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The article presents abstracts of contributed papers submitted for presentation at the Chicago Meeting. The paper "Computer Simulation in a Missile Operational Cycle," by Robert T. Morrison explains a model of a hypothetical weapon system is analyzed by simulation techniques using a digital computer. All the important parameters affecting the model are identified and values selected. Random numbers selected by the computer are used to determine the occurrence of missile and GSE malfunctions according to the failure rates established and also to determine the repair times for the missiles and GSE if malfunctions occur. Another paper "A Measure of Effectiveness for Weapon-System Evaluation," by Robert T. Morrison explains a concept for a measure of effectiveness is developed for evaluating and judging weapon-system design and operation The proposed measure of effectiveness considers the most important factors in any complex system-maximum performance and reliability with minimum cost and time This paper shows how the measure of effectiveness is valuable for system analysis in judging between alternative proposed systems in preliminary design and measuring and evaluating the selected system progress from prototype design through final system operation and maintenance.

To support the 2021 Manufacturing & Service Operations Management (M&SOM) Data-Driven Research Challenge, RiRiShun Logistics (a Haier group subsidiary focusing on logistics service for home appliances) provides MSOM members with logistics operational-level data for data-driven research. This paper provides a detailed description of the data associated with over 14 million orders from 149 clients (the consigners) associated with 4.2 million end consumers (the recipients and end users of the appliances) in China, involving 18,000 stock keeping units operated at 103 warehouses. Researchers are welcomed to develop econometric models, data-driven optimization techniques, analytical models, and algorithm designs by using this data set to address questions suggested by company managers. History: This paper has been accepted as part of the 2021 M&SOM Data-Driven Research Challenge. Funding: This work was supported by the National Natural Science Foundation of China [Grants 72091215/72091210, 71871207, 71991464/71991460, and 71921001]. Supplemental Material: Data and the online appendix are is available at https://doi.org/10.1287/msom.2021.0994. [ABSTRACT FROM AUTHOR]

This article describes an integer programming-based system for diagramming small customer rolls from large bulk rolls of expensive photographic color paper at Kodak Australasia. Certain characteristics of the problem led to a new innovative approach, for example, the need for the majority of customer rolls to be splice free and a lack of homogeneity in the raw material. Since, implementation diagramming waste has improved by over 50 percent, yielding benefits in excess of $2 million in the first year. Other benefits include increased productivity of the cutting machine, less time devoted to diagramming, an increased ability to move to a shorter planning horizon, and the capability to better match supply to demand.

Comments on the paper 'A General Method for Nonlinear Programming,' by Anthony V. Fiacco, Nicholas M. Smith and David Blackwell. Application of the principle of entry into a constrained space to Carroll's technique; Computation of the starting point for the original problem.

This article presents comments by the author on a paper discussing heuristic and special case algorithms for dispersion problems. Problems discussed in this article are the subject of the paper in focus. The results presented in that paper include a simple heuristic for Max-Min Facility Dispersion (MMFD) which provides a performance guarantee of 1/2, and a similar heuristic for Max-Avg Facility Dispersion (MAFD) with a performance guarantee of 1/4. It is also proved there that obtaining a performance guarantee of more than 1/2 for MMFD is NP-hard. The paper also discussed the one- dimensional versions of MMFD and MAFD, where the vertex set V consists of a set of n points on the real line. Section 2 of the paper is devoted to the heuristic for MMPD. It should be noted that this heuristic was analyzed before. In fact, it is shown therein that the performance guarantee of 1/2, holds for a more general model where the selected set p is restricted to be in a compact subset of the network indiced by the edge distances.

The article presents comments on the management science paper "On Sequencing n Jobs on One Machine to Minimize the Number of Late Jobs," by William L. Maxwell. The paper focused on an integer programming formulation of a one-machine job shop problem. The author contends that Maxwell made in error in proving the validity of an optimal algorithm by applying cutting plane constraints to the problem. The author explains that the problem cannot be solved through traditional cutting plane procedures. The author provides a mathematical model in an attempt to correct the proof.

Presents a letter to the editor about the optimal policy in a maintenance cost problem.

Childhood vaccines play a vital role in social welfare, but in hard-to-reach regions, poor transportation, and a weak cold chain limit vaccine availability. This opens the door for the use of vaccine delivery by drones (uncrewed aerial vehicles, or UAVs) with their fast transportation and reliance on little or no infrastructure. In this paper, we study the problem of strategic multimodal vaccine distribution, which simultaneously determines the locations of local distribution centers, drone bases, and drone relay stations, while obeying the cold chain time limit and drone range. Two mathematical optimization models with complementary strengths are developed. The first model considers the vaccine travel time at the aggregate level with a compact formulation, but it can be too conservative in meeting the cold chain time limit. The second model is based on the layered network framework to track the vaccine flow and travel time associated with each origin-destination (OD) pair. It allows the number of transshipments and the number of drone stops in a vaccine flow path to be limited, which reflects practical operations and can be computationally advantageous. Both models are applied for vaccine distribution network design with two types of drones in Vanuatu as a case study. Solutions with drones using our parameter settings are shown to generate large savings, with differentiated roles for large and small drones. To generalize the empirical findings and examine the performance of our models, we conduct comprehensive computational experiments to assess the sensitivity of optimal solutions and performance metrics to key problem parameters. History: This paper has been accepted for the Transportation Science Special Issue on Emerging Topics in Transportation Science and Logistics. Funding: This work was supported by the Association for Supply Chain Management (ASCM) and the University of Missouri Research Board (UMSL Award 0059109). Supplemental Material: The online supplement is available at https://doi.org/10.1287/trsc.2023.1205. [ABSTRACT FROM AUTHOR]

