Operations Research Applications Research Articles

Optimal Kidney Exchange with Immunosuppressants

Algorithms for exchange of kidneys is one of the key successful applications in market design, artificial intelligence, and operations research. Potent immunosuppressant drugs suppress the body's ability to reject a transplanted organ up to the point that a transplant across blood- or tissue-type incompatibility becomes possible. In contrast to the standard kidney exchange problem, we consider a setting that also involves the decision about which recipients receive from the limited supply of immunosuppressants that make them compatible with originally incompatible kidneys. We firstly present a general computational framework to model this problem. Our main contribution is a range of efficient algorithms that provide flexibility in terms of meeting meaningful objectives. Motivated by the current reality of kidney exchanges using sophisticated mathematical-programming-based clearing algorithms, we then present a general but scalable approach to optimal clearing with immunosuppression; we validate our approach on realistic data from a large fielded exchange.

Book Reviews

In Book Reviews, we review an extensive and diverse range of books. They cover theory and applications in operations research, statistics, management science, econometrics, mathematics, computers, and information systems. In addition, we include books in other fields that emphasize technical applications. The editor will be pleased to receive an email from those willing to review a book, with an indication of specific areas of interest. If you are aware of a specific book that you would like to review, or that you think should be reviewed, please contact the editor. The following books are reviewed in this issue of INFORMS Journal on Applied Analytics, 51(3), May–June: Optimization and Control for Systems in the Big-Data Era: Theory and Applications, Tsan-Ming Choi, Jianjun Gao, James H. Lambert, Chi-Kong Ng, Jun Wang; Pricing Lives: Guideposts for a Safer Society, W. Kip Viscusi.

English

The Management Science theory is one of the theories of management that attributes management effectiveness to the application of scientific methods. It goes a step beyond the famous scientific management theory by applying operations research tools and techniques to solving practical problems. Its origin can be traced to the Second World War in Britain. Its method of expressing business factors in form of variables allows for the accurate prediction of business phenomena and overall optimization of profits. The management science approach uses computer applications and operations research tools to solve business problems around quantitative management, operations research, total quality management and management information systems. Its major limitation is its inability to accurately predict business phenomena that contain behavioral elements. The theory ignores the importance of people, relationships and other non-quantifiable factors. Overall, the management science theory provides a new and proactive way of solving business problems by identifying relationships among different business variables that were previously considered unrelated and so, have provided modern businesses with a better way of doing things.   Key words: Management Science theory, scientific management theory, operations research, total quality management, linear programming.

Research on optimal path Modeling based on DP Model

Nowadays, the emergence of all kinds of games greatly enriches our life and enlightens our wisdom; As a vehicle of enlightenment, the game itself involves the choice of a variety of strategies and the choice of routes and solutions. In the case of multiple constraints, the core idea of strategy choice games is to make the optimal solution to a certain problem, and such a choice plan needs the support of a variety of theories, such as game theory dynamic programming, the application of operations research, and so on. In this case, it is essentially a given condition of the game, using the above known mathematical model to find the optimal solution, that is, under the condition of meeting the safety of the end, the most money is leftWhen the weather is known and the map is known, we can make the most optimal solution; by using the DP model and the correlation of the TSP problem, we have found a certain rule: give priority to choosing the mine that can bring us income, and then replenish the resources when there is a problem with the resources, so as to plan the best route. For the calculation of money, we take the reverse program to calculate and deduce, and find that level 1 and level 2 can finally make money, and give the specific value in the detailed explanation of their respective problems. Under normal circumstances, it is impossible to know the changes of the weather in the future, so it is necessary to make different analyses for different weather conditions every day; here, we assume a certain strategy, that is, to accept the relatively non-optimal solution with a certain probability, and then through the increase of the number of iterations, we finally retrieve the optimal solution in this hypothesis.

An exact algorithm for biobjective integer programming problems

We propose an exact algorithm for solving biobjective integer programming problems, which arise in various applications of operations research. The algorithm is based on solving Pascoletti-Serafini scalarizations to search specified regions (boxes) in the objective space and returns the set of nondominated points. We implement the algorithm with different strategies, where the choices of the scalarization model parameters and splitting rule differ. We then derive bounds on the number of scalarization models solved; and demonstrate the performances of the variants through computational experiments both as exact algorithms and as solution approaches under time restriction. The experiments demonstrate that different strategies have advantages in different aspects: while some are quicker in finding the whole set of nondominated solutions, others return good-quality solutions in terms of representativeness when run under time restriction. We also compare the proposed approach with existing algorithms. The results of our experiments show the satisfactory behaviour of our algorithm, especially when run under time limit, as it achieves better coverage of the whole frontier with a smaller number of solutions compared to the existing algorithms.

