Finding Fair and Efficient Allocations for Matroid Rank Valuations

In this article, we present new results on the fair and efficient allocation of indivisible goods to agents whose preferences correspond to matroid rank functions . This is a versatile valuation class with several desirable properties (such as monotonicity and submodularity), which naturally lends itself to a number of real-world domains. We use these properties to our advantage; first, we show that when agent valuations are matroid rank functions, a socially optimal (i.e., utilitarian social welfare-maximizing) allocation that achieves envy-freeness up to one item (EF1) exists and is computationally tractable. We also prove that the Nash welfare-maximizing and the leximin allocations both exhibit this fairness/efficiency combination by showing that they can be achieved by minimizing any symmetric strictly convex function over utilitarian optimal outcomes. To the best of our knowledge, this is the first valuation function class not subsumed by additive valuations for which it has been established that an allocation maximizing Nash welfare is EF1. Moreover, for a subclass of these valuation functions based on maximum (unweighted) bipartite matching, we show that a leximin allocation can be computed in polynomial time. Additionally, we explore possible extensions of our results to fairness criteria other than EF1 as well as to generalizations of the above valuation classes.

Low Programmed Death-Ligand 1–Expressing Subgroup Outcomes of First-Line Immune Checkpoint Inhibitors in Gastric or Esophageal Adenocarcinoma

PURPOSE The US Food and Drug Administration has granted regulatory approval for the use of nivolumab—an immune checkpoint inhibitor (ICI)—in the first-line treatment of advanced gastric or esophageal adenocarcinoma (GEAC), regardless of programmed death-ligand 1 (PD-L1) expression. However, the efficacy of ICIs in low PD-L1–expressing tumors remains unclear. MATERIALS AND METHODS This study aims to reconstruct unreported Kaplan-Meier (KM) plots of PD-L1 combined positive score (CPS) subgroups of randomized phase III trials comparing the addition of ICIs with conventional chemotherapy in the first-line treatment of GEAC. A graphical reconstructive algorithm was adopted to estimate time-to-event outcomes from reported overall survival and progression-free survival (OS and PFS) KM plots describing overall or subgroup cohorts. Using reconstructed time-to-event outcomes, KMSubtraction conducts bipartite matching of patients from the reported subgroup among the overall cohort. By excluding matched patients, KM plots and survival analyses of the unreported subgroups were retrieved. RESULTS CheckMate-649, KEYNOTE-062, and KEYNOTE-590 were included. Two PD-L1 subgroups were identified with data unreported in the primary manuscripts: PD-L1 CPS 1-4 from CheckMate-649 and PD-L1 CPS 1-9 from KEYNOTE-062. No significant differences in OS and PFS were demonstrated in ICI-chemotherapy combinations when compared with chemotherapy among CheckMate-649 PD-L1 CPS 1-4 (OS: hazard ratio [HR] = 0.950, 95% CI, 0.747 to 1.209, P = .678; PFS: HR = 0.958, 95% CI, 0.743 to 1.236, P = .743) and KEYNOTE-062 PD-L1 CPS 1-9 subgroups. In the KEYNOTE-062 PD-L1 CPS 1-9 subgroup, patients treated with pembrolizumab had an increased hazard of tumor progression (HR = 2.092, 95% CI, 1.661 to 2.635, P < .001). CONCLUSION Using KMSubtraction, data of PD-L1 subgroups previously unreported by primary manuscripts of pivotal clinical trials were retrieved. These data suggest the lack of benefit in the addition of ICI to chemotherapy in low PD-L1–expressing GEAC tumors.

Scheduling and Control of Queueing Networks

Applications of queueing network models have multiplied in the last generation, including scheduling of large manufacturing systems, control of patient flow in health systems, load balancing in cloud computing, and matching in ride sharing. These problems are too large and complex for exact solution, but their scale allows approximation. This book is the first comprehensive treatment of fluid scaling, diffusion scaling, and many-server scaling in a single text presented at a level suitable for graduate students. Fluid scaling is used to verify stability, in particular treating max weight policies, and to study optimal control of transient queueing networks. Diffusion scaling is used to control systems in balanced heavy traffic, by solving for optimal scheduling, admission control, and routing in Brownian networks. Many-server scaling is studied in the quality and efficiency driven Halfin–Whitt regime and applied to load balancing in the supermarket model and to bipartite matching in ride-sharing applications.