Competition for the 2017 Daniel H. Wagner Prize for Excellence in Operations Research Practice provided the six finalist papers featured in this special issue of Interfaces. The prestigious Wagner Prize—awarded for achievement in implemented operations research, management science, and advanced analytics—emphasizes quality and originality of mathematical models and clarity of written and oral exposition. Researchers from Lehigh University, in collaboration with the Pennsylvania Department of Corrections, won the competition for their development of a novel hierarchical, multiobjective mixed-integer linear optimization model, which assigns inmates to correctional institutions and schedules their programs, while considering all legal restrictions and best-practice constraints. This successful project opens a rich and untouched area for the application of operations research. The new model and methodology can be utilized for the assignment of inmates in any correctional system. The remaining papers describe work on audience targeting for television advertising, optimizing railroad crew assignments, applying machine-learning models to healthcare and criminal justice, personalized treatment design for managing diabetes, and optimization in bulk tanker transport operations. Full presentation videos with slides are available in the INFORMS Video Library at https://www.informs.org/Resource-Center/Video-Library, and as electronic companions to the Interfaces articles. [ABSTRACT FROM AUTHOR]

There is an error in one of the results of our paper [Huettner F, Boyacı T, Akçay Y (2019) Consumer choice under limited attention when alternatives have different information costs. Oper. Res. 67(3):671–699]. In this erratum, we point out the error and provide a correction based on Walker-Jones [(2023) Rational inattention with multiple attributes. J. Econom. Theory 212:105688]. Our key characterizations, insights, and numerical examples do not depend on this error and, hence, remain valid. The main implication is on the stopping condition used in the algorithm. We propose a fix based on the new sufficient condition and, if needed, standard convex optimization techniques. [ABSTRACT FROM AUTHOR]

As one of the most plausible convex optimization methods for sparse data reconstruction, ℓ1-minimization plays a fundamental role in the development of sparse optimization theory. The stability of this method has been addressed in the literature under various assumptions such as the restricted isometry property, null space property, and mutual coherence. In this paper, we propose a unified means to develop the so-called weak stability theory for ℓ1-minimization methods under the condition called the weak range space property of a transposed design matrix, which turns out to be a necessary and sufficient condition for the standard ℓ1-minimization method to be weakly stable in sparse data reconstruction. The reconstruction error bounds established in this paper are measured by the so-called Robinson's constant. We also provide a unified weak stability result for standard ℓ1-minimization under several existing compressed sensing matrix properties. In particular, the weak stability of this method under the constant-free range space property of the transposed design matrix is established, to our knowledge, for the first time in this paper. Different from the existing analysis, we utilize the classic Hoffman's lemma concerning the error bound of linear systems as well as Dudley's theorem concerning the polytope approximation of the unit ball to show that ℓ1-minimization is robustly and weakly stable in recovering sparse data from inaccurate measurements. [ABSTRACT FROM AUTHOR]

Assortment optimization has received significant attention in recent revenue management and combinatorial optimization literature. In "The Approximability of Assortment Optimization Under Ranking Preferences," A. Aouad, V. Farias, R. Levi, and D. Segev provide best-possible approximability bounds for this problem under an almost general model specification, where preferences are expressed as a distribution over rankings. This paper shows how this optimization problem relates to the computational task of detecting large independent sets in graphs, allowing the establishment of strong complexity lower bounds with respect to various problem parameters. These findings are complemented by a number of algorithms that attain essentially best-possible approximation factors, proving that the hardness results are tight up to lower-order terms. Surprisingly, their results imply that a simple and widely studied policy, known as revenue-ordered assortments, achieves the best possible performance guarantee with respect to prices. The main contribution of this paper is to provide best-possible approximability bounds for assortment planning under a general choice model, where customer choices are modeled through an arbitrary distribution over ranked lists of their preferred products, subsuming most random utility choice models of interest. From a technical perspective, we show how to relate this optimization problem to the computational task of detecting large independent sets in graphs, allowing us to argue that general ranking preferences are extremely hard to approximate with respect to various problem parameters. These findings are complemented by a number of approximation algorithms that attain essentially best-possible factors, proving that our hardness results are tight up to lower-order terms. Surprisingly, our results imply that a simple and widely studied policy, known as revenue-ordered assortments, achieves the best possible performance guarantee with respect to the price parameters. [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]

