a route which minimizes the likelihood that the risk will be greater than a set threshold. Several properties of the VaR model are established. An exact solution procedure is proposed and tested to solve the singletrip problem. To test the applicability of the approach, routes obtained from the VaR model are compared with those obtained from other hazmat objectives, on a numerical example as well as a hazmat routing scenario derived from the Albany district of New York State. Depending on the choice of the confidence level, the VaR model gives different paths from which we conclude that the route choice is a function of the level of risk tolerance of the decisionmaker. Further refinements of the VaR model are also discussed.

Berglund, P. G.^{*} and C. Kwon (2014). Solving a Location Problem of a Stackelberg Firm Competing with CournotNash Firms. Networks and Spatial Economics, 14(1), 117–132. [DOI]
[PDF] Location Analysis; StackelbergCournotNash Equilibrium; Game Theory; Variational Inequality; Simulated Annealing [show abstract]
We study a discrete facility location problem on a network, where the locating firm acts as the leader and other competitors as the followers in a StackelbergCournotNash game. To maximize expected profits the locating firm must solve a mixedinteger problem with equilibrium constraints. Finding an optimal solution is hard for large problems, and fullenumeration approaches have been proposed in the literature for similar problem instances. We present a heuristic solution procedure based on simulated annealing. Computational results are reported.

Kang, Y.^{*}, R. Batta and C. Kwon (2014). Generalized Route Planning Model for Hazardous Material Transportation with VaR and Equity Considerations. Computers & Operations Research, 43, 237–247. [DOI]
[PDF] [DATA] ValueatRisk; multitrip hazmat transportation; social risk mitigation; risk equity; dissimilar path [show abstract]
Recently, the ValueatRisk (VaR) framework was introduced for the routing problem of a single hazmat trip. In this paper, we extend the VaR framework in two important ways. First, we show how to apply the VaR concept to a more realistic multitrip multihazmat type framework, which determines routes that minimize the global VaR value while satisfying equity constraints. Second, we show how to embed the algorithm for the single hazmat trip problem into a Lagrangian relaxation framework to obtain an efficient solution method for this general case. We test our computational experience based on a reallife hazmat routing scenario in the Albany district of New York State. Our results indicate that one can achieve a high degree of risk dispersion while controlling the VaR value within the desired confidence level.

Berglund, P. G.^{*} and C. Kwon (2014). Robust Facility Location Problem for Hazardous Waste Transportation. Networks and Spatial Economics, 14(1), 91–116. [DOI] [PDF]
Location problem; Hazardous waste facility; Robust optimization; Genetic algorithm [show abstract]
We consider a robust facility location problem for hazardous materials (hazmat) transportation considering routing decisions of hazmat carriers. Given a network and a known set of nodes from which hazmat originate, we compute the locations of hazmat processing sites (e.g. incinerators) which will minimize total cost, in terms of fixed facility cost, transportation cost, and exposure risk. We assume that hazmat will be taken to the closest existing processing site. We present an exact full enumeration method, which is useful for small or mediumsize problems. For larger problems, the use of a genetic algorithm is explored. Through numerical experiments, we discuss the impact of uncertainty and robust optimization in the hazmat combined locationrouting problem.

Ahmed, M. T.^{*} and C. Kwon (2014). Optimal ContractSizing in Online Display Advertising for Publishers with Regret Considerations. Omega, 42(1), 201–212. [DOI] [PDF] Newsboy problem; Operations management; Risk [show abstract]
In this paper, we study optimal contract problems for online display advertisements with payperview pricing scheme. We first provide and analyze a single contract model, which is shown to be equivalent to the newsvendor problem. We then consider a stochastic optimization problem with two different advertisements and show that a contract to display both of them is not optimal for a riskneutral publisher. However, we show that a contract to display of both advertisements may be optimal when we consider the risk attitude of the publisher. Numerical experiments illustrate the change of optimal strategy for different risk levels.

