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We study the quadratic cycle cover problem (QCCP), which aims to find a node-disjoint cycle cover in a directed graph with minimum interaction cost between successive arcs. We derive several semidefinite programming (SDP) relaxations and use facial reduction to make these strictly feasible. We investigate a nontrivial relationship between the transformation matrix used in the reduction and the structure of the graph, which is exploited in an efficient algorithm that constructs this matrix for any instance of the problem. To solve our relaxations, we propose an algorithm that incorporates an augmented Lagrangian method into a cutting-plane framework by utilizing Dykstra's projection algorithm. Our algorithm is suitable for solving SDP relaxations with a large number of cutting-planes. Computational results show that our SDP bounds and efficient cutting-plane algorithm outperform other QCCP bounding approaches from the literature. Finally, we provide several SDP-based upper bounding techniques, among which is a sequential Q-learning method that exploits a solution of our SDP relaxation within a reinforcement learning environment. Summary of Contribution: The quadratic cycle cover problem (QCCP) is the problem of finding a set of node-disjoint cycles covering all the nodes in a graph such that the total interaction cost between successive arcs is minimized. The QCCP has applications in many fields, among which are robotics, transportation, energy distribution networks, and automatic inspection. Besides this, the problem has a high theoretical relevance because of its close connection to the quadratic traveling salesman problem (QTSP). The QTSP has several applications, for example, in bioinformatics, and is considered to be among the most difficult combinatorial optimization problems nowadays. After removing the subtour elimination constraints, the QTSP boils down to the QCCP. Hence, an in-depth study of the QCCP also contributes to the construction of strong bounds for the QTSP. In this paper, we study the application of semidefinite programming (SDP) to obtain strong bounds for the QCCP. Our strongest SDP relaxation is very hard to solve by any SDP solver because of the large number of involved cutting-planes. Because of that, we propose a new approach in which an augmented Lagrangian method is incorporated into a cutting-plane framework by utilizing Dykstra's projection algorithm. We emphasize an efficient implementation of the method and perform an extensive computational study. This study shows that our method is able to handle a large number of cuts and that the resulting bounds are currently the best QCCP bounds in the literature. We also introduce several upper bounding techniques, among which is a distributed reinforcement learning algorithm that exploits our SDP relaxations. [ABSTRACT FROM AUTHOR]

A recent study on the classical capacitated vehicle routing problem (CVRP) introduced an adaptive version of the widely used iterated local search paradigm, hybridized with a path-relinking (PR) strategy. The solution method, called adaptive iterated local search (AILS)-PR, outperformed existing meta-heuristics for the CVRP on benchmark instances. However, tests on large-scale instances suggest that PR is too slow, making AILS-PR less advantageous in this case. To overcome this challenge, this paper presents an AILS combined with mechanisms to handle large CVRP instances, called AILS-II. The computational cost of this implementation is reduced, whereas the algorithm also searches the solution space more efficiently. AILS-II is very competitive on smaller instances, outperforming the other methods from the literature with respect to the average gap to the best-known solutions. Moreover, AILS-II consistently outperforms the state of the art on larger instances with up to 30,000 vertices. History: Accepted by Ted Ralphs, Area Editor for Software Tools. This paper has been accepted for the INFORMS Journal on Computing Special Issue on Software Tools for Vehicle Routing. Funding: This work was supported by the Fundação de Amparo à Pesquisa do Estado de São Paulo [Grants 2013/07375-0, 2019/22067-6, and 2022/05803-3] and the Conselho Nacional de Desenvolvimento Científico e Tecnológico [Grants 309385/2021-0 and 403735/2021-1]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0106) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2023.0106). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]

Despite the successful applications of decision diagrams (DDs) to solve various classes of integer programs in the literature, the question of which mixed-integer structures admit a DD representation remains open. The present work addresses this question by developing both necessary and sufficient conditions for a mixed-integer program to be DD-representable through identification of certain rectangular formations in the underlying sets. This so-called rectangularization framework is applicable to all bounded mixed-integer linear programs, providing a notable extension of the DD domain to continuous problems. As an application, the paper uses the developed methods to solve stochastic unit commitment problems in energy systems. Computational experiments conducted on benchmark instances show that the DD approach uniformly and significantly outperforms the existing solution methods and modern solvers. The proposed methodology opens new pathways to solving challenging mixed-integer programs in energy systems more efficiently. Over the past decade, decision diagrams (DDs) have been used to model and solve integer programming and combinatorial optimization problems. Despite successful performance of DDs in solving various discrete optimization problems, their extension to model mixed-integer programs (MIPs), such as those appearing in energy applications, is lacking. More broadly, the question of which problem structures admit a DD representation is still open in the DD community. In this paper, we address this question by introducing a geometric decomposition framework based on rectangular formations that provides both necessary and sufficient conditions for a general MIP to be representable by DDs. As a special case, we show that any bounded mixed-integer linear program admits a DD representation through a specialized Benders decomposition technique. The resulting DD encodes both integer and continuous variables and, therefore, is amenable to the addition of feasibility and optimality cuts through refinement procedures. As an application for this framework, we develop a novel solution methodology for the unit commitment problem (UCP) in the wholesale electricity market. Computational experiments conducted on a stochastic variant of the UCP show a significant improvement of the solution time for the proposed method when compared with the outcome of modern solvers. History: This paper has been accepted for the Operations Research Special Issue on Computational Advances in Short-Term Power System Operations. Funding: This work was supported by the Iowa Economic Development Authority [Grant 20IEC005]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2022.2353. [ABSTRACT FROM AUTHOR]

With the rise of e-commerce and increasing customer requirements, logistics service providers face a new complexity in their daily planning, mainly due to efficiently handling same-day deliveries. Existing multistage stochastic optimization approaches that allow solving the underlying dynamic vehicle routing problem either are computationally too expensive for an application in online settings or—in the case of reinforcement learning—struggle to perform well on high-dimensional combinatorial problems. To mitigate these drawbacks, we propose a novel machine learning pipeline that incorporates a combinatorial optimization layer. We apply this general pipeline to a dynamic vehicle routing problem with dispatching waves, which was recently promoted in the EURO Meets NeurIPS Vehicle Routing Competition at NeurIPS 2022. Our methodology ranked first in this competition, outperforming all other approaches in solving the proposed dynamic vehicle routing problem. With this work, we provide a comprehensive numerical study that further highlights the efficacy and benefits of the proposed pipeline beyond the results achieved in the competition, for example, by showcasing the robustness of the encoded policy against unseen instances and scenarios. History: This paper has been accepted for the Transportation Science special issue on DIMACS Implementation Challenge: Vehicle Routing Problems. Funding: This work was supported by Deutsche Forschungsgemeinschaft [Grant 449261765]. [ABSTRACT FROM AUTHOR]

An introduction to the journal is presented which discusses various papers published within the issue, including one on a deterministic maritime inventory routing problem, one on an integrated mixed integer linear programming model for linear companies alliances, and another on scheduling disruption scenarios for liner companies.

