Estimating dynamic Origin-Destination (OD) traffic flow is crucial for understanding traffic patterns and the traffic network. While dynamic origin-destination estimation (DODE) has been studied for decades as a useful tool for estimating traffic flow, few existing models have considered its potential in evaluating the influence of policy on travel activity. This paper proposes a data-driven approach to estimate OD traffic flow using sensor data on highways and local roads. We extend prior DODE models to improve accuracy and realism in order to estimate how policies affect OD traffic flow in large urban networks. We applied our approach to a case study in Los Angeles County, where we developed a traffic network, estimated OD traffic flow between health districts during COVID-19, and analyzed the relationship between OD traffic flow and population income. Our findings demonstrate that the proposed approach provides valuable insights into traffic flow patterns and their underlying demographic factors for a large-scale traffic network. The approach has practical applications for transportation planning and traffic management, enabling a better understanding of traffic flow patterns and the impact of policy changes on travel activity.

During the COVID-19 pandemic, selecting vaccination sites and allocating limited doses required balancing accessibility, disease control, and fairness. We formulate a multi-objective mixed-integer linear programming model that jointly determines the locations of mega-sites and allocates vaccine doses while explicitly incorporating travel inconvenience, disease dynamics, and equitable distribution. The model incorporates commuting patterns from both residential and workplace origins to more accurately capture population mobility, and employs a tractable objective formulation that proxies key public health goals, enabling efficient and equitable mass vaccination planning. Compared with the solution empirically used in Los Angeles County in 2020, we recommend more dispersed mega-site locations that result in a 26% reduction in travel inconvenience and avert an additional 200 infections.

In major metropolitan areas, ride-sharing systems can help reduce traffic congestion and increase the transportation system's efficiency. In this paper, we propose a Branch-and-Price based approach for solving the ride-share routing problem with flexible pickup and drop-off points. We assume a ride-sharing system where drivers have their own origins and destinations, where all the drivers' and passengers' information is known beforehand, and all the problem data information is static and deterministic. We assume that drivers can pick up or drop off passengers from or to flexible meeting points that are within a passenger's walking time limit from their origin or destination and are determined on a continuous plane. We formulate a mixed integer nonlinear model for routing and selecting pickup and drop-off points. Our solution approach decomposes this problem in two: selecting pickup and drop-off points and a rideshare routing problem. We develop an efficient algorithm to select the best pickup and drop-off points and show computationally that it is more efficient at finding pickup and drop-off points than considering a fixed set of discrete meeting points. To evaluate the performance of our approach, we perform numerical experiments on a San Francisco Taxicab dataset. Results show that our approach is efficient, solving instances with up to 600 points within 31 CPU minutes. For these datasets, incorporating flexible pickup and drop-off points can reduce the total vehicle travel time of the rideshare system by 4% on average.

Anticipating the strategies of potential attackers is crucial for protecting critical infrastructure. We can represent the challenge of the defenders of such infrastructure as a Stackelberg security game. The defender must decide how to allocate limited resources to protect specific targets, aiming to maximize their expected utility (such as minimizing the extent of damage) and considering that attackers will respond in a way that is most advantageous to them.We present novel valid inequalities to find a Strong Stackelberg Equilibrium in both Stackelberg games and Stackelberg security games. We also consider a Stackelberg security game that aims to protect targets with a defined budget. We use branch-and-price in this game to show that our approach outperforms the standard formulation in the literature, in terms of both solution speed and memory usage.Additionally, we present an extensive computational study to assess the impact of various parameters in branch-and-price, such as the number of initial columns, the number of columns generated per iteration, and the effects of stabilization techniques. The results show that our approach reduces the solution time of the problem to less than a fifth of the time required by the state-of-the art methods.

Companies frequently offer wholesale prices for their products that decrease with the number of items purchased. However, individual buyers may not be willing or able to purchase large quantities of a single item. To address this consumers can form groups to purchase at wholesale prices and gain bargaining power. This practice can be extended from single products to product bundles. This paper proposes a combinatorial coalition formation problem to create groups of buyers who wish to optimally purchase product bundles. We propose a generic mathematical model and present mixed-integer programming formulations for nonincreasing price and step price functions. To handle large instances, a Benders decomposition method is proposed for step price functions. Computational experiments conducted on a large set of synthetic instances illustrate the performance of the method.