Over the last two decades, robust optimization has emerged as a popular means to address decision-making problems affected by uncertainty. This includes single-stage and multi-stage problems involving real-valued and/or binary decisions and affected by exogenous (decision-independent) and/or endogenous (decision-dependent) uncertain parameters. Robust optimization techniques rely on duality theory potentially augmented with approximations to transform a (semi-)infinite optimization problem to a finite program, the robust counterpart. Whereas writing down the model for a robust optimization problem is usually a simple task, obtaining the robust counterpart requires expertise. To date, very few solutions are available that can facilitate the modeling and solution of such problems. This has been a major impediment to their being put to practical use. In this paper, we propose ROC++, an open-source C++ based platform for automatic robust optimization, applicable to a wide array of single-stage and multi-stage robust problems with both exogenous and endogenous uncertain parameters, that is easy to both use and extend. It also applies to certain classes of stochastic programs involving continuously distributed uncertain parameters and endogenous uncertainty. Our platform naturally extends existing off-the-shelf deterministic optimization platforms and offers ROPy, a Python interface in the form of a callable library, and the ROB file format for storing and sharing robust problems. We showcase the modeling power of ROC++ on several decision-making problems of practical interest. Our platform can help streamline the modeling and solution of stochastic and robust optimization problems for both researchers and practitioners. It comes with detailed documentation to facilitate its use and expansion. The latest version of ROC++ can be downloaded from https://sites.google.com/usc.edu/robust-opt-cpp/. Summary of Contribution: The paper "ROC++: Robust Optimization in C++" proposes a new open-source C++ based platform for modeling, automatically reformulating, and solving robust optimization problems. ROC++ can address both single-stage and multi-stage problems involving exogenous and/or endogenous uncertain parameters and real- and/or binary-valued adaptive variables. The ROC++ modeling language is similar to the one provided for the deterministic case by state-of-the-art deterministic optimization solvers. ROC++ comes with detailed documentation to facilitate its use and expansion. It also offers ROPy, a Python interface in the form of a callable library. The latest version of ROC++ can be downloaded from https://sites.google.com/usc.edu/robust-opt-cpp/. History: Accepted by Ted Ralphs, Area Editor for Software Tools. Funding: This material is based upon work supported by the National Science Foundation under Grant No. 1763108. This support is gratefully acknowledged. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplementary Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.1209) or is available from the IJOC GitHub software repository (https://github.com/INFORMSJoC) at (https://dx.doi.org/10.5281/zenodo.6360996). [ABSTRACT FROM AUTHOR]

This Note points out a minor error in a technique developed by Soyster and Lev [1] for determining if a linear goal can be substituted for a fractional goal in a goal programming problem. A revised formulation is provided. [ABSTRACT FROM AUTHOR]

An important problem in the theory of dynamic programming is that of characterizing sufficient conditions under which the optimal policies for Markov decision processes (MDPs) under the infinite-horizon discounted cost criterion converge to an optimal policy under the average cost criterion as the discount factor approaches 1. In this paper, we provide, for stochastic inventory models, a set of such sufficient conditions. These conditions, unlike many others in the dynamic programming literature, hold when the action space is noncompact and the underlying transition law is weakly continuous. Moreover, we verify that these conditions hold for almost all conceivable single-stage inventory models with few assumptions on cost and demand parameters. As a consequence of our analysis, we partially characterize, for the first time, optimal policies for the following inventory systems under the infinite-horizon average-cost criterion, which have thus far been a challenge: (a) capacitated systems with setup costs, (b) uncapacitated systems with convex ordering costs plus a setup cost, and (c) systems with lost sales and lead times. [ABSTRACT FROM AUTHOR]

In this paper, we use the penalty approach in order to study constrained minimization problems in infinite dimensional spaces. A penalty function is said to have the exact penalty property if there is a penalty coefficient for which a solution of an unconstrained penalized problem is a solution of the corresponding constrained problem. In this paper, we establish the exact penalty property for a large class of inequality-constrained minimization problems. [ABSTRACT FROM AUTHOR]

In this paper, we focus on a subclass of quadratic optimization problems, that is, disjoint bilinear optimization problems. We first show that disjoint bilinear optimization problems can be cast as two-stage robust linear optimization problems with fixed-recourse and right-hand-side uncertainty, which enables us to apply robust optimization techniques to solve the resulting problems. To this end, a solution scheme based on a blending of three popular robust optimization techniques is proposed. For disjoint bilinear optimization problems with a polyhedral feasible region and a general convex feasible region, we show that, under mild regularity conditions, the convex relaxations of the original bilinear formulation and its two-stage robust reformulation obtained from a reformulation-linearization-based technique and linear decision rules, respectively, are equivalent. For generic bilinear optimization problems, the convex relaxations from the reformulation-linearization-based technique are generally tighter than the one from linear decision rules. Numerical experiments on bimatrix games, synthetic disjoint bilinear problem instances, and convex maximization problems demonstrate the efficiency and effectiveness of the proposed solution scheme. Summary of Contribution: Computing solutions for disjoint bilinear optimization problems are of much interest in real-life applications, yet they are, in general, computationally intractable. This paper proposes a computationally tractable approximation as well as a convergent algorithm to the optimal values of such problems. Extensive computational experiments on (i) (constrained) bimatrix games, (ii) synthetic disjoint bilinear problems, and (iii) convex maximization problems are conducted to demonstrate the effectiveness and efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