The BusPlus project aims at improving the off-peak hours public transit service in Canberra, Australia. To address the difficulty of covering a large geographic area, proposes a hub and shuttle model consisting of a combination of a few high-frequency bus routes between key hubs and a large number of shuttles that bring passengers from their origin to the closest hub and take them from their last bus stop to their destination. This paper focuses on the design of the bus network and proposes an efficient solving method to this multimodal network design problem based on the Benders decomposition method. Starting from a mixed-integer programming (MIP) formulation of the problem, the paper presents a Benders decomposition approach using dedicated solution techniques for solving independent subproblems, Pareto-optimal cuts, cut bundling, and core point update. Computational results on real-world data from Canberra's public transit system justify the design choices and show that the approach outperforms the MIP formulation by two orders of magnitude. Moreover, the results show that the hub and shuttle model may decrease transit time by a factor of two, while staying within the costs of the existing transit system. [ABSTRACT FROM AUTHOR]

This paper presents a review of the available literature on solid waste management problems, with a particular focus on vehicle routing problems. The available papers are classified into different categories with the purpose of providing the reader with a guide that facilitates his or her search for papers in his or her field of interest. For each category, a table is presented that gives a summary of how each paper scores from that perspective. Additional explanation is presented about the characteristics of each category using some key references. Finally, this paper discovers unexplored areas of research and identifies trends in the literature. [ABSTRACT FROM AUTHOR]

Model calibration is challenging for large-scale system models with a great number of variables. Existing approaches to partitioning system models and prioritizing data acquisition rely on heuristics rather than formal treatments. The sensor placement problem in physical dynamic systems points to a promising avenue for formalizing data acquisition priorities, which addresses the following question for system models: With the model at hand and pre-existing data availability on a subset of model variables, what are the (next) k model variables that would bring the largest utility to model calibration, once their data are acquired? In this study, we formalize this problem as a combinatorial optimization and adapt two solutions, the information-entropy approach and the miss-probability approach, from physical dynamic systems to system models in management sciences. Next, based on the idea of the data availability partition, we develop a third solution. The new approach can be understood from the entropy perspective and is embedded in the theoretical framework for the evaluation of side information. Our solution applies to system models of all topologies: analytical results of the optimal placement are derived for binary/multinary trees; for general (directed) tree structures, an algorithm to determine the optimal placement is devised, whose complexity is upper-bounded by O(nlog2(n)) for an n-variable system; for arbitrary model topologies with the presence of loops, sequential-optimal and simulated-annealing schemes are formulated. Three approaches are compared on a validating example; our solution outperforms the two alternatives. Application on a multicompartment system demonstrates the toolkit's practical use. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0128) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2022.0128). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]

The time-dependent traveling salesman problem with time windows (TDTSPTW) is a variant of the well-known traveling salesman problem with time windows, in which travel times are not assumed to be constant. The TDTSPTW accounts for the effects of congestion at the planning level, being particularly suited for distribution problems in large cities. In this paper we develop a labeling-based algorithm for the TDTSPTW that incorporates partial dominance and generalizes several state-of-the-art components from the time-independent related literature. We propose a framework general enough to be applied to the TDTSPTW and its variant without time windows, with the objective of minimizing the duration or the makespan. As part of the framework, we introduce a new state-space relaxation specifically designed for the time-dependent context. Extensive computational experiments show the effectiveness of the overall approach and the impact of the new relaxation, outperforming several recent algorithms proposed for these variants on more than 9,000 benchmark instances. In addition, we frame the minimum tour duration problem within the time-dependent literature and include it as a benchmark for our algorithm, obtaining improved computation times and 31 new optimal solutions. Summary of Contribution: In this paper, we study the time-dependent traveling salesman problem with time windows (TDTSPTW), a difficult single-vehicle routing problem that incorporates more realistic travel time functions than its classic time-independent counterpart. As a result, the TDTSPTW is harder to solve, as it requires more complex models and algorithms. Using state-of-the-art optimization techniques, we propose an efficient solution approach for the TDTSPTW and some related variants that outperforms the previous approaches in the literature. Our paper emphasizes the importance of algorithmic design and efficient implementations to tackle relevant practical combinatorial optimization problems—in particular, for time-dependent problems. Moreover, the resulting algorithm fosters a new research direction regarding exact algorithms for time-dependent problems using dynamic programming and relaxation techniques. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms—Discrete. Funding: This research has been funded by Fondo para la Investigación Científica y Tecnológica (FONCyT) [Grants PICT-2016-2677 and PICT-2018-2961] from the Ministry of Science, Argentina, and by the Google Latin America Research Award (LARA) 2019. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2022.1236. [ABSTRACT FROM AUTHOR]

In designing ideal multiple recursive random number (RN) generators (MRGs), the best set of multipliers, in terms of the lattice structure of the RNs produced, is sought. As the order of the MRG increases, the number of possible sets of multipliers to be examined grows exponentially This paper proposes a genetic algorithm for designing good MRGs. The set of multipliers associated with the MRG is encoded as a binary string. Via the operations of reproduction, crossover, and mutation, new sets of multipliers are generated. The spectral values of the MRGs are calculated to guide the search process. As an illustration, the proposed algorithm is employed to find good sets of multipliers for MRGs of orders three and four. The results are better than those derived from other studies. To conclude, this paper not only finds better MRGs of orders three and four, but also develops an algorithm for designing MRGs of higher orders. [ABSTRACT FROM AUTHOR]

In this paper, we consider a variant of adaptive robust combinatorial optimization problems where the decision maker can prepare K solutions and choose the best among them upon knowledge of the true data realizations. We suppose that the uncertainty may affect the objective and the constraints through functions that are not necessarily linear. We propose a new exact algorithm for solving these problems when the feasible set of the nominal optimization problem does not contain too many good solutions. Our algorithm enumerates these good solutions, generates dynamically a set of scenarios from the uncertainty set, and assigns the solutions to the generated scenarios using a vertex p-center formulation, solved by a binary search algorithm. Our numerical results on adaptive shortest path and knapsack with conflicts problems show that our algorithm compares favorably with the methods proposed in the literature. We additionally propose a heuristic extension of our method to handle problems where it is prohibitive to enumerate all good solutions. This heuristic is shown to provide good solutions within a reasonable solution time limit on the adaptive knapsack with conflicts problem. Finally, we illustrate how our approach handles nonlinear functions on an all-or-nothing subset problem taken from the literature. Summary of Contribution: Our paper describes a new exact algorithm for solving adaptive robust combinatorial optimization problems when the feasible set of the nominal optimization problems does not contain too many good solutions. Its development relies on a progressive relaxation of the problem augmented with a row-and-column generation technique. Its efficient execution requires a reformulation of this progressive relaxation, coupled with dominance rules and a binary search algorithm. The proposed algorithm is amenable to exploiting the special structures of the problems considered as illustrated with various applications throughout the paper. A practical view is provided by the proposition of a heuristic variant. Our computational experiments show that our proposed exact solution method outperforms the existing methodologies and therefore pushes the computational envelope for the class of problems considered. [ABSTRACT FROM AUTHOR]

We propose and evaluate branch-and-price approaches for vehicle routing problems with picking, loading, and soft time windows. This general type of vehicle routing problem is of particular relevance in the same-day delivery context, in which fast routing algorithms are required because of the commitment to real-time delivery in the presence of high customer order frequencies. To boost the performance of the branch-and-price algorithms, we introduce the new method of tree-compatible labeling with nondominance trees. This method represents cost functions by a fixed number of breakpoints and uses a specialized tree-based data structure to store Pareto-optimal labels. We prove the theoretical soundness of the new method and evaluate its performance numerically with respect to pricing, column generation, and branch-and-price. Our numerical results show that the method yields substantial performance gains. In particular, we show that, with the new method, branch-and-price is able to reliably generate within a few minutes close to optimal solutions for problem instances with 50 customers. By additional experiments with classic vehicle routing problems with hard time windows, we show that the performance gains of our method result from its ability to handle cost functions in the pricing step. Our approach is the first branch-and-price approach for vehicle routing with picking, loading, and soft time windows. As such, it represents an exact routing algorithm that is able to reliably satisfy the runtime requirements of real-time delivery services. Summary of Contribution: In this paper, we propose the first branch-and-price approaches for a general class of vehicle routing problems with picking, loading, and soft time windows. This problem class is of particular importance for real-time delivery services, for which customers expect to be served within only a few hours after their order has been placed. We provide a problem formulation that takes into account that short runtimes of routing algorithms are required, that the upper bounds of the customers' time windows may be violated at a certain cost, and that a significant part of the delivery time window is consumed by picking orders from a warehouse and loading orders into vehicles. Solving the problem with branch-and-price requires the use of cost functions as elements of the labels in the pricing step. We propose a method that approximates these cost functions and leverages the computational performance of nondominance tree data structures for solving the pricing problem. We prove the theoretical soundness of this new method for exact branch-and-price, and we show numerically that the method leads to a significant performance increase of branch-and-price. The paper lies at the intersection of computing and operations research, in particular because our algorithms are designed to leverage the computational performance of advanced data structures for solving a combinatorial optimization problem. [ABSTRACT FROM AUTHOR]

