arXiv subjects

Siqian Shen

Publications and source records attributed to Siqian Shen.

26 records · Page 2Linked to original sources

arXiv2022

On the Value of Multistage Risk-Averse Stochastic Facility Location With or Without Prioritization

We consider a multiperiod stochastic capacitated facility location problem under uncertain demand and budget in each period. Using a scenario tree representation of the uncertainties, we formulate a multistage stochastic integer program to dynamically locate facilities in each period and compare it with a two-stage approach that determines the facility locations up front. In the multistage model, in each stage, a decision maker optimizes facility locations and recourse flows from open facilities to demand sites, to minimize certain risk measures of the cost associated with current facility location and shipment decisions. When the budget is also uncertain, a popular modeling framework is to prioritize the candidate sites. In the two-stage model, the priority list is decided in advance and fixed through all periods, while in the multistage model, the priority list can change adaptively. In each period, the decision maker follows the priority list to open facilities according to the realized budget, and optimizes recourse flows given the realized demand. Using expected conditional risk measures (ECRMs), we derive tight lower bounds for the gaps between the optimal objective values of risk-averse multistage models and their two-stage counterparts in both settings with and without prioritization. Moreover, we propose two approximation algorithms to efficiently solve risk-averse two-stage and multistage models without prioritization, which are asymptotically optimal under an expanding market assumption. We also design a set of super-valid inequalities for risk-averse two-stage and multistage stochastic programs with prioritization to reduce the computational time. We conduct numerical studies using both randomly generated and real-world instances with diverse sizes, to demonstrate the tightness of the analytical bounds and efficacy of the approximation algorithms and prioritization cuts.

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arXiv2022

A Model-based Multi-agent Framework to Enable an Agile Response to Supply Chain Disruptions

Due to the COVID-19 pandemic, the global supply chain is disrupted at an unprecedented scale under uncertain and unknown trends of labor shortage, high material prices, and changing travel or trade regulations. To stay competitive, enterprises desire agile and dynamic response strategies to quickly react to disruptions and recover supply-chain functions. Although both centralized and multi-agent approaches have been studied, their implementation requires prior knowledge of disruptions and agent-rule-based reasoning. In this paper, we introduce a model-based multi-agent framework that enables agent coordination and dynamic agent decision-making to respond to supply chain disruptions in an agile and effective manner. Through a small-scale simulated case study, we showcase the feasibility of the proposed approach under several disruption scenarios that affect a supply chain network differently, and analyze performance trade-offs between the proposed distributed and centralized methods.

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arXiv2021

An Optimization-and-Simulation Framework for Redesigning University Campus Bus System with Social Distancing

The outbreak of coronavirus disease 2019 (COVID-19) has led to significant challenges for schools, workplaces and communities to return to operations during the pandemic, requiring policymakers to balance individuals' safety and operational efficiency. In this paper, we present our work using mixed-integer programming and simulation for redesigning routes and bus schedules for University of Michigan (UM)'s campus bus system during the COVID-19 pandemic. We propose a hub-and-spoke design and utilize real data of student activities to identify hub locations and bus stops to be used in the new routes. Using the same total number of buses to operate, each new bus route has 50\% or fewer seats being used and takes maximumly 15 minutes, to reduce disease transmission through expiratory aerosol. We sample a variety of scenarios that cover variations of peak demand, social-distancing requirements, and break-down buses, to demonstrate the system resiliency of the new routes and schedules via simulation. The new bus routes are implemented and used by all UM campuses during the academic year 2020-2021, to ensure social distancing and short travel time. Our approach can be generalized to redesign public transit systems with social distancing requirement during the pandemic to reduce passengers' infection risk.

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arXiv2020

Distributionally Robust Partially Observable Markov Decision Process with Moment-based Ambiguity

We consider a distributionally robust Partially Observable Markov Decision Process (DR-POMDP), where the distribution of the transition-observation probabilities is unknown at the beginning of each decision period, but their realizations can be inferred using side information at the end of each period after an action being taken. We build an ambiguity set of the joint distribution using bounded moments via conic constraints and seek an optimal policy to maximize the worst-case (minimum) reward for any distribution in the set. We show that the value function of DR-POMDP is piecewise linear convex with respect to the belief state and propose a heuristic search value iteration method for obtaining lower and upper bounds of the value function. We conduct numerical studies and demonstrate the computational performance of our approach via testing instances of a dynamic epidemic control problem. Our results show that DR-POMDP can produce more robust policies under misspecified distributions of transition-observation probabilities as compared to POMDP, but has less costly solutions than robust POMDP. The DR-POMDP policies are also insensitive to varying parameter in the ambiguity set and to noise added to the true transition-observation probability values obtained at the end of each decision period.