The article presents the author's comments about the article "Supply, Shortage, and Service Reliability Decisions by Gas Distribution Utilities: A Chance-Constrained Approach," by Jean-Michel Guildmann. The author focuses on the cost effectiveness associated with Guildmann's mathematical model. It is suggested that management scientists consider the applications of Guildmann's mathematical optimization problem when faced with critical decisions regarding the future of the gas market. The author proposes that the analytical framework proposed by Guildman may be useful when making decisions regarding industrial capacity.

We address the problem of wallpapering a room so as to minimize the paper wasted. We show that the problem is equivalent to finding a shortest hamiltonian chain in a highly structured graph. When the chain connects two equivalent nodes (traveling salesman problem), the "nearest-neighbor" technique yields an optimal solution. [ABSTRACT FROM AUTHOR]

This paper presents a classified bibliography organized into six sections--static design models, dynamic control models, models involving queue discipline control, miscellaneous models, tutorial and survey papers, and books that have specific portions devoted to design and control. Some of the above categories are further subdivided when appropriate, and explanations of the types of models in each category and subcategory precede the actual list of references. Papers that fall into more than one category are cross-referenced. [ABSTRACT FROM AUTHOR]

The technique of perturbation analysis has recently been introduced as an efficient way to compute parameter sensitivities for discrete event systems. Thus far, the statistical properties of perturbation analysis have been validated mainly through experiments. This paper considers, for an M/G/1 queueing system, the sensitivity of mean system time of a customer to a parameter of the arrival or service distribution. It shows analytically that (i) the steady state value of the perturbation analysis estimate of this sensitivity is unbiased, and (ii) a perturbation analysis algorithm implemented on a single sample path of the system gives asymptotically unbiased and strongly consistent estimates of this sensitivity. (No previous knowledge of peturbation analysis is assumed, so the paper also serves to introduce this technique to the unfamiliar reader.) Numerical extensions to GI/G/1 queues, and applications to optimization problems, are also illustrated. [ABSTRACT FROM AUTHOR]

This paper deals with undiscounted infinite stage two-person zero-sum stochastic games with finite state and action spaces. It was recently shown that such games possess a value. But in general there are no optimal strategies. We prove that for each player there exists a nonempty set of easy initial states, i.e. starting states for which the player possesses an optimal stationary strategy. This result is proved with the aid of facts derived by Bewley and Kohlberg for the limit discount equation for stochastic games. [ABSTRACT FROM AUTHOR]

One of the important uses of an EOQ item's distribution of lead time demand is to set its reorder point. This paper shows that a realistic model of observed demand patterns can be chosen from the compound Poisson family of distributions. Actual historical data from several U.S. Air Force bases are analyzed using the geometric-Poisson and constant-Poisson distributions. The control discipline is order quantity, reorder point with continuous review. The service level is based on percent of demand supplied during lead time and is consistent with current USAF methodology. The reorder point is based on independent calculations and no attempt is made to jointly optimize the order quantity and reorder point. Lead time is assumed to be known and constant. [ABSTRACT FROM AUTHOR]

This article informs about the Operations Research Society of America's "Thirteenth National Meeting" which was held at Boston, Massachusetts from May 15-17, 1958. From a total 521 registrations, there were 301 were members, 186 were non-members, 34 were students. Seventy-one contributed and twelve invited papers were read. For the purpose twelve sessions were held, nine of which were half-day sessions. All-day sessions were held on Dynamic Programming, on Operational Gaming and Simulation and on Techniques of Simulation Using Digital Computers, the latter was the only session on May 17 and was held at the Computation Center of the Massachusetts Institute of Technology. The subjects of some of the individual sessions, and their chairmen, were: George E. Kimball for Dynamic Programming; Philip M. Morse for Forecasting; William Young for Contributed Papers; John M. Magee for Experimentation; Jay W. Forrester for Operations Research in Data Processing and Leon S. Pocinky for Techniques in Simulations Using Digital Computers.