In this paper, we tackle the resolution of chance-constrained problems reformulated via sample average approximation. The resulting data-driven deterministic reformulation takes the form of a large-scale mixed-integer program (MIP) cursed with Big-Ms. We introduce an exact resolution method for the MIP that combines the addition of a set of valid inequalities to tighten the linear relaxation bound with coefficient strengthening and constraint screening algorithms to improve its Big-Ms and considerably reduce its size. The proposed valid inequalities are based on the notion of k-envelopes and can be computed off-line using polynomial-time algorithms and added to the MIP program all at once. Furthermore, they are equally useful to boost the strengthening of the Big-Ms and the screening rate of superfluous constraints. We apply our procedures to a probabilistically constrained version of the DC optimal power flow problem with uncertain demand. The chance constraint requires that the probability of violating any of the power system's constraints be lower than some positive threshold. In a series of numerical experiments that involve five power systems of different size, we show the efficiency of the proposed methodology and compare it with some of the best performing convex inner approximations currently available in the literature. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms – Discrete. Funding: This work was supported in part by the European Research Council under the EU Horizon 2020 research and innovation program [Grant 755705], in part by the Spanish Ministry of Science and Innovation [Grant AEI/10.13039/501100011033] through project PID2020-115460GB-I00, and in part by the Junta de Andalucía and the European Regional Development Fund through the research project P20_00153. Á. Porras is also financially supported by the Spanish Ministry of Science, Innovation and Universities through the University Teacher Training Program with fellowship number FPU19/03053. Supplemental Material: The online supplement is available at https://doi.org/10.1287/ijoc.2022.0302. [ABSTRACT FROM AUTHOR]

We study the uncapacitated lot-sizing problem with uncertain demand and costs. The problem is modeled as a multistage stochastic mixed-integer linear program in which the evolution of the uncertain parameters is represented by a scenario tree. To solve this problem, we propose a new extension of the stochastic dual dynamic integer programming algorithm (SDDiP). This extension aims at being more computationally efficient in the management of the expected cost-to-go functions involved in the model, in particular by reducing their number and by exploiting the current knowledge on the polyhedral structure of the stochastic uncapacitated lot-sizing problem. The algorithm is based on a partial decomposition of the problem into a set of stochastic subproblems, each one involving a subset of nodes forming a subtree of the initial scenario tree. We then introduce a cutting plane–generation procedure that iteratively strengthens the linear relaxation of these subproblems and enables the generation of an additional strengthened Benders' cut, which improves the convergence of the method. We carry out extensive computational experiments on randomly generated large-size instances. Our numerical results show that the proposed algorithm significantly outperforms the SDDiP algorithm at providing good-quality solutions within the computation time limit. Summary of Contribution: This paper investigates a combinatorial optimization problem called the uncapacitated lot-sizing problem. This problem has been widely studied in the operations research literature as it appears as a core subproblem in many industrial production planning problems. We consider a stochastic extension in which the input parameters are subject to uncertainty and model the resulting stochastic optimization problem as a multistage stochastic integer program. To solve this stochastic problem, we propose a novel extension of the recently published stochastic dual dynamic integer programming (SDDiP) algorithm. The proposed extension relies on two main ideas: the use of a partial decomposition of the scenario tree and the exploitation of existing knowledge on the polyhedral structure of the stochastic uncapacitated lot-sizing problem. We provide the results of extensive computational experiments carried out on large-size randomly generated instances. These results show that the proposed extended algorithm significantly outperforms the SDDiP at providing good-quality solutions for the stochastic uncapacitated lot-sizing problem. Although the paper focuses on a basic lot-sizing problem, the proposed algorithmic framework may be useful to solve more complex practical production planning problems. [ABSTRACT FROM AUTHOR]

This paper presents a survey of vehicle routing problems with multiple synchronization constraints. These problems exhibit, in addition to the usual task covering constraints, further synchronization requirements between the vehicles, concerning spatial, temporal, and load aspects. They constitute an emerging field in vehicle routing research and are becoming a "hot" topic. The contribution of the paper is threefold: (i) It presents a classification of different types of synchronization. (ii) It discusses the central issues related to the exact and heuristic solution of such problems. (iii) It comprehensively reviews pertinent literature with respect to applications as well as successful solution approaches, and it identifies promising algorithmic avenues. [ABSTRACT FROM AUTHOR]

Selecting the optimal policy using simulation is subject to input model risk when input models that mimic real-world randomness in the simulation have estimation error due to finite sample sizes. Instead of trying to find the optimal solution under unknown real-world input distributions by taking a conservative stance or with low statistical guarantee, the input–output uncertainty comparisons (IOU-C) procedure finds a set of solutions that cannot be separated from the best given the resolution decided by the finite sample sizes. The common-input-data (CID) effects measure how differently solutions are affected by the common estimated input models. When CID effects of two systems are positively correlated, the comparison becomes easier than estimating the performance measures of two systems precisely under input model risk; the IOU-C procedure takes advantage of the CID effects to develop a sharp comparison and thereby provides a small subset even in the presence of input model risk. When input distributions to a simulation model are estimated from real-world data, they naturally have estimation error causing input uncertainty in the simulation output. If an optimization via simulation (OvS) method is applied that treats the input distributions as "correct," then there is a risk of making a suboptimal decision for the real world, which we call input model risk. This paper addresses a discrete OvS (DOvS) problem of selecting the real-world optimal from among a finite number of systems when all of them share the same input distributions estimated from common input data. Because input uncertainty cannot be reduced without collecting additional real-world data—which may be expensive or impossible—a DOvS procedure should reflect the limited resolution provided by the simulation model in distinguishing the real-world optimal solution from the others. In light of this, our input–output uncertainty comparisons (IOU-C) procedure focuses on comparisons rather than selection: it provides simultaneous confidence intervals for the difference between each system's real-world mean and the best mean of the rest with any desired probability, while accounting for both stochastic and input uncertainty. To make the resolution as high as possible (intervals as short as possible) we exploit the common input data effect to reduce uncertainty in the estimated differences. Under mild conditions we prove that the IOU-C procedure provides the desired statistical guarantee asymptotically as the real-world sample size and simulation effort increase, but it is designed to be effective in finite samples. The electronic companion of this paper is available at https://doi.org/10.1287/opre.2018.1796. [ABSTRACT FROM AUTHOR]

This paper considers a vehicle routing problem where the customer demands are stochastic variables. Because of uncertainty along a route, the vehicle may be unable to load all planned customers' demand. Thus, the vehicle must return to the depot, unload, and then resume its trip. To avoid unplanned return trips to the depot, one may decide to make some preventive return: Even if it is not full, the vehicle returns to the depot, unloads, and resumes its trip at the next customer. These preventive returns avoid visiting the same customer twice at the expense of possibly making an unneeded return. In this paper, we propose an exact procedure for designing routes to minimize the total expected cost of the routes. It consists of a branch-and-cut algorithm based on the L-shaped method for stochastic programs with binary first-stage variables. The paper provides lower bounds and cuts on the expected costs, and describes the results of computational analysis of a computer implementation on benchmark instances. Instances involving up to 100 customers have been solved to optimality. [ABSTRACT FROM AUTHOR]