Optimization of Collection and Consolidation Operations in Cross-Border Multi-modal Distribution Networks

This study introduces a model to solve a dynamic network optimization model on a heterogeneous graph. We use this model to optimize the collection and consolidation operations on a cross-country multi-modal distribution network. The model's dynamic objects are trucks, trailers, orders, unvisited collection and customs check points. Information about dynamic objects is extracted from a real-time database. The model's static objects include objects that are known in advance, such as warehouses. The constraints of the problem include due dates, vehicle capacity, availability of vehicles, and precedence constraints of visiting locations. We propose a mixed-integer programming model and provide a solution using matheuristics. We decompose the master MIP model into subproblems that can be solved to optimality with LP solvers. We also reduce the graph complexity by variable fixing due to optimized subproblems or by bounding the maximum number of paths to be selected due to the solutions of priority-based bin packing algorithms. Finally, we convert the resulting problem into a bipartite matching problem by expanding the graph nodes which can then be solved in polynomial time. We implement our solution method on real-time data retrieved from the tracking system of a third-party logistics company. Experiments show that our solution method significantly outperforms other heuristics in terms of solution quality which is measured with respect to lateness, empty kilometers traveled, travel times, number of required/used vehicles, load factors, and ratio of served orders.

Optimization of Collection and Consolidation Operations in Cross-Border Multi-modal Distribution Networks

This study introduces a model to solve a dynamic network optimization model on a heterogeneous graph. We use this model to optimize the collection and consolidation operations on a cross-country multi-modal distribution network. The model's dynamic objects are trucks, trailers, orders, unvisited collection and customs check points. Information about dynamic objects is extracted from a real-time database. The model's static objects include objects that are known in advance, such as warehouses. The constraints of the problem include due dates, vehicle capacity, availability of vehicles, and precedence constraints of visiting locations. We propose a mixed-integer programming model and provide a solution using matheuristics. We decompose the master MIP model into subproblems that can be solved to optimality with LP solvers. We also reduce the graph complexity by variable fixing due to optimized subproblems or by bounding the maximum number of paths to be selected due to the solutions of priority-based bin packing algorithms. Finally, we convert the resulting problem into a bipartite matching problem by expanding the graph nodes which can then be solved in polynomial time. We implement our solution method on real-time data retrieved from the tracking system of a third-party logistics company. Experiments show that our solution method significantly outperforms other heuristics in terms of solution quality which is measured with respect to lateness, empty kilometers traveled, travel times, number of required/used vehicles, load factors, and ratio of served orders.

KMSubtraction: Reconstruction of unreported subgroup survival data utilizing published Kaplan-Meier survival curves

ABSTRACTBACKGROUNDData from certain subgroups of clinical interest may not be presented in primary manuscripts or conference abstract presentations. In an effort to enable secondary data analyses, we propose a workflow to retrieve unreported subgroup survival data from published Kaplan-Meier (KM) curves.METHODSWe developed KMSubtraction, an R-package that retrieves patients from unreported subgroups by matching participants on KM curves of the overall cohort to participants on KM curves of a known subgroup with follow-up time. By excluding matched patients, the opposing unreported subgroup may be retrieved. Reproducibility and limits of error of the KMSubtraction workflow were assessed by comparing unmatched patients against the original survival data of subgroups from published datasets and simulations. Monte Carlo simulations were utilized to evaluate the effect of the reported subgroup proportion, missing data, censorship proportion in the overall and subgroup cohort, sample size and number-at-risk table intervals on the limits of error of KMSubtraction. 3 matching algorithms were explored – minimal cost bipartite matching, Mahalanobis distance matching, and nearest neighbor matching by logistic regression.RESULTSThe validation exercise found no material systematic error and demonstrates the robustness of KMSubtraction in deriving unreported subgroup survival data. Limits of error were small and negligible on marginal Cox proportional hazard models comparing reconstructed and original survival data of unreported subgroups. Extensive Monte Carlo simulations demonstrate that datasets with high reported subgroup proportion (r=0.467, p<0.001), small dataset size (r=-0.374, p<0.001) and high proportion of missing data in the unreported subgroup (r=0.553, p<0.001) were associated with uncertainty are likely to yield high limits of error with KMSubtraction.CONCLUSIONWhile KMSubtraction demonstrates robustness in deriving survival data from unreported subgroups, the implementation of KMSubtraction should take into consideration the aforementioned limitations. The limits of error of KMSubtraction, as reflected by the mean |ln(HR)| from converged Monte Carlo simulations may guide the interpretation of reconstructed survival data of unreported subgroups.