In many statistical learning problems, it is desired that the optimal solution conform to an a priori known sparsity structure represented by a directed acyclic graph. Inducing such structures by means of convex regularizers requires nonsmooth penalty functions that exploit group overlapping. Our study focuses on evaluating the proximal operator of the latent overlapping group lasso developed by Jacob et al. in 2009. We implemented an alternating direction method of multiplier with a sharing scheme to solve large-scale instances of the underlying optimization problem efficiently. In the absence of strong convexity, global linear convergence of the algorithm is established using the error bound theory. More specifically, the paper contributes to establishing primal and dual error bounds when the nonsmooth component in the objective function does not have a polyhedral epigraph. We also investigate the effect of the graph structure on the speed of convergence of the algorithm. Detailed numerical simulation studies over different graph structures supporting the proposed algorithm and two applications in learning are provided. Summary of Contribution: The paper proposes a computationally efficient optimization algorithm to evaluate the proximal operator of a nonsmooth hierarchical sparsity-inducing regularizer and establishes its convergence properties. The computationally intensive subproblem of the proposed algorithm can be fully parallelized, which allows solving large-scale instances of the underlying problem. Comprehensive numerical simulation studies benchmarking the proposed algorithm against five other methods on the speed of convergence to optimality are provided. Furthermore, performance of the algorithm is demonstrated on two statistical learning applications related to topic modeling and breast cancer classification. The code along with the simulation studies and benchmarks are available on the corresponding author's GitHub website for evaluation and future use. [ABSTRACT FROM AUTHOR]

In this paper, we consider uncertain second-order cone (SOC) and semidefinite programming (SDP) constraints with polyhedral uncertainty, which are in general computationally intractable. We propose to reformulate an uncertain SOC or SDP constraint as a set of adjustable robust linear optimization constraints with an ellipsoidal or semidefinite representable uncertainty set, respectively. The resulting adjustable problem can then (approximately) be solved by using adjustable robust linear optimization techniques. For example, we show that if linear decision rules are used, then the final robust counterpart consists of SOC or SDP constraints, respectively, which have the same computational complexity as the nominal version of the original constraints. We propose an efficient method to obtain good lower bounds. Moreover, we extend our approach to other classes of robust optimization problems, such as nonlinear problems that contain wait-and-see variables, linear problems that contain bilinear uncertainty, and general conic constraints. Numerically, we apply our approach to reformulate the problem on finding the minimum volume circumscribing ellipsoid of a polytope and solve the resulting reformulation with linear and quadratic decision rules as well as Fourier-Motzkin elimination. We demonstrate the effectiveness and efficiency of the proposed approach by comparing it with the state-of-the-art copositive approach. Moreover, we apply the proposed approach to a robust regression problem and a robust sensor network problem and use linear decision rules to solve the resulting adjustable robust linear optimization problems, which solve the problem to (near) optimality. Summary of Contribution: Computing robust solutions for nonlinear optimization problems with uncertain second-order cone and semidefinite programming constraints are of much interest in real-life applications, yet they are in general computationally intractable. This paper proposes a computationally tractable approximation for such problems. Extensive computational experiments on (i) computing the minimum volume circumscribing ellipsoid of a polytope, (ii) robust regressions, and (iii) robust sensor networks are conducted to demonstrate the effectiveness and efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper introduces the formal study of process flexibility to the novel domain of sports analytics. In baseball, positional flexibility is the analogous concept to process flexibility from manufacturing. We study the flexibility of players (plants) on a baseball team who produce innings-played at different positions (products). We develop models and metrics to evaluate expected and worst-case performance under injury risk (capacity uncertainty) with continuous player-position capabilities. Using Major League Baseball data, we quantify the impact of flexibility on team and individual performance and explore the player chains that arise when injuries occur. We discover that top teams can attribute at least one to two wins per season to flexibility alone, generally as a result of long subchains in the infield or outfield. The least robust teams to worst-case injury, those whose performance is driven by one or two star players, are over four times as fragile as the most robust teams. We evaluate several aspects of individual flexibility, such as how much value individual players bring to their team in terms of average and worst-case performance. Finally, we demonstrate the generalizability of our framework for player evaluation by quantifying the value of potential free agent additions and uncovering the true "MVP" of a team. Data are available at https://doi.org/10.1287/mnsc.2017.3004. This paper was accepted by Vishal Gaur, operations management. [ABSTRACT FROM AUTHOR]

In classical inverse linear optimization, one assumes that a given solution is a candidate to be optimal. Real data are imperfect and noisy, so there is no guarantee that this assumption is satisfied. Inspired by regression, this paper presents a unified framework for cost function estimation in linear optimization comprising a general inverse optimization model and a corresponding goodness-of-fit metric. Although our inverse optimization model is nonconvex, we derive a closed-form solution and present the geometric intuition. Our goodness-of-fit metric, ρ, the coefficient of complementarity, has similar properties to R2 from regression and is quasi-convex in the input data, leading to an intuitive geometric interpretation. While ρ is computable in polynomial time, we derive a lower bound that possesses the same properties, is tight for several important model variations, and is even easier to compute. We demonstrate the application of our framework for model estimation and evaluation in production planning and cancer therapy. This paper was accepted by Yinyu Ye, optimization. [ABSTRACT FROM AUTHOR]