Operators and passengers need to adjust their plans in cases of large-scale disruptions in railway networks. Where most previous research has focused on the operators, this paper studies the combined support of both in a system where passengers have free route choice. In cases of disruption, passengers receive route advice, which they are not required to follow: passengers' route choice depends on the route advice and the timetable information available to them. Simultaneous to providing advice, rolling stock is rescheduled to accommodate the anticipated passenger demand. The duration of the disruption is uncertain, and passenger flows arise from a complex interaction between the passengers' route choices and the seat capacity allocated to the trains. We present an optimization-based algorithm that aims to minimize passenger inconvenience through provision of route advice and rolling stock rescheduling, where the advice optimization and rolling stock rescheduling modules are supported by a passenger simulation model. The algorithm aims to include and evaluate solutions under realistic passenger behavior assumptions. Our computational tests on realistic instances of Netherlands Railways indicate that the addition of the travel advice effectively improves the service quality to the passengers more than only rescheduling rolling stock, even when not all passengers follow the advice. The online appendix is available at https://doi.org/10.1287/trsc.2017.0759. [ABSTRACT FROM AUTHOR]

This paper makes a contribution to the branch and cut approach to the capacitated vehicle-routing problem (CVRP). In the CVRP, the demands of a set of customers have to be met at minimum total travel cost using vehicles of identical capacity based at a single depot. The potential of maximally violated mod-p cutting-planes (Caprara et al. 2000) for the CVRP is investigated via a computational study. The foundation of the assessment is formed by classes of problem-specific constraints taken from the literature. In several separation algorithms for the CVRP, it is advantageous to shrink inclusionwise maximal minimum-weight cuts in support graphs as preprocessing. It is mentioned how a partition of the set of customers into such mincuts can be computed in a fast and elegant way using the mincut algorithm of Hao and Orlin (1994). Interestingly, maximally violated mod-p cuts, which are general-purpose cuts of Chvátal-Gomory type, stand comparison with problem-specific cuts for the CVRP and they are clearly useful on top of such cuts. The first-time proven optimal solution of the CVRP instance B-n68-k9 is reported. The computation used a branching strategy with far lookahead and relied on maximally violated mod-p cuts. This paper on maximally violated cuts belongs to a set of papers originating from Applegate et al. (1995) where a separation of maximally violated combs for the traveling-salesman problem (TSP) is suggested. [ABSTRACT FROM AUTHOR]

Recent studies employ collections of binary decision diagrams (BDDs) to solve combinatorial optimization problems. This paper focuses on the problem of optimally aligning two BDDs, that is, transforming them to enforce a common order of variables while keeping the total size of the diagrams as small as possible. We address this problem, which is known to be NP-hard, by introducing and studying a simplified problem instead of working with the more complex original diagrams. We discuss some basic properties of the simplified problem, design a corresponding heuristic for the original problem, and show empirically that this approach yields good quality alignments while significantly reducing the complexity of intermediate diagram transformations. We highlight the practicality of this approach in the context of a variation of the uncapacitated facility location problem. History: Accepted by Andrea Lodi, Area Editor for Design and Analysis of Algorithms–Discrete. Funding: This work was supported by the Office of Naval Research [Grant N00014-17-1-2421]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/ijoc.2023.1293. [ABSTRACT FROM AUTHOR]

This paper presents an exact algorithm for the team formation problem, in which the aim is, given a project and its required skills, to construct a capable team that can communicate and collaborate effectively. This combinatorial optimization problem is modeled as a quadratic set covering problem. The study provides a novel branch-and-bound algorithm where a reformulation of the problem is relaxed so that it decomposes into a series of linear set covering problems, and the relaxed constraints are imposed through branching. The algorithm is able to solve instances that are intractable for commercial solvers. The study illustrates an efficient usage of algorithmic methods and modeling techniques for an operations research problem. It contributes to the field of computational optimization by proposing a new application and a new algorithm to solve a quadratic version of a classical combinatorial optimization problem. The team formation problem (TFP) aims to construct a capable team that can communicate and collaborate effectively. The cost of communication is quantified using the proximity of the potential members in a social network. We study a TFP with two measures for communication effectiveness; namely, we minimize the sum of communication costs, and we impose an upper bound on the largest communication cost. This problem can be formulated as a constrained quadratic set covering problem. Our experiments show that a general-purpose solver is capable of solving small and medium-sized instances to optimality. We propose a branch-and-bound algorithm to solve larger sizes: we reformulate the problem and relax it in such a way that it decomposes into a series of linear set covering problems, and we impose the relaxed constraints through branching. Our computational experiments show that the algorithm is capable of solving large-size instances, which are intractable for the solver. Summary of Contribution: This paper presents an exact algorithm for the Team Formation Problem (TFP), in which the aim is, given a project and its required skills, to construct a capable team that can communicate and collaborate effectively. This combinatorial optimization problem is modeled as a quadratic set covering problem. The study provides a novel branch-and-bound algorithm where a reformulation of the problem is relaxed so that it decomposes into a series of linear set covering problems and the relaxed constraints are imposed through branching. The algorithm is able to solve instances that are intractable for commercial solvers. The study illustrates an efficient usage of algorithmic methods and modelling techniques for an operations research problem. It contributes to the field of computational optimization by proposing a new application as well as a new algorithm to solve a quadratic version of a classical combinatorial optimization problem. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the one-machine scheduling problem with release and delivery times with the minimum makespan objective. Both heuristics and branch-and-bound algorithms have been formulated for the problem. One such branch-and-bound algorithm solves the problem and a variation that requires a delay between the completion of one job and the start of another (delayed precedence constraints). This paper analyzes key components of this branch-and-bound algorithm and proposes an improved heuristic to be used in conjunction with a different search strategy. Computational experiments demonstrate that the modifications lead to substantial improvements in running time and number of iterations on the one-machine problem instances both with and without delayed precedence constraints. [ABSTRACT FROM AUTHOR]

We consider a general class of online optimization problems, called online selection problems, where customers arrive sequentially, and one has to decide upon arrival whether to accept or reject each customer. If a customer is rejected, then a rejection cost is incurred. The accepted customers are served with minimum possible cost, either online or after all customers have arrived. The goal is to minimize the total production costs for the accepted customers plus the rejection costs for the rejected customers. These selection problems are related to online variants of offline prize collecting combinatorial optimization problems that have been widely studied in the computer science literature. In this paper, we provide a general framework to develop online algorithms for this class of selection problems. In essence, the algorithmic framework leverages any cost sharing mechanism with certain properties into a poly-logarithmic competitive online algorithm for the respective problem; the competitive ratios are shown to be near-optimal. We believe that the general and transparent connection we establish between cost sharing mechanisms and online algorithms could lead to additional online algorithms for problems beyond the ones studied in this paper. [ABSTRACT FROM AUTHOR]

In many classical combinatorial optimization problems, including critical and shortest paths, maximum flow, and network reliability, the introduction of uncertainty considerably complicates the calculation of system performance. In fact, in these contexts, computing system performance exactly can often be an impossible task. Therefore, obtaining (stochastic) bounds on the system's performance becomes an attractive and useful alternative. This paper studies several stochastic bounds that are applicable to these contexts and to a broader set of problems that can be described by the general combinatorial concepts of clutters and blocking clutters. We begin our discussion by defining these unifying concepts and illustrating their specialization in several problem contexts. [ABSTRACT FROM AUTHOR]

Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets. The objective is to minimize the sum of the distances of the chosen set of edges for the worst positions of the vertices in their uncertainty sets. We first prove that these problems are N P -hard even when the feasible sets consist either of all spanning trees or of all s – t paths. Given this hardness, we propose an exact solution algorithm combining integer programming formulations with a cutting plane algorithm, identifying the cases where the separation problem can be solved efficiently. We also propose a conservative approximation and show its equivalence to the affine decision rule approximation in the context of Euclidean distances. We compare our algorithms to three deterministic reformulations on instances inspired by the scientific literature for the Steiner tree problem and a facility location problem. History: Accepted by David Alderson, Area Editor for Network Optimization: Algorithms & Applications. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2023.1276. [ABSTRACT FROM AUTHOR]

