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openAccessArticle: FalsePage Range: 172-172doi: 10.1016/j.disopt.2012.07.001Harvest Date: 2016-01-12 15:11:17issueName:cover date: 2012-08-01pubType

We examine variants of the critical node problem on specially structured graphs, which aim to identify a subset of nodes whose removal will maximally disconnect the graph. These problems lie at the intersection of network interdiction and graph theory research and are relevant to several practical optimization problems. The two different connectivity metrics that we consider regard the number of maximal connected components (which we attempt to maximize) and the largest component size (which we attempt to minimize). We develop optimal polynomial-time dynamic programming algorithms for solving these problems on tree structures and on series-parallel graphs, corresponding to each graphconnectivity metric. We also extend our discussion by considering node deletion costs, node weights, and solving the problems on generalizations of tree structures. Finally, we demonstrate the computational efficacy of our approach on randomly generated graph instances.

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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We consider a single-server scheduling problem given a fixed sequence of appointment arrivals with random no-shows and service durations. The probability distribution of the uncertain parameters is assumed to be ambiguous and only the support and first moments are known. We formulate a class of distributionally robust (DR) optimization models that incorporate the worst-case expectation/conditional Value-at-Risk (CVaR) penalty cost of appointment waiting, server idleness, and overtime as the objective or constraints.Our models flexibly adapt to different prior beliefs of no-show uncertainty. We obtain exact mixed-integer nonlinear programming reformulations, and derive valid inequalities to strengthen the reformulations that are solved by decomposition algorithms. In particular, we derive convex hulls for special cases of no-show beliefs, yielding polynomial-sized linear programming models for the least and the most conservative supports of no shows. We test various instances to demonstrate the computational efficacy of our approaches, the results and solution performance of various DR models given perfect or ambiguous distributional information.Article submitted; manuscript no. (Please, provide the manuscript number!) to strengthen the reformulations, which can significantly reduce computational time of solving various instances by using decomposition algorithms. For special no-show beliefs, our derivation leads to polynomial-sized LP reformulations that can readily be implemented in LP solvers.3. We test diverse instances to show the computational efficacy and demonstrate the performance of DR models under various uncertainties and levels of conservativeness. We provide guidelines for choosing appropriate DR models and no-show beliefs, depending on historical no-show rates, computation budget, and targeted tradeoffs between quality of service and operational cost. Structure of the PaperThe remainder of the paper is organized as follows. Section 2 formulates the DR expectation/CVaR models, and their variants based on different risk preferences. In Section 3, we derive an MINLP of the DR expectation model, as well as valid inequalities for accelerating a generic cutting-plane algorithm. In Section 4, we derive polynomial-sized LP reformulations for special cases of no-show beliefs. In Section 5, we test various instances to demonstrate the computational efficacy and solution performance of different DR models. Section 6 summarizes the paper and provides future research directions. In the e-companion (EC), we describe models and approaches for problems under a general waiting-time cost and a DR CVaR setting, respectively. We present all the proofs, as well as optimal solution patterns of different models.Notation: The convex hull of a set X is denoted by conv(X). The abbreviation "w.l.o.g." represents "without loss of generality." We follow the convention that j k=i a k = 0 if i > j. Formulations of DR Appointment SchedulingWe consider n appointments arriving at a single server following a fixed order of arrivals g...

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Carsharing has been considered as an effective means to increase mobility and reduce personal vehicle usage and related carbon emissions. In this paper, we consider problems of allocating a carshare fleet to service zones under uncertain one-way and round-trip rental demand. We employ a two-stage stochastic integer programming model, in the first stage of which we allocate shared vehicle fleet and purchase parking lots or permits in reservation-based or free-floating systems. In the second stage, we generate a finite set of samples to represent demand uncertainty and construct a spatial–temporal network for each sample to model vehicle movement and the corresponding rental revenue, operating cost, and penalties from unserved demand. We minimize the expected total costs minus profit and develop branch-and-cut algorithms with mixed-integer, rounding-enhanced Benders cuts, which can significantly improve computation efficiency when implemented in parallel computing. We apply our model to a data set of Zipcar in the Boston–Cambridge, Massachusetts, area to demonstrate the efficacy of our approaches and draw insights on carshare management. Our results show that exogenously given one-way demand can increase carshare profitability under given one-way and round-trip price differences and vehicle relocation cost whereas endogenously generated one-way demand as a result of pricing and strategic customer behavior may decrease carshare profitability. Our model can also be applied in a rolling-horizon framework to deliver optimized vehicle relocation decisions and achieve significant improvement over an intuitive fleet-rebalancing policy. The online appendix is available at https://doi.org/10.1287/msom.2017.0644 .