This paper investigates a decomposition approach for binary optimization problems with nonlinear objectives and linear constraints. Our methodology relies on the partition of the objective function into separate low-dimensional dynamic programming (DP) models, each of which can be equivalently represented as a shortest-path problem in an underlying state-transition graph. We show that the associated transition graphs can be related by a mixed-integer linear program (MILP) so as to produce exact solutions to the original nonlinear problem. To address DPs with large state spaces, we present a general relaxation mechanism that dynamically aggregates states during the construction of the transition graphs. The resulting MILP provides both lower and upper bounds to the nonlinear function, and it may be embedded in branch-and-bound procedures to find provably optimal solutions. We describe how to specialize our technique for structured objectives (e.g., submodular functions) and consider three problems arising in revenue management, portfolio optimization, and healthcare. Numerical studies indicate that the proposed technique often outperforms state-of-the-art approaches by orders of magnitude in these applications. Data and the online appendix are available at https://doi.org/10.1287/mnsc.2017.2849. This paper was accepted by Yinyu Ye, optimization. [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]

This paper presents a new information acquisition problem motivated by business applications where customer data has to be acquired with a specific modeling objective in mind. In the last two decades, there has been substantial work in two different fields—optimal experimental design and machine learning—that has addressed the issue of acquiring data in a selective manner with a specific objective in mind. We show that the problem presented here is different from the classic model-based data acquisition problems considered thus far in the literature in both fields. Building on work in optimal experimental design and in machine learning, we develop a new active learning technique for the information acquisition problem presented in this paper. We demonstrate that the proposed method performs well based on results from applying this method across 20 Web usage and machine learning data sets. [ABSTRACT FROM AUTHOR]

In this paper we address the problem of finding the simulated system with the best (maximum or minimum) expected performance when the number of systems is large and initial samples from each system have already been taken. This problem may be encountered when a heuristic search procedure--perhaps one originally designed for use in a deterministic environment --has been applied in a simulation-optimization context. Because of stochastic variation, the system with the best sample mean at the end of the search procedure may not coincide with the true best system encountered during the search. This paper develops statistical procedures that return the best system encountered by the search (or one near the best) with a prespecified probability. We approach this problem using combinations of statistical subset selection and indifference-zone ranking procedures. The subset-selection procedures, which use only the data already collected, screen out the obviously inferior systems, while the indifference-zone procedures, which require additional simulation effort, distinguish the best from the less obviously inferior systems. [ABSTRACT FROM AUTHOR]

This paper deals with nonhomogeneous Markov decision processes with Borel state space and nonuniformly bounded rewards under the average criterion. First, under the minorant-type assumption we prove the existence of an appropriate solution to the optimality equations. Second, from the optimality equations we also establish the existence of ε(≥ 0)-optimal Markov policies under the additional conditions. Third, some sufficient conditions for the validity of the assumptions in this paper and several examples such as inventory/production systems are provided. Finally, as an application of the optimality equations, a rolling horizon algorithm is given. [ABSTRACT FROM AUTHOR]

This paper proposes a simulation-based optimization technique for high-dimensional toll optimization problems of large-scale road networks. We formulate a novel analytical network model. The latter is embedded within a metamodel simulation-based optimization (SO) algorithm. It provides analytical and differentiable structural information of the underlying problem to the SO algorithm. Hence, the algorithm no longer treats the simulator as a black box. The analytical model is formulated as a system of nonlinear equations that can be efficiently evaluated with standard solvers. The dimension of the system of equations scales linearly with network size. It scales independently of the dimension of the route choice set and of link attributes such as link length. Hence, it is a scalable formulation suitable for the optimization of large-scale networks. For instance, the model is used in the case study of the paper for toll optimization of a Singapore network with more than 4,050 OD (origin-destination) pairs and 18,200 feasible routes. The corresponding analytical model is implemented as a system of 860 nonlinear equations. The analytical network model is validated based on one-dimensional toy network problems. It captures the main trends of the simulation-based objective function and, more importantly, accurately locates the global optimum for all experiments. The proposed SO approach is then used to optimize a set of 16 tolls for the network of expressways and major arterials of Singapore. The proposed method is compared with a general-purpose algorithm. The proposed method identifies good quality solutions at the very first iteration. The benchmark method identifies solutions with similar performance after 2 days of computation or similarly after more than 30 points have been simulated. The case study indicates that the analytical structural information provided to the algorithm by the analytical network model enables it to (i) identify good quality solutions fast and (ii) become robust to both the quality of the initial points and to the stochasticity of the simulator. The final solutions identified by the proposed algorithm outperform those of the benchmark method by an average of 18%. [ABSTRACT FROM AUTHOR]