This paper studies a novel decomposition scheme, utilizing decision diagrams for modeling elements of a problem where typical linear relaxations fail to provide sufficiently tight bounds. Given a collection of decision diagrams, each representing a portion of the problem, together with linear inequalities modeling other portions of the problem, how can one efficiently optimize over such a representation? In this paper, we model the problem as a consistent path problem, where a path in each diagram has to be identified, all of which agree on the value assignments to variables. We establish complexity results and propose a branch-and-cut framework for solving the decomposition. Through application to binary cubic optimization and a variant of the market split problem, we show that the decomposition approach provides significant improvement gains over standard linear models. The application of decision diagrams in combinatorial optimization has proliferated in the last decade. In recent years, authors have begun to investigate how to use not one, but a set of diagrams, to model constraints and objective function terms. Optimizing over a collection of decision diagrams, the problem we refer to as the consistent path problem (CPP) can be addressed by associating a network-flow model with each decision diagram, jointly linked through channeling constraints. A direct application of integer programming to the ensuing model has already been shown to result in algorithms that provide orders-of-magnitude performance gains over classical methods. Lacking, however, is a careful study of dedicated solution methods designed to solve the CPP. This paper provides a detailed study of the CPP, including a discussion on complexity results and a complete polyhedral analysis. We propose a cut-generation algorithm, which, under a structured ordering property, finds a cut, if one exists, through an application of the classical maximum flow problem, albeit in an exponentially sized network. We use this procedure to fuel a cutting-plane algorithm that is applied to unconstrained binary cubic optimization and a variant of the market split problem, resulting in an algorithm that compares favorably with CPLEX, using standard integer programming formulations for both problems. [ABSTRACT FROM AUTHOR]

The growth in air traffic (before the Covid-19 pandemic) made airport time slots an increasingly scarce resource (and it is believed that this growth will continue after recovery). It is widely acknowledged that the grandfathering schemes used nowadays lead to inefficient allocations and that auctions would be a means to allocate valuable airport time slots efficiently. It has, however, also been pointed out that the design of such slot auctions is challenging due to the various constraints that need to be considered. The present paper proposes a market design for the sales of airport time slots at EU airports that complies with the Worldwide Scheduling Guidelines of the International Air Transport Association (IATA), most notably the reference value systems at level 3 airports. These guidelines need to be considered but lead to significant additional complexity in the market design. Capacity constraints are defined for overlapping time windows, which render the maximum welfare flight scheduling problem NP-hard. Auction formats with good incentive properties such as the Vickrey-Clarke-Groves mechanism or core-selecting auctions require an exact solution to the allocation problem. Given its hardness, it is far from obvious that the allocation problem can be solved to optimality sufficiently fast for practically relevant sizes of real-world problems. We introduce a mathematical model formulation for the maximum welfare flight scheduling problem that complies with all specified IATA constraints and evaluate it on near real-world data sets of flight requests for a full season of a major international airport. We show that the allocation can be computed within minutes and that all the payment computations for the winners can be done in less than two hours on average for realistic problem sizes. The consideration of values of airlines within the proposed auction mechanism leads to significant welfare gains of more than 35% as compared with benchmarks resulting from different standard objectives. These include the maximization of the number of movements, the minimization of the number of movements for which deviations from requested times occur, and the minimization of the total deviation of scheduled from requested times. Whereas the results indicate that auctions can be solved quickly for realistic problem sizes and promise significant welfare gains under the standard independent private values assumptions, the implementation of auctions in the field leads to additional serious challenges. For example, the regulator might have to impose allocation constraints to mitigate the market power of incumbent airlines. In addition, the valuation of slots and the interdependencies of the slot assignment with those at other coordinated airports need careful attention. Funding: This work was supported by the Deutsche Forschungsgemeinschaft [Grants BI-1057/I-9 and 405008493]. M. Bichler gratefully acknowledges funding by the German National Science Foundation [DFG BI 1057/9-1]. [ABSTRACT FROM AUTHOR]

In this paper, a new branch-and-price-and-cut algorithm is proposed to solve the one-dimensional bin-packing problem (1D-BPP). The 1D-BPP is one of the most fundamental problems in combinatorial optimization and has been extensively studied for decades. Recently, a set of new 500 test instances were proposed for the 1D-BPP, and the best exact algorithm proposed in the literature can optimally solve 167 of these new instances, with a time limit of 1 hour imposed on each execution of the algorithm. The exact algorithm proposed in this paper is based on the classical set-partitioning model for the 1DBPPs and the subset row inequalities. We describe an ad hoc label-setting algorithm to solve the pricing problem, dominance, and fathoming rules to speed up its computation and a new primal heuristic. The exact algorithm can easily handle some practical constraints, such as the incompatibility between the items, and therefore, we also apply it to solve the one-dimensional bin-packing problem with conflicts (1D-BPPC). The proposed method is tested on a large family of 1D-BPP and 1D-BPPC classes of instances. For the 1D-BPP, the proposed method can optimally solve 237 instances of the new set of difficult instances; the largest instance involves 1,003 items and bins of capacity 80,000. For the 1D-BPPC, the experiments show that the method is highly competitive with state-of-the-art methods and that it successfully closed several open 1D-BPPC instances. [ABSTRACT FROM AUTHOR]

In this paper, an improved sequence-based selection hyper-heuristic method for the Air Liquide inventory routing problem, the subject of the ROADEF/EURO 2016 challenge, is described. The organizers of the challenge have proposed a real-world problem of inventory routing as a difficult combinatorial optimization problem. An exact method often fails to find a feasible solution to such problems. On the other hand, heuristics may be able to find a good quality solution that is significantly better than those produced by an expert human planner. There is a growing interest toward self-configuring automated general-purpose reusable heuristic approaches for combinatorial optimization. Hyper-heuristics have emerged as such methodologies. This paper investigates a new breed of hyper-heuristics based on the principles of sequence analysis to solve the inventory routing problem. The primary point of this work is that it shows the usefulness of the improved sequence-based selection hyper-heuristic, and in particular demonstrates the advantages of using a data science technique of hidden Markov model for the heuristic selection. [ABSTRACT FROM AUTHOR]

The quadratic assignment problem (QAP) consists of assigning n facilities to n locations to minimize the total weighted cost of interactions between facilities. The QAP arises in many diverse settings, is known to be NP-hard, and can be solved to optimality only for fairly small instances (typically, n ⩽ 30). Neighborhood search algorithms are the most popular heuristic algorithms for solving larger instances of the QAP. The most extensively applied neighborhood structure for the QAP is the 2-exchange neighborhood. This neighborhood is obtained by swapping the locations of two facilities; its size is therefore O(n2). Previous efforts to explore larger neighborhoods (such as 3-exchange or 4-exchange neighborhoods) were not very successful, as it took too long to evaluate the larger set of neighbors. In this paper, we propose very large-scale neighborhood (VLSN) search algorithms when the size of the neighborhood is very large, and we propose a novel search procedure to enumerate good neighbors heuristically. Our search procedure relies on the concept of an improvement graph that allows us to evaluate neighbors much faster than existing methods. In this paper, we present extensive computational results of our algorithms when applied to standard benchmark instances. [ABSTRACT FROM AUTHOR]

The multiple vehicle routing problem with time windows (VRPTW) is a hard and extensively studied combinatorial optimization problem. This paper considers a dynamic VRPTW with stochastic customers, where the goal is to maximize the number of serviced customers. It presents a multiple scenario approach (MSA) that continuously generates routing plans for scenarios including known and future requests. Decisions during execution use a distinguished plan chosen, at each decision, by a consensus function. The approach was evaluated on vehicle routing problems adapted from the Solomon benchmarks with a degree of dynamism varying between 30% and 80%. They indicate that MSA exhibits dramatic improvements over approaches not exploiting stochastic information, that the use of consensus function improves the quality of the solutions significantly, and that the benefits of MSA increase with the (effective) degree of dynamism. [ABSTRACT FROM AUTHOR]