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arXiv2020

Benders Cut Classification via Support Vector Machines for Solving Two-stage Stochastic Programs

We consider Benders decomposition for solving two-stage stochastic programs with complete recourse based on finite samples of the uncertain parameters. We define the Benders cuts binding at the final optimal solution or the ones significantly improving bounds over iterations as valuable cuts. We propose a learning-enhanced Benders decomposition (LearnBD) algorithm, which adds a cut classification step in each iteration to selectively generate cuts that are more likely to be valuable cuts. The LearnBD algorithm includes two phases: (i) sampling cuts and collecting information from training problems and (ii) solving testing problems with a support vector machine (SVM) cut classifier. We run the LearnBD algorithm on instances of capacitated facility location and multi-commodity network design under uncertain demand. Our results show that SVM cut classifier works effectively for identifying valuable cuts, and the LearnBD algorithm reduces the total solving time of all instances for different problems with various sizes and complexities.

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arXiv2020

Multistage Distributionally Robust Mixed-Integer Programming with Decision-Dependent Moment-Based Ambiguity Sets

We study multistage distributionally robust mixed-integer programs under endogenous uncertainty, where the probability distribution of stage-wise uncertainty depends on the decisions made in previous stages. We first consider two ambiguity sets defined by decision-dependent bounds on the first and second moments of uncertain parameters and by mean and covariance matrix that exactly match decision-dependent empirical ones, respectively. For both sets, we show that the subproblem in each stage can be recast as a mixed-integer linear program (MILP). Moreover, we extend the general moment-based ambiguity set in (Delage and Ye, 2010) to the multistage decision-dependent setting, and derive mixed-integer semidefinite programming (MISDP) reformulations of stage-wise subproblems. We develop methods for attaining lower and upper bounds of the optimal objective value of the multistage MISDPs, and approximate them using a series of MILPs. We deploy the Stochastic Dual Dynamic integer Programming (SDDiP) method for solving the problem under the three ambiguity sets with risk-neutral or risk-averse objective functions, and conduct numerical studies on multistage facility-location instances having diverse sizes under different parameter and uncertainty settings. Our results show that the SDDiP quickly finds optimal solutions for moderate-sized instances under the first two ambiguity sets, and also finds good approximate bounds for the multistage MISDPs derived under the third ambiguity set. We also demonstrate the efficacy of incorporating decision-dependent distributional ambiguity in multistage decision-making processes.

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arXiv2020

Distributionally Robust Facility Location Problem under Decision-dependent Stochastic Demand

Facility location decisions significantly impact customer behavior and consequently the resulting demand in a wide range of businesses. Furthermore, sequentially realized uncertain demand enforces strategically determining locations under partial information. To address these issues, we study a facility location problem where the distribution of customer demand is dependent on location decisions. We represent moment information of stochastic demand as a piecewise linear function of facility-location decisions. Then, we propose a decision-dependent distributionally robust optimization model, and develop its exact mixed-integer linear programming reformulation. We further derive valid inequalities to strengthen the formulation. We conduct an extensive computational study, in which we compare our model with the existing (decision-independent) stochastic and robust models. Our results demonstrate superior performance of the proposed approach with remarkable improvement in profit and quality of service by extensively testing problem characteristics, in addition to computational speed-ups due to the formulation enhancements. These results draw attention to the need of considering the impact of location decisions on customer demand within this strategic-level planning problem.

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arXiv2018

Ambiguous Chance-Constrained Binary Programs under Mean-Covariance Information

We consider chance-constrained binary programs, where each row of the inequalities that involve uncertainty needs to be satisfied probabilistically. Only the information of the mean and covariance matrix is available, and we solve distributionally robust chance-constrained binary programs (DCBP). Using two different ambiguity sets, we equivalently reformulate the DCBPs as 0-1 second-order cone (SOC) programs. We further exploit the submodularity of 0-1 SOC constraints under special and general covariance matrices, and utilize the submodularity as well as lifting to derive extended polymatroid inequalities to strengthen the 0-1 SOC formulations. We incorporate the valid inequalities in a branch-and-cut algorithm for efficiently solving DCBPs. We demonstrate the computational efficacy and solution performance using diverse instances of a chance-constrained bin packing problem.

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