During the COVID-19 pandemic, there were over three million infections in Los Angeles County (LAC). To facilitate distribution when vaccines first became available, LAC set up six mega-sites for dispensing a large number of vaccines to the public. To understand if another choice of mega-site location would have improved accessibility and health outcomes, and to provide insight into future vaccine allocation problems, we propose a multi-objective mixed integer linear programming model that balances travel convenience, infection reduction, and equitable distribution. We provide a tractable objective formulation that effectively proxies real-world public health goals of reducing infections while considering travel inconvenience and equitable distribution of resources. Compared with the solution empirically used in LAC in 2020, we recommend more dispersed mega-site locations that result in a 28% reduction in travel inconvenience and avert an additional 1,000 infections.

Estimating dynamic Origin-Destination (OD) traffic flow is crucial for understanding traffic patterns and the traffic network. While dynamic origin-destination estimation (DODE) has been studied for decades as a useful tool for estimating traffic flow, few existing models have considered its potential in evaluating the influence of policy on travel activity. This paper proposes a data-driven approach to estimate OD traffic flow using sensor data on highways and local roads. We extend prior DODE models to improve accuracy and realism in order to estimate how policies affect OD traffic flow in large urban networks. We applied our approach to a case study in Los Angeles County, where we developed a traffic network, estimated OD traffic flow between health districts during COVID-19, and analyzed the relationship between OD traffic flow and demographic characteristics such as income. Our findings demonstrate that the proposed approach provides valuable insights into traffic flow patterns and their underlying demographic factors for a large-scale traffic network. Specifically, our approach allows for evaluating the impact of policy changes on travel activity. The approach has practical applications for transportation planning and traffic management, enabling a better understanding of traffic flow patterns and the impact of policy changes on travel activity.

Anticipating the strategies of potential attackers is crucial for protecting critical infrastructure. We can represent the challenge of the defenders of such infrastructure as a Stackelberg security game. The defender must decide how to allocate limited resources to protect specific targets, aiming to maximize their expected utility (such as minimizing the extent of damage) and considering that attackers will respond in a way that is most advantageous to them. We present novel valid inequalities to find a Strong Stackelberg Equilibrium in both Stackelberg games and Stackelberg security games. We also consider a Stackelberg security game that aims to protect targets with a defined budget. We use branch-and-price in this game to show that our approach outperforms the standard formulation in the literature, and we conduct an extensive computational study to analyze the impact of various branch-and-price parameters on the performance of our method in different game settings.

The ability to estimate future velocity on a road network is relevant for applications such as vehicle navigation systems and emergency vehicle dispatching. The existence of traffic congestion severely impacts travellers' travel time. In this paper, we investigate the use of congestion prediction in velocity forecasting models. Using a data-driven approach, we classify traffic observations into classes with and without congestion. We find that this classification improves velocity forecasting, showing that using congestion as an attribute reduces the MAE by at least 6.15% for different machine and deep learning models including random forests, multi-layer perceptrons and recurrent neural networks. We propose a random forest model that identifies the future congestion state from past traffic velocity and volume data and then use it to build new short-term velocity forecasting models. These models reduce the MAE prediction error up to 3.37% over the best models that do not consider congestion. This improvement represents overcoming a 53.75% of the error due to not precisely knowing the future congestion state.

Protecting critical infrastructure from intentional damage requires foreseeing the strategies of possible attackers. We formulate this problem as a Stackelberg Security Game. A defender must decide which specific targets to protect with limited resources, thus maximizing their expected utility (e.g., minimizing damage value) and considering that a second player (or players), called an attacker, responds in the best possible way.Since Stackelberg Security Games are generally NP-hard, the main challenge in finding optimal strategies in real applications is to develop efficient methodologies for large instances.We propose a general methodology to find a Strong Stackelberg Equilibrium for Stackelberg Security Games, exploiting the structure in the defender’s strategy set. This methodology consists of two steps. First, we formulate the problem by using variables representing the probability of defending each target. The formulation must be either a polynomial-size MILP and/or an MILP with an exponential number of constraints that are separable in polynomial time through branch-and-cut. In the second step, we recover the mixed strategies in the original space efficiently (in polynomial time) by using column generation. We apply this methodology to various security applications studied in the last decade. We generalize known examples and propose new examples. Finally, we provide an extensive computational study of the various formulations based on marginal probabilities.