In this paper we introduce the time window assignment vehicle routing problem (TWAVRP). In this problem, I time windows have to be assigned before demand is known. Next, a realization of demand is revealed, and a vehicle routing schedule is made that satisfies the assigned time windows. The objective is to minimize the expected traveling costs. We propose a branch-price-and-cut algorithm to solve the TWAVRP to optimality. We provide results of computational experiments performed using this algorithm. Finally, we offer insight on the value of an exact approach for the TWAVRP by comparing the optimal solution to the solution found by assigning time windows based on solving a vehicle routing problem with time windows with average demand. [ABSTRACT FROM AUTHOR]

We consider the problem of finding the minimum number of vehicles required to visit once a set of nodes subject to time window constraints, for a homogeneous fleet of vehicles located at a common depot. This problem can be formulated as a network flow problem with additional time constraints. The paper presents an optimal solution approach using the augmented Lagrangian method. Two Lagrangian relaxations are studied. In the first one, the time constraints are relaxed producing network subproblems which are easy to solve, but the bound obtained is weak. In the second relaxation, constraints requiring that each node be visited are relaxed producing shortest path subproblems with time window constraints and integrality conditions. The bound produced is always excellent. Numerical results for several actual school busing problems with up to 223 nodes are discussed. Comparisons with a set partitioning formulation solved by column generation are given. [ABSTRACT FROM AUTHOR]

Makespan minimization in permutation flow-shop scheduling is a well-known hard combinatorial optimization problem. Among the 120 standard benchmark instances proposed by E. Taillard in 1993, 23 have remained unsolved for almost three decades. In this paper, we present our attempts to solve these instances to optimality using parallel Branch-and-Bound (BB) on the GPU-accelerated Jean Zay supercomputer. We report the exact solution of 11 previously unsolved problem instances and improved upper bounds for eight instances. The solution of these problems requires both algorithmic improvements and leveraging the computing power of peta-scale high-performance computing platforms. The challenge consists in efficiently performing parallel depth-first traversal of a highly irregular and fine-grained search tree on distributed systems composed of hundreds of massively parallel accelerator devices and multicore processors. We present and discuss the design and implementation of our permutation-based BB and experimentally evaluate its parallel performance on up to 384 V100 GPUs (2 million CUDA cores) and 3840 CPU cores. The optimality proof for the largest solved instance requires about 64 CPU-years of computation—using 256 GPUs and over 4 million parallel search agents, the traversal of the search tree is completed in 13 hours, exploring 339 × 10 12 nodes. [ABSTRACT FROM AUTHOR]

We consider binary integer programming problems with the min-max regret objective function under interval objective coefficients. We propose a heuristic framework, the iterated dual substitution (iDS) algorithm, which iteratively invokes a dual substitution heuristic and excludes from the search space any solution already checked in previous iterations. In iDS, we use a best scenario–based lemma to improve performance. We apply iDS to four typical combinatorial optimization problems: the knapsack problem, the multidimensional knapsack problem, the generalized assignment problem, and the set covering problem. For the multidimensional knapsack problem, we compare the iDS approach with two algorithms widely used for problems with the min-max regret criterion: a fixed-scenario approach, and a branch-and-cut approach. The results of computational experiments on a broad set of benchmark instances show that the proposed iDS approach performs best on most tested instances. For the knapsack problem, the generalized assignment problem, and the set covering problem, we compare iDS with state-of-the-art results. The iDS algorithm successfully updates best-known records for a number of benchmark instances. Summary of Contribution: This paper proposes a heuristic framework for binary integer programming (BIP) problems with the min-max regret objective function under interval objective coefficients. We selected four representative NP-hard combinatorial optimization problems: the knapsack problem, the multidimensional knapsack problem, the set covering problem, and the generalized assignment problem. We show the effectiveness and efficiency of the approach by comparing with state-of-the-art results. [ABSTRACT FROM AUTHOR]

Splitting methods in optimization arise when one can divide an optimization problem into two or more simpler subproblems. They have proven particularly successful for relaxations of problems involving discrete variables. We revisit and strengthen splitting methods for solving doubly nonnegative relaxations of the particularly difficult, NP-hard quadratic assignment problem. We use a modified restricted contractive splitting method approach. In particular, we show how to exploit redundant constraints in the subproblems. Our strengthened bounds exploit these new subproblems and new dual multiplier estimates to improve on the bounds and convergence results in the literature. Summary of Contribution: In our paper, we consider the quadratic assignment problem (QAP). It is one of the fundamental combinatorial optimization problems in the fields of optimization and operations research and includes many fundamental applications. We revisit and strengthen splitting methods for solving doubly nonnegative (DNN) relaxation of the QAP. We use a modified restricted contractive splitting method. We obtain strengthened bounds from improved lower and upper bounding techniques, and in fact, we solve many of these NP-hard problems to (provable) optimality, thus illustrating both the strength of the DNN relaxation and our new bounding techniques. [ABSTRACT FROM AUTHOR]

Most airline revenue optimization models assume capacity to be fixed by fleet assignment, and thus treat it as deterministic. However, empirical data show that on 40% of flights, capacity is updated at least once within the booking horizon. Capacity updates can be caused by fleet-assignment reoptimizations or by short-term operational problems. This paper proposes a first model to integrate the resulting capacity uncertainty in the leg-based airline revenue management process. While assuming deterministic demand, the proposed model includes stochastic scenarios to represent potential capacity updates. To derive optimal inventory controls, we provide both a mixed-integer program and a combinatorial solution approach, and discuss efficient ways of optimizing the special case of a single capacity update. We also explore effects of denied boarding cost and the model's relationship to the static overbooking problem. We numerically evaluate the model on empirically calibrated demand instances and benchmark it on the established deterministic approach and an upper bound based on perfect hindsight. In addition, we show that the combinatorial solution approach reduces the computational effort. Finally, we compare the static overbooking approach derived from the capacity uncertainty model to existing approaches based on the expected marginal seat revenue (EMSR). [ABSTRACT FROM AUTHOR]

The split delivery vehicle routing problem with time windows (SDVRPTW) is a notoriously hard combinatorial optimization problem. First, it is hard to find a useful compact mixed-integer programming (MIP) formulation for the SDVRPTW. Standard modeling approaches either suffer from inherent symmetries (mixed-integer programs with a vehicle index) or cannot exactly capture all aspects of feasibility. Because of the possibility to visit customers more than once, the standard mechanisms to propagate load and time along the routes fail. Second, the lack of useful formulations has rendered any direct MIP-based approach impossible. Up to now, the most effective exact algorithms for the SDVRPTW have been branch-and-price-and-cut approaches using path-based formulations. In this paper, we propose a new and tailored branch-and-cut algorithm to solve the SDVRPTW. It is based on a new, relaxed compact model, in which some integer solutions are infeasible for the SDVRPTW. We use known and introduce some new classes of valid inequalities to cut off such infeasible solutions. One new class is path-matching constraints that generalize infeasible-path constraints. However, even with the valid inequalities, some integer solutions to the new compact formulation remain to be tested for feasibility. For a given integer solution, we build a generally sparse subnetwork of the original instance. On this subnetwork, all time-window-feasible routes can be enumerated, and a path-based residual problem then solved to decide on the selection of routes, the delivery quantities, and thereby the overall feasibility. All infeasible solutions need to be cut off. For this reason, we derive some strengthened feasibility cuts exploiting the fact that solutions often decompose into clusters. Computational experiments show that the new approach is able to prove optimality for several previously unsolved instances from the literature. The e-companion is available at https://doi.org/10.1287/trsc.2018.0825. [ABSTRACT FROM AUTHOR]

This paper considers the vehicle routing problem with soft time windows, a challenging routing problem where customers' time windows may be violated at a certain cost. The vehicle routing problem with soft time windows has a lexicographic objective function, aimed at minimizing first the number of routes, then the number of violated time windows, and finally the total routing distance. We present a multistage very large-scale neighborhood search for this problem. Each stage corresponds to a variable neighborhood descent over a parameterizable very large-scale neighborhood. These neighborhoods contain an exponential number of neighbors, as opposed to classical local search neighborhoods. Often, searching very large-scale neighborhoods can produce local optima of a higher quality than polynomial-sized neighborhoods can. Furthermore, we use a sophisticated heuristic to determine service start times allowing us to minimize the number of violated time windows. We test our approach on a number of different problem types, and compare the results to the relevant state of the art. The experimental results show that our algorithm improves best known solutions on 53% of the most studied instances. Many of these improvements stem from a reduction of the number of vehicles, a critical objective in vehicle routing problems. [ABSTRACT FROM AUTHOR]