Toumazis, I.^{*} and C. Kwon (2013). Routing Hazardous Materials on TimeDependent Networks using Conditional ValueatRisk. Transportation Research Part C: Emerging Technologies, 37,
73–92. [DOI] [PDF] [DATA] dynamic shortest path; timedependent network; conditional valueatrisk; hazardous materials transportation [show abstract]
We propose a new method for mitigating risk in routing hazardous materials (hazmat), based on the conditional valueatrisk (CVaR) measure, on timedependent vehicular networks. The CVaR models are shown to be flexible and general routing models for hazmat transportation, and can be solved efficiently. This paper extends the previous research by considering CVaR for hazmat transportation in the case where accident probabilities and accident consequences are timedependent. We provide a numerical method to determine an optimal departure time and an optimal route for a given origindestination pair. The proposed algorithm is tested in a realistic road network in Buffalo, NY, USA and the results are discussed.

Kwon, C., T. Lee, P. G. Berglund^{*} (2013). Robust Shortest Path Problems with Two Uncertain Multiplicative Cost Coefficients. Naval Research Logistics, 60(5), 375–394. [DOI] [PDF]
[CODE] robust shortest path; budgeted uncertainty; hazardous materials transportation [show abstract]
We consider a robust shortest path problem when the cost coefficient is the product of two uncertain factors. We first show that the robust problem can be solved in polynomial time by a dual variable enumeration with shortest path problems as subproblems. We also propose a path enumeration approach using a $K$shortest paths finding algorithm that may be efficient in many real cases. An application in hazardous materials transportation is discussed and the solution methods are illustrated by numerical examples.

Ahmed, M.T.^{*} , and C. Kwon (2012). Pricing Game of Online Display Advertisement Publishers. European Journal of Operational Research, 219, 477487.
[DOI] [PDF] online display advertising; optimal pricing; Nash equilibrium; newsvendor problem [show abstract]
We consider an online display advertisement publisher who maximizes the revenue by optimal pricing in an oligopoly setting. Each publisher interacts with others though setting costperimpression (CPM) that affects the demand for everyone. Using the pseudoconcavity of the objective function, we study the best response of the publisher while her strategy space changes. We also consider the sensitivity of the publisher while other publishers changes their CPM. In both cases, the best response of the publisher depends entirely on her current best response CPM. We provide an algorithm for finding the equilibrium and illustrate by numerical examples.

Srinivasan, A.^{*} and C. Kwon (2012). Operations of Online Advertising Services and Publisher's Option. Journal of the Operational Research Society, 63, 674–682.
[DOI] [PDF] online advertising; Nash bargaining game; option contract [show abstract]
We analyse the use of options for online advertisement publishers. By providing a discount or rewards to advertisers, publishers can utilize their uncertain service capacity, pageviews, more efficiently. We use Generalized Nash Bargaining to study the feasibility of the option contract and solve for an optimal value for the option price. We compare the revenues and benefits from advertisements under the option contract, with those without the options using numerical studies. We also study the impact of pricing and other components in the game on the optimal option price, the publisher's revenues, and the advertiser's benefits from the advertisements.

Chung, B.D., J. Li, T. Yao, C. Kwon and T. L. Friesz (2012). Demand Learning and Dynamic Pricing under Competition in a StateSpace Framework. IEEE Transactions on Engineering
Management, 59(2), 240–249. [DOI] [PDF] Competition, demand learning, differential variational inequality, dynamic pricing, Markov chain Monte Carlo, nonlinear time series [show abstract]
In this paper, we propose a revenue optimization framework integrating demand learning and dynamic pricing for firms in monopoly or oligopoly markets. We introduce a statespace model for this revenue management problem, which incorporates gametheoretic demand dynamics and nonparametric techniques for estimating the evolution of underlying state variables. Under this framework, stringent model assumptions are removed. We develop a new demand learning algorithm using Markov chain Monte Carlo methods to estimate model parameters, unobserved state variables, and functional coefficients in the nonparametric part. Based on these estimates, future price sensitivities can be predicted, and the optimal pricing policy for the next planning period is obtained. To test the performance of demand learning strategies, we solve a monopoly firm's revenue maximizing problem in simulation studies. We then extend this paradigm to dynamic competition, where the problem is formulated as a differential variational inequality. Numerical examples show that our demand learning algorithm is efficient and robust.

Wang, J.^{*}, Y. Kang^{*}, C. Kwon and R. Batta (2012). Dual Toll Pricing for Hazardous Material Transport with Linear Delay. Networks and Spatial Economics, 12, 147–165.
[DOI] [PDF] hazardous materials; toll pricing; congestion; risk [show abstract]
In this paper, we propose a dual toll pricing method to mitigate risk of hazardous materials (hazmat) transportation. We aim to simultaneously control both regular and hazmat vehicles to reduce the risk. In our model, we incorporate a new risk measure to consider durationpopulationfrequency of hazmat exposure. We first formulate the model as a Mathematical Program with Equilibrium Constraints (MPEC). Then we decompose the MPEC formulation into firststage and secondstage problems. Separate methods are developed to solve each stage. A numerical example is provided and possible extensions are discussed.