Computational complexity of three-dimensional discrete tomography with missing data

Discrete tomography deals with problems of determining shape of a discrete object from a set of projections. In this paper, we deal with a fundamental problem in discreet tomography: reconstructing a discrete object in $$\mathbb {R}^3$$ from its orthogonal projections, which we call three-dimensional discrete tomography. This problem has been mostly studied under the assumption that complete data of the projections are available. However, in practice, there might be missing data in the projections, which come from, e.g., the lack of precision in the measurements. In this paper, we consider the three-dimensional discrete tomography with missing data. Specifically, we consider the following three fundamental problems in discrete tomography: the consistency, counting, and uniqueness problems, and classify the computational complexities of these problems in terms of the length of one dimension. We also generalize these results to higher-dimensional discrete tomography, which has applications in operations research and statistics.

Chance-Constrained Multiple Bin Packing Problem with an Application to Operating Room Planning

We study the chance-constrained bin packing problem, with an application to hospital operating room planning. The bin packing problem allocates items of random sizes that follow a discrete distribution to a set of bins with limited capacity, while minimizing the total cost. The bin capacity constraints are satisfied with a given probability. We investigate a big-M and a 0-1 bilinear formulation of this problem. We analyze the bilinear structure of the formulation and use the lifting techniques to identify cover, clique, and projection inequalities to strengthen the formulation. We show that in certain cases these inequalities are facet-defining for a bilinear knapsack constraint that arises in the reformulation. An extensive computational study is conducted for the operating room planning problem that minimizes the number of open operating rooms. The computational tests are performed using problems generated based on real data from a hospital. A lower-bound improvement heuristic is combined with the cuts proposed in this paper in a branch-and-cut framework. The computations illustrate that the techniques developed in this paper can significantly improve the performance of the branch-and-cut method. Problems with up to 1,000 scenarios are solved to optimality in less than an hour. A safe approximation based on conditional value at risk (CVaR) is also solved. The computations show that the CVaR approximation typically leaves a gap of one operating room (e.g., six instead of five) to satisfy the chance constraint. Summary of Contribution: This paper investigates a branch-and-cut algorithm for a chance-constrained bin packing problem with multiple bins. The chance-constrained bin packing provides a modeling framework for applied operations research problems, such as health care, scheduling, and so on. This paper studies alternative computational approaches to solve this problem. Moreover, this paper uses real data from a hospital operating room planning setting as an application to test the algorithmic ideas. This work, therefore, is at the intersection of computing and operations research. Several interesting ideas are developed and studied. These include a strengthened big-M reformulation, analysis of a bilinear reformulation, and identifying certain facet-defining inequalities for this formulation. This paper also gives a lower-bound generation heuristic for a model that minimizes the number of bins. Computational experiments for an operating room planning model that uses data from a hospital demonstrate the computational improvement and importance of the proposed approaches. The techniques proposed in this paper and computational experiments further enhance the interface of computing and operations research.

Statistical Query Algorithms for Mean Vector Estimation and Stochastic Convex Optimization

Stochastic convex optimization, by which the objective is the expectation of a random convex function, is an important and widely used method with numerous applications in machine learning, statistics, operations research, and other areas. We study the complexity of stochastic convex optimization given only statistical query (SQ) access to the objective function. We show that well-known and popular first-order iterative methods can be implemented using only statistical queries. For many cases of interest, we derive nearly matching upper and lower bounds on the estimation (sample) complexity, including linear optimization in the most general setting. We then present several consequences for machine learning, differential privacy, and proving concrete lower bounds on the power of convex optimization–based methods. The key ingredient of our work is SQ algorithms and lower bounds for estimating the mean vector of a distribution over vectors supported on a convex body in Rd. This natural problem has not been previously studied, and we show that our solutions can be used to get substantially improved SQ versions of Perceptron and other online algorithms for learning halfspaces.

Understanding the Impact of COVID–19 on Global Financial Network Using Graph Based Algorithm: Minimum Spanning Tree Approach

Abstract In this paper effects of COVID–19 pandemic on stock market network are analyzed by an application of operational research with a mathematical approach. For this purpose two minimum spanning trees for each time period namely before and during COVID–19 pandemic are constructed. Dynamic time warping algorithm is used to measure the similarity between each time series of the investigated stock markets. Then, clusters of investigated stock markets are constructed. Numerical values of the topology evaluation for each cluster and time period is computed.