Unit Commitment Problem with Energy Storage Under Correlated Renewables Uncertainty” introduces a novel approach to address the challenges of renewable integration. The study acknowledges the growing variability and correlation in power availability due to renewable generation and proposes a day-ahead unit commitment (UC) problem formulation that incorporates energy storage and considers multistage correlated uncertainty. Using a variant of the stochastic dual dynamic programming (SDDP) method, which can handle temporal correlations effectively, the researchers solve the complex UC problem. Results obtained from the IEEE 118-bus system demonstrate the significant advantages of considering multistage uncertainty and correlations. Applying their approach to the Chilean power system, the researchers present superior UC solutions that adapt generation to changing uncertainty at a lower cost. Additionally, they propose a more efficient deterministic UC solution that outperforms current industry practices. These advancements promise to enhance the integration of renewable energy sources, enabling a more sustainable and environmentally friendly future.

In Stackelberg security games, a leader locates security resources to protect a set of targets from strategic adversaries that aim to attack these targets after observing the leader’s strategy. In this setting, the leader decision problem is to optimize an uncertain reward that can take a discrete set of values with a probability distribution that depends on the decision variable. We show how diverse risk aversion models of the leader decision problem can be formulated as tractable optimization problems, such as imposing a bound on the expected disutility, chance constraints, bounded distortion risk, and first- and second-order stochastic dominance constraints or optimizing a value at risk and conditional value at risk. We detail the resulting optimization problems and present computational results that show how the solution changes in two specific settings: (1) an entropic risk measure or value-at-risk minimization with a quantal response follower and (2) a prospect theory model with optimal follower response.

This paper addresses the vehicle routing problem with time windows and stochastic demands (VRPTWSD). The problem is modeled as a two-stage stochastic program with recourse, in which routes are designed in the first stage and executed in the second. A failure occurs if the load of the vehicle is insufficient to meet the observed demand of a customer, implying recourse actions to recover feasibility. We consider the classical recourse policy where reactive trips to the depot are made in case of failures and a fixed rule-based recourse policy where, in addition, preventive trips are allowed. These recourse actions delay the vehicle and may cause further failures if the arrival times on the remaining customers of the planned route do not satisfy their time windows. An additional recourse action is used to service the customers whose time windows would be violated in the planned routes. We propose an Integer L-shaped algorithm considering the mentioned recourse actions. To the best of our knowledge, this is the first tailored exact approach for the VRPTWSD. Computational experiments using 112 benchmark in-stances evaluate the performance of this algorithm as well as the quality of the stochastic problem solu-tions. The results indicate significant savings in the solutions when using the fixed rule-based policy and round-trip recourse actions instead of the classical policy. Additionally, the algorithm performed better with the fixed rule-based policy, solving to optimality all instances with up to 34 customers, and taking less time on instances that were solved to optimality with both policies.(c) 2022 Elsevier B.V. All rights reserved.

We consider a Stackelberg game that arises in a security domain (SSG), where a defender can simultaneously protect m out of n targets from an adversary that observes the defense strategy before deciding on an utility maximizing attack. Given the high stakes in security settings, it is reasonable that the defender in this game is risk averse with respect to the attacker’s decisions. Here we focus on developing efficient solution algorithms for a specific SSG, where the defender uses an entropic risk measure to model risk aversion to the attacker’s strategies, and where multiple attackers select targets following logit quantal response equilibrium models. This problem can be formulated as a nonconvex nonlinear optimization problem. We propose two solution methods: (1) approximate the problem through convex mixed integer nonlinear programs (MINR) and (2) a general purpose methodology (CELL) to optimize nonconvex and nonseparable fractional problems through mixed integer linear programming approximations. Both methods provide arbitrarily good incumbents and lower bounds on SSG. We present cutting plane methods to solve these problems for large instances. Our computational experiments illustrate the advantages of introducing risk aversion into the defender’s behavior and show that MINR dominates CELL, producing in 2 h solutions that are within 2% of optimal on average.

In this work, we study Stackelberg equilibria for discounted stochastic games. We consider two solution concepts for these games: stationary strong Stackelberg equilibrium (SSSE) and fixed point equilibrium (FPE) solutions. The SSSE solution is obtained by explicitly solving the Stackelberg equilibrium conditions, whereas the FPE can be computed efficiently using value or policy iteration algorithms. However, previous work has overlooked the relationship between these two different solution concepts. Here, we investigate the conditions for existence and equivalence of these solution concepts. Our theoretical results prove that the FPE and SSSE exist and coincide for important classes of games, including myopic follower strategy and team games. This, however, does not hold in general, and we provide numerical examples where one of SSSE or FPE does not exist, or when they both exist, they differ. Our computational results compare the solutions obtained by value iteration, policy iteration, and a mathematical programming formulations for this problem. Finally, we present a discounted stochastic Stackelberg game for a security application to illustrate the solution concepts and the efficiency of the algorithms studied.