The authors developed a model based on constraint programming to provide the best feasible solution(s) for minimizing the dispatching delays within a given planning horizon. At Howrah Station, the largest railway station in India, planners manually determine the routing and scheduling of train movements (referred to as train dispatching) at present. This approach to train dispatching, which is a complex combinatorial optimization problem, can result in long delays because planners have many resource-allocation options in the spatial and temporal domains. In this paper, we discuss a computational model to provide the best feasible solution(s) for minimizing the dispatching delays within a planning horizon. We consider an integrated station dispatching problem that consists of allocating and scheduling platforms and routes for trains at Howrah Station, and we develop a constraint programming (CP)-based approach to model the problem. We show that the delay that the model generates is approximately half the delay currently observed in practice. The solutions have been verified by Howrah Station authority, and the model is being considered for implementation. The novelty of the solution is that it uses a CP-based model for the integrated station dispatching problem and successfully deals with a large station with specific operational protocols. [ABSTRACT FROM AUTHOR]

Accurate yield prediction in integrated circuit manufacturing enables accurate estimation of production cost and early detection of processing problems. It is known that defects tend to be clustered and a chip is likely to be defective if its neighbors are defective. This neighborhood effect is not well captured in traditional yield modeling approaches. We propose a new yield prediction model, called adjacency-clustering which addresses, for the first time, the neighborhood effect, and delivers prediction results that are significantly better than state-of-the-art methods. Adjacency-clustering (AC) model is a form of the Markov random field minimum energy model (MRF) that is primarily known in the context of image segmentation. AC model is a novel use of MRF for identifying defect patterns that enable diagnosis of failure causes in the manufacturing process. In this paper we utilize the defect patterns obtained by the AC model for yield prediction. We compare the performance of the AC model to that of leading yield prediction models including the Poisson, the negative binomial, the Poisson regression, and negative binomial regression models, on real data sets and on simulated data sets. The results demonstrate that the adjacency-clustering model captures the neighborhood effect and delivers superior prediction accuracy. Moreover, the concept and methodology of adjacency-clustering are not limited to integrated circuit manufacturing. Rather, it is applicable in any context where a neighborhood effect is present, such as disease risk mapping and energy consumption prediction. The e-companion is available at https://doi.org/10.1287/opre.2018.1741. [ABSTRACT FROM AUTHOR]

The container relocation problem (CRP) is concerned with finding a sequence of moves of containers that minimizes the number of relocations needed to retrieve all containers, while respecting a given order of retrieval. However, the assumption of knowing the full retrieval order of containers is particularly unrealistic in real operations. This paper studies the stochastic CRP, which relaxes this assumption. A new multistage stochastic model, called the batch model, is introduced, motivated, and compared with an existing model (the online model). The two main contributions are an optimal algorithm called Pruning-Best-First-Search (PBFS) and a randomized approximate algorithm called PBFS-Approximate with a bounded average error. Both algorithms, applicable in the batch and online models, are based on a new family of lower bounds for which we show some theoretical properties. Moreover, we introduce two new heuristics outperforming the best existing heuristics. Algorithms, bounds, and heuristics are tested in an extensive computational section. Finally, based on strong computational evidence, we conjecture the optimality of the "leveling" heuristic in a special "no information" case, where, at any retrieval stage, any of the remaining containers is equally likely to be retrieved next. The online appendix is available at https://doi.org/10.1287/trsc.2018.0828. [ABSTRACT FROM AUTHOR]

Binary programs with a quadratic objective function are NP-hard in general, even if the linear optimization problem over the same feasible set is tractable. In this paper, we address such problems by computing quadratic global underestimators of the objective function that are separable but not necessarily convex. Exploiting the binary constraint on the variables, a minimizer of the separable underestimator over the feasible set can be computed by solving an appropriate linear minimization problem over the same feasible set. Embedding the resulting lower bounds into a branch-and-bound framework, we obtain an exact algorithm for the original quadratic binary program. The main practical challenge is the fast computation of an appropriate underestimator, which in our approach reduces to solving a series of semidefinite programs.We exploit the special structure of the resulting problems to obtain a tailored coordinate-descent method for their solution. Our extensive experimental results on various quadratic combinatorial optimization problems show that our approach outperforms both CPLEX and the related QCR method as well as the SDP-based software BiqCrunch on instances of the quadratic shortest path problem and the quadratic assignment problem. [ABSTRACT FROM AUTHOR]

Deferred-acceptance auctions are mechanisms whose allocation rule can be implemented using an adaptive reverse greedy algorithm. Milgrom and Segal recently introduced these auctions and proved that they satisfy remarkable incentive guarantees: in addition to being dominant strategy and incentive compatible, they are weakly group-strategyproof and can be implemented by ascending-clock auctions. Neither forward greedy mechanisms nor the VCG mechanism generally possess any of these additional incentive properties. The goal of this paper is to initiate the study of deferred-acceptance auctions from an approximation standpoint. We study what fraction of the optimal social welfare can be guaranteed by these auctions in two canonical problems, knapsack auctions and combinatorial auctions with single-minded bidders. For knapsack auctions, we prove a separation between deferred-acceptance auctions and arbitrary dominant-strategy incentive-compatible mechanisms. For combinatorial auctions with single-minded bidders, we design novel polynomial-time mechanisms that achieve the best of both worlds: the incentive guarantees of a deferred-acceptance auction, and approximation guarantees close to the best possible. [ABSTRACT FROM AUTHOR]

We investigate the discrete parallel machine scheduling and location problem, which consists of locating multiple machines to a set of candidate locations, assigning jobs from different locations to the located machines, and sequencing the assigned jobs. The objective is to minimize the maximum completion time of all jobs, that is, the makespan. Though the problem is of theoretical significance with a wide range of practical applications, it has not been well studied as reported in the literature. For this problem, we first propose three new mixed-integer linear programs that outperform state-of-the-art formulations. Then, we develop a new logic-based Benders decomposition algorithm for practical-sized instances, which splits the problem into a master problem that determines machine locations and job assignments to machines and a subproblem that sequences jobs on each machine. The master problem is solved by a branch-and-cut procedure that operates on a single search tree. Once an incumbent solution to the master problem is found, the subproblem is solved to generate cuts that are dynamically added to the master problem. A generic no-good cut is first proposed, which is later improved by some strengthening techniques. Two optimality cuts are also developed based on optimality conditions of the subproblem and improved by strengthening techniques. Numerical results on small-sized instances show that the proposed formulations outperform state-of-the-art ones. Computational results on 1,400 benchmark instances with up to 300 jobs, 50 machines, and 300 locations demonstrate the effectiveness and efficiency of the algorithm compared with current approaches. Summary of Contribution: This paper employs operations research methods and computing techniques to address an NP-hard combinatorial optimization problem: the parallel discrete machine scheduling and location problem. The problem is of practical significance but has not been well studied in the literature. For the problem, we formulate three novel mixed-integer linear programs that outperform state-of-the-art formulations and develop a new logic-based Benders decomposition algorithm. Extensive computational experiments on 1,400 benchmark instances with up to 300 jobs, 50 machines, and 300 locations are conducted to evaluate the performance of the proposed models and algorithms. [ABSTRACT FROM AUTHOR]