This paper proposes a computationally efficient simulation-based optimization (SO) algorithm suitable to address large-scale generally constrained urban transportation problems. The algorithm is based on a novel metamodel formulation. We embed the metamodel within a derivative-free trust region algorithm and evaluate the performance of this SO approach considering tight computational budgets. We address a network-wide traffic signal control problem using a calibrated microscopic simulation model of evening peak period traffic of the full city of Lausanne, Switzerland, which consists of more than 600 links and 200 intersections. We control 99 signal phases of 17 intersections distributed throughout the entire network. This SO problem is a high-dimensional nonlinear constrained problem. It is considered large-scale and complex in the fields of derivative-free optimization, traffic signal optimization, and simulation-based optimization. We compare the performance of the proposed metamodel method to that of a traditional metamodel method and that of a widely used commercial signal control software. The proposed method systematically and efficiently identifies signal plans with improved average city-wide travel times. [ABSTRACT FROM AUTHOR]

This paper considers the problem of test design and implementation when testing is imperfect. Items that are classified as conforming may be nonconforming, resulting in a poor outgoing quality level. Items that are classified as nonconforming may be conforming, resulting in excessive scrapping of conforming items. The failed items are commonly retested to reduce the scrapping problem. Alternatively, the accepted items may be retested to improve outgoing quality. In this paper, we examine the question of whether it is better to repetitively test rejected items, or to repetitively test accepted items. We also examine the relationship between the two testing policies, testing equipment accuracy and capacity, incoming quality, and outgoing quality requirements. [ABSTRACT FROM AUTHOR]

We reconsider the stochastic dynamic program of revenue management with flexible products and customer choice behavior as proposed by Gallego et al. [Gallego G, Iyengar G, Phillips RL, Dubey A (2004) Managing flexible products on a network. Working paper, Columbia University, New York]. In the scientific literature on revenue management, as well as in practice, the prevailing strategy to operationalize dynamic programs is to decompose the network by resources and solve the resulting one-dimensional problems. However, to date, these dynamic programming decomposition approaches have not been applicable to problems with flexible products, because sold flexible products must be included in the dynamic program's state space and do not correspond directly to resources. In this paper, we contribute to the existing research by presenting a general approach to operationalizing revenue management with flexible products and customer choice in a dynamic programming environment. In particular, we reformulate the original dynamic program by means of Fourier-Motzkin elimination to obtain an equivalent dynamic program with a standard resource-based state space. This reformulation allows the application of dynamic programming decomposition approaches. Numerical experiments show that the new approach has a superior revenue performance and that its average revenues are close to the upper bound on the optimal expected revenue from the choice-based deterministic linear program. Moreover, our reformulation improves the revenues by up to 8% compared to an extended variant of a standard choice-based approach that immediately assigns flexible products after their sale. The online appendix is available at . [ABSTRACT FROM AUTHOR]

Bilevel optimization problems are very challenging optimization models arising in many important practical contexts, including pricing mechanisms in the energy sector, airline and telecommunication industry, transportation networks, critical infrastructure defense, and machine learning. In this paper, we consider bilevel programs with continuous and discrete variables at both levels, with linear objectives and constraints (continuous upper level variables, if any, must not appear in the lower level problem). We propose a general-purpose branch-and-cut exact solution method based on several new classes of valid inequalities, which also exploits a very effective bilevel-specific preprocessing procedure. An extensive computational study is presented to evaluate the performance of various solution methods on a common testbed of more than 800 instances from the literature and 60 randomly generated instances. Our new algorithm consistently outperforms (often by a large margin) alternative state-of-the-art methods from the literature, including methods exploiting problem-specific information for special instance classes. In particular, it solves to optimality more than 300 previously unsolved instances from the literature. To foster research on this challenging topic, our solver is made publicly available online. The online appendix is available at . [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]

This paper is concerned with a linear fractional problem of the form: max[sub x] min[sub y] F(X, Y) = (cX + dY + α)/(fX + gY + β), subject to AX + BY less than or equal to b; X, Y greater than or equal to O. This problem represents a generalization of a problem considered in the literature in which F(X, Y) is assumed to be linear. A number of results for the linear case are extended; and, in particular, it is shown that this fractional max-min problem is equivalent to a quasi-convex programming problem whose optimal solution lies at a vertex of the feasible region. Using these results, we develop an algorithm for solving this problem. The paper concludes with a numerical example. [ABSTRACT FROM AUTHOR]

This paper develops rolling horizon procedures for solving a multistage inventory problem with facilities-in-series. In such an inventory system, we assume that the raw material is processed successively through several facilities before reaching the customer. The input to a facility comes from one preceding facility (or the raw material) and the output from the facility goes to one succeeding facility (or the customer). The rolling horizon procedures form rolling production schedules by solving a finite horizon multiperiod problem and implementing only the first period's decisions. One period later, the multiperiod problem is updated as better forecasts become available and the process is repeated. The paper considers a simple case when holding costs are linear, production costs on a facility consist of a setup cost and a constant marginal cost of production, and production and holding costs are stationary in time. Demand is allowed to be nonstationary in time. Several rolling horizon procedures are developed for this case and a computational comparison is given. [ABSTRACT FROM AUTHOR]