Jung, T.^{*} and C. Kwon (2011). RetailerSupplier Matching: an Application of the Deferred Acceptance Algorithm. International Journal of Services Operations and Informatics,
6(3), 248–258. [DOI] [PDF] [show abstract]
In this paper, we apply matching theory to supply chain coordination. We present mathematical optimization models similar to the newsvendor problem to provide appropriate conditions for retailersupplier matching. In particular, our matching algorithm, compared to the general matching theory, has uniquely been affected by contract sizes and ordering sequences. We also study that our matching application guarantees stable and optimal outcomes. Numerical examples with various parameter settings are provided to test the feasibility of the matching algorithms. We find that we can avoid the worst matching case when we use the proposed matching algorithms.

Friesz, T. L., T. I. Kim, C. Kwon and M. A. Rigdon (2011). Approximate Network Loading and Dual Time Scale Dynamic User Equilibrium. Transportation Research Part B,
45(1), 176207. [DOI] [PDF] dynamic user equilibrium; differential variational inequalities; differential algebraic equations; dualtimescale; fixedpoint algorithm in Hilbert space [show abstract]
In this paper we present a dualtimescale formulation of dynamic user equilibrium (DUE) with demand evolution. Our formulation belongs to the problem class that Pang and Stewart (2008) refer to as differential variational inequalities. It combines the withinday time scale for which route and departure time choices fluctuate in continuous time with the daytoday time scale for which demand evolves in discrete time steps. Our formulation is consistent with the often told story that drivers adjust their travel demands at the end of every day based on their congestion experience during one or more previous days. We show that analysis of the withinday assignment model is tremendously simplified by expressing dynamic user equilibrium as a differential variational inequality. We also show there is a class of daytoday demand growth models that allow the dualtimescale formulation to be decomposed by timestepping to yield a sequence of continuous time, singleday, dynamic user equilibrium problems. To solve the singleday DUE problems arising during timestepping, it is necessary to repeatedly solve a dynamic network loading problem. We observe that the network loading phase of DUE computation generally constitutes a differential algebraic equation (DAE) system, and we show that the DAE system for network loading based on the link delay model (LDM) of Friesz et al. (1993) may be approximated by a system of ordinary differential equations (ODEs). That system of ODEs, as we demonstrate, may be efficiently solved using traditional numerical methods for such problems. To compute an actual dynamic user equilibrium, we introduce a continuous time fixedpoint algorithm and prove its convergence for effective path delay operators that allow a limited type of nonmonotone path delay. We show that our DUE algorithm is compatible with network loading based on the LDM and the cell transmission model (CTM) due to Daganzo (1995). We provide a numerical example based on the much studied Sioux Falls network.

Moon. Y. and C. Kwon (2011). Online Advertisement Service Pricing and an Option. Electronic Commerce Research and Applications, 10(1), 3848.
[DOI] [PDF] online advertisements, option contract, Nash bargaining, clickthrough rate, utility maximization [show abstract]
For the Internet advertisement market, we consider a contract problem between advertisers and publishers. Among several ways of pricing online advertisements, the methods based on costperimpression (CPM) and costperclick (CPC) are the two most popular. The CPC fee is proportional to the clickthrough rate (CTR), which is uncertain and makes decisions of advertisers and publishers difficult. In this paper, we suggest a hybrid pricing scheme: advertisers pay the minimum of CPM and CPC fees by purchasing an option from publishers. To determine the option price, we consider a Nash bargaining game for negotiation between an advertiser and a publisher and provide the solution. Further, we show that such option contracts will help the advertiser avoid high cost and the publisher generate more revenue. The option contract will also improve the contract feasibility, compared to CPM and CPC.