Structured Robust Submodular Maximization: Offline and Online Algorithms

Constrained submodular function maximization has been used in subset selection problems such as selection of most informative sensor locations. Although these models have been quite popular, the solutions obtained via this approach are unstable to perturbations in data defining the submodular functions. Robust submodular maximization has been proposed as a richer model that aims to overcome this discrepancy as well as increase the modeling scope of submodular optimization. In this work, we consider robust submodular maximization with structured combinatorial constraints and give efficient algorithms with provable guarantees. Our approach is applicable to constraints defined by single or multiple matroids and knapsack as well as distributionally robust criteria. We consider both the offline setting where the data defining the problem are known in advance and the online setting where the input data are revealed over time. For the offline setting, we give a general (nearly) optimal bicriteria approximation algorithm that relies on new extensions of classical algorithms for submodular maximization. For the online version of the problem, we give an algorithm that returns a bicriteria solution with sublinear regret.Summary of Contribution: Constrained submodular maximization is one of the core areas in combinatorial optimization with a wide variety of applications in operations research and computer science. Over the last decades, both communities have been interested on the design and analysis of new algorithms with provable guarantees. Sensor location, influence maximization and data summarization are some of the applications of submodular optimization that lie at the intersection of the aforementioned communities. Particularly, our work focuses on optimizing several submodular functions simultaneously. We provide new insights and algorithms to the offline and online variants of the problem which significantly expand the related literature. At the same time, we provide a computational study that supports our theoretical results.

Near-Linear Time Local Polynomial Nonparametric Estimation with Box Kernels

Summary of Contribution: Big data analytics has become essential for modern operations research and operations management applications. Statistics methods, such as nonparametric density and function estimation, play important roles in predictive and exploratory data analysis for economics and operations management problems. In this paper, we concentrate on efficiently computing local polynomial regression estimates. We significantly accelerate the computation of such local polynomial estimates by novel applications of multidimensional binary indexed trees ( Fenwick 1994 ) and lazy memory allocation via hashing. Both time and space complexity of our proposed algorithm are nearly linear in the number of inputs. Simulation results confirm the efficiency and effectiveness of our proposed methods.

Operations Research Improves Biomanufacturing Efficiency at MSD Animal Health

Biomanufacturing methods use living organisms (i.e., viruses and bacteria) to generate active ingredients, and this leads to challenges that are different from those incurred by other industries. For example, biomanufacturers often deal with high levels of uncertainty and batch-to-batch variability in production yield, lead times, and costs. Biosafety requirements impose constraints, such as a no-wait requirement throughout the production process. In addition, biomanufacturing operations are cost and labor intensive and involve high risks of failure. To address these challenges, a multidisciplinary team of researchers collaborated over three years to develop a portfolio of optimization models and decision support tools. These tools were aimed at improving biomanufacturing efficiency using a variety of operations research methodologies, including stochastic optimization, Bayesian design of experiments, and simulation optimization. The developed models link the underlying biology and chemistry of biomanufacturing processes with financial trade-offs and business risks. The research has been conducted in close collaboration with MSD Animal Health in Boxmeer, Netherlands. Industry implementation at MSD AH had a significant impact, with up to 50% increase in batch yield and an additional revenue of €50 million per year. The application of operations research is very new to the biomanufacturing industry. As more companies such as MSD AH embrace operations research, we believe that this will significantly help the industry provide faster and more affordable access to new treatments.

Becoming Visible: Why We Should be Better Communicators Now

Several Operations Research (OR) applications have been presented at the 4^{th} AIROYoung Workshop in Bozen (February 5-7, 2020). We start this essay by reporting the main research topics studied and discussed nowadays by young OR researchers. Once again, these have shown the potential and the effect of exploiting applied mathematics, in particular OR, to solve problems arising from reality. Indeed, speaking about the present, OR has been already contributing to fight the COVID-19 pandemic from its beginning, integrated with other techniques to forecast and simulate future scenarios. For instance, OR can help decide how to optimally allocate resources and how to manage the supply chain of food, medical and essential items. We illustrate a few examples of the efforts done to tackle several aspects of the COVID-19 pandemic. Given its strong impact and wide applicability, we wonder about the visibility problem of OR: why is it still unknown to people and has not become a buzzword such as the terms ”machine learning” or ”artificial intelligence”? And, still, what does it mean to ”become visible”? We compare some search terms with Google Trends and report several opinions on this topic. The main purpose of this essay is to refuel the discussion on OR communication to laypeople, by highlighting issues while considering different contexts. Starting from our young community itself, we would like to encourage researchers to take action to make OR more visible.

Bidual Approaches in Risk Representation

Downside and deviation risk measures are becoming more and more important in many disciplines with clear interfaces with Applied Mathematics and Operations Research. Their dual representations have played critical roles in most of their applications (risk management, portfolio selection, pricing and hedging, etc.), but, to the best of our knowledge, bidual representations were never profoundly studied. New linear bidual representations will be provided, and their great capacity to linearize many problems will be proved, with special focus on risk optimization. This is important because there are very tractable necessary and sufficient optimality conditions and resolution algorithms in Linear Programming. Moreover, in the linearization process, one will have to introduce new decision variables providing us with very important information, such as sensitivities with respect to the selected risk measure and sensitivities with respect to the selected model (model risk). The theory will be presented for general Banach spaces, and an illustrative example will be given.