Banking has been a fertile area for management science applications, as is evident from the review provided in this paper. The relevant management science models are discussed in terms of the areas of bank management for which they were intended. Under dynamic balance sheet management (i.e., internal bank financial planning) we consider forecasting techniques, simulation models and optimization models. Other areas of banking included are bond portfolio management, bank operations, corporate services, bank marketing and management of the loan portfolio. The authors provide an evaluation of the applicability of management science models in practice, discuss the extent to which some have been implemented and consider the philosophy of using management science models in banking. [ABSTRACT FROM AUTHOR]

This paper extends previous work on the use of sequential building heuristics for the design of a collection system, a linear fixed-charge problem that includes the design of a lock-box system as an important subproblem. The heuristic extensions in this paper first present simple methods for eliminating "premature termination" (stopping the heuristics while there are still worthwhile alternatives not included in the collection system) and unprofitable inclusion (including collection alternatives with net benefits less than the fixed cost). Initiation procedures that increase computational efficiency and reduce the likelihood of significant suboptimization are presented. Finally, the simple one-at-a-time building procedure is extended to include joint exclusion-building (a limited switching plus building) and combination switching-building rules that consider combinations of alternatives rather than one-at-a-time evaluation. [ABSTRACT FROM AUTHOR]

This paper combines two rival preference modeling techniques in a new approach to multi-attribute decision making. Currently existing multi-attribute procedures use either global or local preference modeling. In the global modeling technique, a single preference function is constructed in the large; its maximum is the optimal alternative. In the local procedure, sequential approximations of the preference function are constructed in the small. Each approximation generates a trial solution. Under suitable conditions, each trial solution is preferred to its predecessor, so the trial sequence eventually reaches the optimum. Each technique has advantages and disadvantages; this paper combines the desirable features of both techniques in a new improved method. This new method, called the proxy approach, uses the advantages of one technique to overcome the disadvantages of the other. This paper first develops the theoretical aspects of the proxy approach and then compares it to existing procedures. Finally, the proxy algorithm is applied to a curriculum planning problem and numerous insights are gained. [ABSTRACT FROM AUTHOR]

The motivation for this paper is a problem faced by banks which process large volumes of deposited checks. The checks must be separated by bank number before shipment to the Federal Reserve or other banks. The sorting is usually accomplished using a reader-sorter which reads the magnetic ink characters on the checks and separates them into different "pockets." This paper characterizes the optimal sorting strategy and describes an efficient procedure for finding the optimal solution for problems of the size generally found in practice. The algorithm is based on a two state dynamic programming recursion in which characterization theorems are used to drastically reduce the size of the state space and in which the storage requirements are minimal. The paper includes an analysis of computational experience and describes how the algorithm can be used in a real time environment with deadlines. [ABSTRACT FROM AUTHOR]

This paper extends the Bierman-Hausman credit-granting model by proving that although the distribution on the probability of collection in the case of failure is no longer a conjugate Beta, it remains tractable; the model therefore need no longer be terminated in the case of failure. Further theorems on the structure of optimal policies, which result in a considerable reduction of the dynamic programming state space, are then presented, and the paper concludes with a discussion of extensions and applications. [ABSTRACT FROM AUTHOR]

This paper examines properties and interrelations of several concepts of generalized concavity. It shows that the class of functions that are both ‘generalized concave’ and ‘generalized convex’ is closely related to the class of monotone functions of a single variable. After excluding a certain small class of exceptions, the paper shows that, for arbitrary (perhaps not differentiable) functions, concave implies pseudoconcave, pseudoconcave implies strictly quasiconcave, and strictly quasiconcave implies quasiconcave. Several results characterizing the extreme values of generalized concave functions are given. [ABSTRACT FROM AUTHOR]

This paper considers the case of a product consisting of several components, each of which is batch manufactured. It assumes that the product demands occur singly, and that the components are manufactured in equal-batch quantities in a reorder level-batch quantity system. The paper is concerned with the optimal phasing of the components in order to minimize the variance of holding cost for the product. It shows that the optimal policy is independent of the order of sequencing of the components and is given when the phase lag between consecutive components in the cycle is equal to [(Ai+Aj)/∑all i Ai. (q/2), where Ai, Aj are the unit values of the components, and q is the batch quantity. A specific example is included to illustrate the three-component case and the discrete practical solution for any number of components is indicated. [ABSTRACT FROM AUTHOR]

The past decade has given rise to a considerable amount of research in the fields of inventory control and production planning. One of the most useful mathematical models originated with the paper of K. D. ARROW, T. E. HARRIS, AND J. MARSCHAK, "Optimal Inventory Policy," Econometrica 19, 250-272 (1951). This model was further improved in RICRARD BELLMAN'S book, Dynamic Programming, pp. 152-182, Princeton University Press, Princeton, New Jersey, 1957. In the present paper, another formulation of the same problem is exhibited. The attentive reader will observe many similarities to the dynamic programming formulation. [ABSTRACT FROM AUTHOR]