Kwon, C. (2011). SinglePeriod Balancing of PayPerClick and PayPerView Online Display Advertisements. Journal of Revenue and Pricing Management, 10(3), 261270. [DOI] [PDF] online advertising; display advertisements; costperimpression; costperclick; clickthroughrate; web publisher [show abstract]
In this article, we study a balancing problem of web publishers for payperview and payperclick contracts for online display advertising. Considering the details of contracts, we refine prior research results on the recommendation of optimal strategies. We examine the problem by formalizing a simple stochastic optimization problem for a single period of advertising contracts. We investigate how pricing and other contract components will affect the optimal display strategies analytically and numerically.

Kwon, C., T. L. Friesz, R. Mookherjee, T. Yao and B. Feng (2009). Noncooperative Competition Among Revenue Maximizing Service Providers with Demand Learning. European Journal of
Operational Research, 197(3), 981996. [DOI] [PDF] Revenue management, Pricing, Demand learning, Differential games, Kalman filters [show abstract]
This paper recognizes that in many decision environments in which revenue optimization is attempted, an actual demand curve and its parameters are generally unobservable. Herein, we describe the dynamics of demand as a continuous time differential equation based on an evolutionary game theory perspective. We then observe realized sales data to obtain estimates of parameters that govern the evolution of demand; these are refined on a discrete time scale. The resulting model takes the form of a differential variational inequality. We present an algorithm based on a gap function for the differential variational inequality and report its numerical performance for an example revenue optimization problem.

Kwon, C. and T. L. Friesz (2008). Valuation of American Options by the Gradient Projection Method. Applied Mathematics and Computation, 206(1), 380388. [DOI]
[PDF] American options, variational inequalities, gradient projection [show abstract]
We study an equivalent optimization problem with an inequality constraint and boundary conditions, whose necessary condition for optimality is the variational inequality presentation of American options. To solve the problem, we use the gradient projection method, with discretizations both in time and space. We tested the algorithm and compared with the projective successive overrelaxation method.

Friesz, T. L. and C. Kwon (2008). Supply Chain Design in Perfect Competition. International Journal of Services Operations and Informatics,
3(3/4), 340356. [DOI] [PDF] [show abstract]
In this paper, we apply the theory of optimal control and theory of traffic assignment for supply chain design in perfect competition. We model the time staging and generalised routing of input factors needed for production by a firm. The production process will typically involve several stages, and as such is described by paths through a production network whose nodes are the various stages of production. We develop an algorithm and test it for a small numerical example.

Friesz, T. L., C. Kwon and R. Mookherjee (2007). A Computable Theory of Dynamic Congestion Pricing. In: Transportation and Traffic Theory 2007:
Papers selected for presentation at ISTTT17, a peer reviewed series since 1959, R. E. Allsop,
M. G. H. Bell and B. G. Heydecker (Eds.), pp. 126. (The ISTTT proceedings carry the status
of a peerreviewed international journal.) [PDF] Dynamic congestion pricing; Dynamic user equilibrium; Differential Variational Inequality; Optimal Control [show abstract]
In this paper we present a theory of dynamic congestion pricing for the daytoday as well as the withinday time scales. The equilibrium design problem emphasized herein takes the form of an MPEC, which we call the Dynamic Optimal Toll Problem with Equilibrium Constraints, or DOTPEC. The DOPTEC formulation we employ recalls an important earlier result that allows the equilibrium design problem to be stated as a single level problem, a result which is surprisingly little known. The DOPTEC maintains the usual design objective of minimizing the system travel cost by appropriate toll pricing. We describe how an infinite dimensional mathematical programming perspective may be employed to create an algorithm for the DOTPEC. A numerical example is provided.

Miller, T. C., T. L. Friesz, R. L. Tobin and C. Kwon (2007). Reaction Function Based Dynamic Location Modeling in StackelbergNashCournot Competition. Networks and Spatial Economics,
7(1), 7797. [DOI] [PDF] Dynamic Stackelberg equilibrium location modeling, reaction functions [show abstract]
We formulate a dynamic facility location model for a firm locating on a discrete network. It is assumed that this locating firm will act as the leader firm in an industry characterized by Stackelberg leaderfollower competition. The firm's I competitors are assumed to act as Cournot firms and are each assumed to operate under the assumption of zero conjectural variation with respect to their I1 Cournot competitors. Using sensitivity analysis of variational inequalities within a hierachical mathematical programming approach, we develop reaction function based dynamic models to optimize the Stackelberg firm's location decision. In the second half of this paper, we use these models to illustrate through a numerical example the insights yielded by our approach.