Adding domain knowledge to a learning system is known to improve results. In multiparameter Bayesian frameworks, such knowledge is incorporated as a prior. On the other hand, the various model parameters can have different learning rates in real-world problems, especially with skewed data. Two often-faced challenges in operation management and management science applications are the absence of informative priors and the inability to control parameter learning rates. In this study, we propose a hierarchical empirical Bayes approach that addresses both challenges and that can generalize to any Bayesian framework. Our method learns empirical meta-priors from the data itself and uses them to decouple the learning rates of first-order and second-order features (or any other given feature grouping) in a generalized linear model. Because the first-order features are likely to have a more pronounced effect on the outcome, focusing on learning first-order weights first is likely to improve performance and convergence time. Our empirical Bayes method clamps features in each group together and uses the deployed model's observed data to empirically compute a hierarchical prior in hindsight. We report theoretical results for the unbiasedness, strong consistency, and optimal frequentist cumulative regret properties of our meta-prior variance estimator. We apply our method to a standard supervised learning optimization problem as well as an online combinatorial optimization problem in a contextual bandit setting implemented in an Amazon production system. During both simulations and live experiments, our method shows marked improvements, especially in cases of small traffic. Our findings are promising because optimizing over sparse data is often a challenge. This paper was accepted by Hamid Nazerzadeh, Management Science Special Section on Data-Driven Prescriptive Analytics. [ABSTRACT FROM AUTHOR]

The traveling salesman problem (TSP) is a fundamental problem in combinatorial optimization. Several semidefinite programming relaxations have been proposed recently that exploit a variety of mathematical structures including, for example, algebraic connectivity, permutation matrices, and association schemes. The main results of this paper are twofold. First, de Klerk and Sotirov [de Klerk E, Sotirov R (2012) Improved semidefinite programming bounds for quadratic assignment problems with suitable symmetry. Math. Programming 133(1):75–91.] present a semidefinite program (SDP) based on permutation matrices and symmetry reduction; they show that it is incomparable to the subtour elimination linear program but generally dominates it on small instances. We provide a family of simplicial TSP instances that shows that the integrality gap of this SDP is unbounded. Second, we show that these simplicial TSP instances imply the unbounded integrality gap of every SDP relaxation of the TSP mentioned in the survey on SDP relaxations of the TSP in section 2 of Sotirov [Sotirov R (2012) SDP relaxations for some combinatorial optimization problems. Anjos MF, Lasserre JB, eds., Handbook on Semidefinite, Conic and Polynomial Optimization (Springer, New York), 795–819.]. In contrast, the subtour linear program performs perfectly on simplicial instances. The simplicial instances thus form a natural litmus test for future SDP relaxations of the TSP. [ABSTRACT FROM AUTHOR]

We study the design of large-scale group testing schemes under a heterogeneous population (i.e., subjects with potentially different risk) and with the availability of multiple tests. The objective is to classify the population as positive or negative for a given binary characteristic (e.g., the presence of an infectious disease) as efficiently and accurately as possible. Our approach examines components often neglected in the literature, such as the dependence of testing cost on the group size and the possibility of no testing, which are especially relevant within a heterogeneous setting. By developing key structural properties of the resulting optimization problem, we are able to reduce it to a network flow problem under a specific, yet not too restrictive, objective function. We then provide results that facilitate the construction of the resulting graph and finally provide a polynomial time algorithm. Our case study, on the screening of HIV in the United States, demonstrates the substantial benefits of the proposed approach over conventional screening methods. Summary of Contribution: This paper studies the problem of testing heterogeneous populations in groups in order to reduce costs and hence allow for the use of more efficient tests for high-risk groups. The resulting problem is a difficult combinatorial optimization problem that is NP-complete under a general objective. Using structural properties specific to our objective function, we show that the problem can be cast as a network flow problem and provide a polynomial time algorithm. [ABSTRACT FROM AUTHOR]

Given an integer dimension K and a simple, undirected graph G with positive edge weights, the Distance Geometry Problem (DGP) aims to find a realization function mapping each vertex to a coordinate in R K such that the distance between pairs of vertex coordinates is equal to the corresponding edge weights in G. The so-called discretization assumptions reduce the search space of the realization to a finite discrete one, which can be explored via the branch-and-prune (BP) algorithm. Given a discretization vertex order in G, the BP algorithm constructs a binary tree where the nodes at a layer provide all possible coordinates of the vertex corresponding to that layer. The focus of this paper is on finding optimal BP trees for a class of discretizable DGPs. More specifically, we aim to find a discretization vertex order in G that yields a BP tree with the least number of branches. We propose an integer programming formulation and three constraint programming formulations that all significantly outperform the state-of-the-art cutting-plane algorithm for this problem. Moreover, motivated by the difficulty in solving instances with a large and low-density input graph, we develop two hybrid decomposition algorithms, strengthened by a set of valid inequalities, which further improve the solvability of the problem. Summary of Contribution: We present a new model to solve a combinatorial optimization problem on graphs, MIN DOUBLE, which comes from the highly active area of distance geometry and has applications in a wide variety of fields. We use integer programming (IP) and present the first constraint programming (CP) models and hybrid decomposition methods, implemented as a branch-and-cut procedure, for MIN DOUBLE. Through an extensive computational study, we show that our approaches advance the state of the art for MIN DOUBLE. We accomplish this by not only combining generic techniques from IP and CP but also exploring the structure of the problem in developing valid inequalities and variable fixing rules. Our methods significantly improve the solvability of MIN DOUBLE, which we believe can also provide insights for tackling other problem classes and applications. [ABSTRACT FROM AUTHOR]

We solve the type-2 assembly line balancing problem in the presence of sequence-dependent setup times, denoted SUALBP-2. The problem consists of a set of tasks of a product, requiring to be processed in different assembly stations. Each task has a definite processing and setup times. The magnitude of setup times for each task is dependent on the processing sequence within each station. Processing and setup times of tasks assigned to each station constitute the station time. The goal is to minimize the cycle time (the maximum station time) by optimally (i) assigning tasks to assembly stations and (ii) sequencing these tasks within each station. To solve this challenging optimization problem, we first improve upon an existing mixed-integer programming (MIP) model by our proposed lower and upper bounds. These enhancements reduce the MIP model's (solved CPLEX) average optimality gap from 41.61% to 20.77% on extra-large instances of the problem. To further overcome the intractability of the MIP model, we develop an exact logic-based Benders decomposition (LBBD) algorithm. The LBBD algorithm effectively incorporates a novel two-phase solution approach, the lower and upper bounds, various preprocessing techniques, relaxations, and valid inequalities. Using existing benchmarks in the literature, we demonstrate that our LBBD algorithm finds integer feasible solutions for 100% of all 788 instances (64% for the MIP), verifies optimality for 47% of instances (37% for the MIP), and achieves an average optimality gap of 5.04% (7.72% for the MIP obtained over 64% solved small instances). The LBBD algorithm also significantly reduces the computational time required to solve these benchmarks. Summary of Contribution: Assembly line balancing plays a crucial role in productivity enhancement in manufacturing and service companies. A balanced assembly line ensures higher throughput rate and fairer distribution of workload among assembly stations (workers). Assembly line balancing, in its simplest form, is one of the most challenging combinatorial optimization problems. Its complexity is further intensified when the sequence of executing tasks assigned to each station influences the magnitude of the setup performed between any two successive tasks. In view of such complexity, most assembly line balancing problems have been solved by randomized search techniques that do not provide any guarantee on the quality of solutions found. The mission of this paper is to understand whether there is any special structure within the existing mathematical models in the literature and, if so, exploit them toward developing computationally efficient exact techniques that can provide guarantee on the quality of solutions. Indeed, we demonstrate that such a special mathematical structure exists and we thus develop the first decomposition technique in form of a logic-based Benders decomposition (LBBD) to efficiently solve the type-2 sequence-dependent assembly line balancing problem. Specifically, we show that our LBBD significantly reduces cycle time and the time required for decision making. Our LBBD generalizes the scope of exact techniques for decision-making beyond the assembly line problems and is extendable to many other shop scheduling problems that arrange their stations (machines) serially and there are sequence-dependent setup times among their tasks. [ABSTRACT FROM AUTHOR]