A linear algorithm for a minimax location of a path-shaped facility with a specific length in a weighted tree network

This paper considers the problem of locating a path-shaped facility of a specific size on a weighted tree network. The criterion for optimality used in this paper is the minimax criterion in which the weighted distance to the farthest vertex from the facility is minimised. The minimax criterion gives acceptable results from the point of view of the fast response for the clients who are located far away from the facility. This location problem usually has applications in computer science, information science, and operations research. An O(n) time algorithm is proposed for finding the optimal location of a path-shaped facility of a bounded length on a weighted tree network, where n is the number of vertices in the tree.

Multi-parametric approach for multilevel multi-leader-multi-follower games using equivalent reformulations

Multilevel multi-leader multi-follower games address compromises among multiple interacting decision agents within a hierarchical system in which multiple followers are involved at each lower-level unit and more than one decision maker (multiple leaders) are involved in the upper-level. The leaders' decisions are affected not only by reactions of the followers but also by various relationships among the leaders themselves. In general, multiple-leaders multiple-followers (MLMF) game serve as an important modeling tool in game theory with many applications in economics, engineering, operations research and other fields. In this paper, we have reformulated a multilevel-MLMF game into an equivalent multilevel single-leader multi-follower (SLMF) game by introducing a suppositional (or dummy) leader, and hence the multiple leaders in the original problem become followers in the second level. If the resulting multilevel-SLMF game consists of separable terms and parameterized common terms across all the followers, then the problem is further transformed into equivalent multilevel programs having a single leader and single follower at each level of the hierarchy. The proposed solution approach can solve multilevel multi-leader multi-follower problems whose objective values at all levels have common but having different positive weights of non-separable terms. This result improves the work of Kulkarni and Shanbhag (2015).

A Linear Algorithm for a Minimax Location of a Path-Shaped Facility with a Specific Length in a Weighted Tree Network

This paper considers the problem of locating a path-shaped facility of a specific size on a weighted tree network. The criterion for optimality used in this paper is the minimax criterion in which the weighted distance to the farthest vertex from the facility is minimised. The minimax criterion gives acceptable results from the point of view of the fast response for the clients who are located far away from the facility. This location problem usually has applications in computer science, information science, and operations research. An O(n) time algorithm is proposed for finding the optimal location of a path-shaped facility of a bounded length on a weighted tree network, where n is the number of vertices in the tree.

Dynamic Multiagent Incentive Contracts: Existence, Uniqueness, and Implementation

Multiagent incentive contracts are advanced techniques for solving decentralized decision-making problems with asymmetric information. The principal designs contracts aiming to incentivize non-cooperating agents to act in his or her interest. Due to the asymmetric information, the principal must balance the efficiency loss and the security for keeping the agents. We prove both the existence conditions for optimality and the uniqueness conditions for computational tractability. The coupled principal-agent problems are converted to solving a Hamilton–Jacobi–Bellman equation with equilibrium constraints. Extending the incentive contract to a multiagent setting with history-dependent terminal conditions opens the door to new applications in corporate finance, institutional design, and operations research.

“What’s the evidence?”—Towards more empirical evaluations of the impact of OR interventions in healthcare

ABSTRACT Despite an increasing number of papers reporting applications of operational research (OR) to problems in healthcare, there remains little empirical evidence of OR improving healthcare delivery in practice. Without such evidence it is harder both to justify the usefulness of OR to a healthcare audience and to learn and continuously improve our approaches. To progress, we need to build the evidence-base on whether and how OR improves healthcare delivery through careful empirical evaluation. This position paper reviews evaluation standards in healthcare improvement research and dispels some common myths about evaluation. It highlights the current lack of robust evaluation of healthcare OR and makes the case for addressing this. It then proposes possible ways for building better empirical evaluations of OR interventions in healthcare.

Nonconvex robust programming via value-function optimization

Convex programming based robust optimization is an active research topic in the past two decades, partially because of its computational tractability for many classes of optimization problems and uncertainty sets. However, many problems arising from modern operations research and statistical learning applications are nonconvex even in the nominal case, let alone their robust counterpart. In this paper, we introduce a systematic approach for tackling the nonconvexity of the robust optimization problems that is usually coupled with the nonsmoothness of the objective function brought by the worst-case value function. A majorization-minimization algorithm is presented to solve the penalized min-max formulation of the robustified problem that deterministically generates a “better” solution compared with the starting point (that is usually chosen as an unrobustfied optimal solution). A generalized saddle-point theorem regarding the directional stationarity is established and a game-theoretic interpretation of the computed solutions is provided. Numerical experiments show that the computed solutions of the nonconvex robust optimization problems are less sensitive to the data perturbation compared with the unrobustfied ones.