We consider the problem faced by a retail chain that must select what mutual-substitute items to display in each one of its stores to maximize revenues. The number of items cannot exceed the limit space capacity of each store. Customers purchase the one product that maximizes their utility, which depends on the product price, travel cost to the store, and reservation price, known to the retailer. The retailer can set different price markdowns at different stores and products. The retailer considers the decisions of customers, and solves a mixed-integer bilevel optimization problem, which can be formulated as a single-level optimization problem by using optimality conditions for the lower level. We propose Branch and Cut and Cut and Branch methods and include a family of valid inequalities to solve the problem. We compare the results with those of a Benders decomposition method. Our computational results show that the proposed Cut and Branch method obtains the best performance and improves the current state of the art.

The COVID-19 pandemic has caused great disruption to the service sector, and it has, in turn, adapted by implementing measures that reduce physical contact among employees and users; examples include home-office work and the setting of occupancy restrictions at indoor locations. The design of services in the context of a pandemic requires balancing between two objectives: (i) special measures must be implemented to maintain physical separation among people to reduce the risk of infection, and (ii) these sanitary measures also reduce process capacity, thereby increasing the waiting times of users. We study this problem in the context of election processes, in which balancing waiting time with public safety is of first order relevance to ensuring voter turnout, using as a real-world application the Chilean 2020 national referendum. Analyzing this problem requires a multidisciplinary approach that consists of integrating randomized experiments to measure how voters weigh infection risk relative to waiting time and stochastic modeling/discrete event simulation to prescribe recommendations for the service design—specifically setting capacity limits to trade off between overcrowding and process efficiency. Overall, our results shows that infection risk is an important factor affecting voter turnout during a pandemic and that capacity limits can be a useful design tool to balance these risks with other service quality measures. Some of these findings were considered in the guidelines that Servel provided to manage capacity and voter arrival patterns at voting centers.

An effective patrol of a large area can require the coordinated action of diverse security resources. In this work we formulate a Stackelberg Security game that coordinates such resources in a border patrol problem. In this security domain, resources from different precincts have to be paired to conduct patrols in the border due to logistic constraints. Given this structure the set of pure defender strategies is of exponential size. We describe the set of mixed strategies using a polynomial number of variables but exponentially many constraints that come from the matching polytope. We then include this description in a mixed integer formulation to compute the Strong Stackelberg Equilibrium efficiently with a branch and cut scheme. Since the optimal patrol solution is a probability distribution over the set of exponential size, we also introduce an efficient sampling method that can be used to deploy the security resources every shift. Our computational results evaluate the efficiency of the branch and cut scheme developed and the accuracy of the sampling method. We show the applicability of the methodology by solving a real world border patrol problem.

In this work we formulate a Stackelberg Security Game that coordinates resources in a border patrol problem. In this security domain, resources from different precincts have to be paired to conduct patrols in the border due to logistic constraints. Given this structure, models that enumerate the pure defender strategies scale poorly. We describe the set of mixed strategies using a polynomial number of variables but exponentially many constraints that come from the matching polytope. We then include this description in a mixed integer formulation to compute the Strong Stackelberg Equilibrium efficiently with a branch and cut scheme. Since the optimal patrol solution is a probability distribution over the set of exponential size, we also introduce an efficient sampling method that can be used to deploy the security resources every shift. Our computational results evaluate the efficiency of the branch and cut scheme developed and the accuracy of the sampling method. (C) 2019 Elsevier B.V. All rights reserved.

Being able to estimate future velocity on a road network has applications from vehicle navigation systems to emergency vehicle dispatching systems. The existence of traffic congestion can severely impact travelers’ travel time and in this paper we explore methods to take it into account in velocity forecasting models. Using a data approach, different traffic observations can be classified into classes with and without congestion. Our research shows that using congestion as an attribute can reduce the prediction error when implementing machine learning models, such as random forest or multi-layer perceptron. Furthermore, training separate models for each class performs better than using congestion as an extra attribute. A methodology for the congestion pattern identification is proposed, based only in the velocity and volume values.