Operations Research最新文献

We consider the inventory control problem of a multiwarehouse, multistore system over a time horizon when the warehouses receive no external replenishment. This problem is prevalent in retail settings, and it is referred to in the work of [Jackson PL (1988) Stock allocation in a two-echelon distribution system or “what to do until your ship comes in.” Management Sci. 34(7):880–895] as the problem of “what to do until your (external) shipment comes in.” The warehouses are stocked with initial inventories, and the stores are dynamically replenished from the warehouses in each period of the planning horizon. Excess demand in each period at a store is lost. The optimal policy for this problem is complex and state dependent, and because of the curse of dimensionality, computing the optimal policy using standard dynamic programming is numerically intractable. Static Lagrangian base-stock (LaBS) policies have been developed for this problem [Miao S, Jasin S, Chao X (2022) Asymptotically optimal Lagrangian policies for one-warehouse multi-store system with lost sales. Oper. Res. 70(1):141–159] and shown to be asymptotically optimal. In this paper, we develop adaptive policies that dynamically adjust the control parameters of a vanilla static LaBS policy using realized historical demands. We show, both theoretically and numerically, that adaptive policies significantly improve the performance of the LaBS policy, with the magnitude of improvement characterized by the number of policy adjustments. In particular, when the number of adjustments is a logarithm of the length of time horizon, the policy is rate optimal in the sense that the rate of the loss (in terms of the dependency on the length of the time horizon) matches that of the theoretical lower bound. Among other insights, our results also highlight the benefit of incorporating the “pooling effect” in designing a dynamic adjustment scheme.

Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2022.0668.

This paper makes progress toward learning Nash equilibria in two-player, zero-sum Markov games from offline data. Specifically, consider a γ-discounted, infinite-horizon Markov game with S states, in which the max-player has A actions and the min-player has B actions. We propose a pessimistic model–based algorithm with Bernstein-style lower confidence bounds—called the value iteration with lower confidence bounds for zero-sum Markov games—that provably finds an ε-approximate Nash equilibrium with a sample complexity no larger than $\frac{C_{\mathsf{\text{clipped}}}^{\star }S(A+B)}{{(1-\gamma )}^3{\epsilon }^2}$ (up to some log factor). Here, $C_{\mathsf{\text{clipped}}}^{\star }$ is some unilateral clipped concentrability coefficient that reflects the coverage and distribution shift of the available data (vis-à-vis the target data), and the target accuracy ε can be any value within $\left(0,\frac{1}{1-\gamma }\right]$. Our sample complexity bound strengthens prior art by a factor of $\min \{A,B\}$, achieving minimax optimality for a broad regime of interest. An appealing feature of our result lies in its algorithmic simplicity, which reveals the unnecessity of variance reduction and sample splitting in achieving sample optimality.

Funding: Y. Yan is supported in part by the Charlotte Elizabeth Procter Honorific Fellowship from Princeton University and the Norbert Wiener Postdoctoral Fellowship from MIT. Y. Chen is supported in part by the Alfred P. Sloan Research Fellowship, the Google Research Scholar Award, the Air Force Office of Scientific Research [Grant FA9550-22-1-0198], the Office of Naval Research [Grant N00014-22-1-2354], and the National Science Foundation [Grants CCF-2221009, CCF-1907661, IIS-2218713, DMS-2014279, and IIS-2218773]. J. Fan is supported in part by the National Science Foundation [Grants DMS-1712591, DMS-2052926, DMS-2053832, and DMS-2210833] and Office of Naval

Malleable scheduling is a model that captures the possibility of parallelization to expedite the completion of time-critical tasks. A malleable job can be allocated and processed simultaneously on multiple machines, occupying the same time interval on all these machines. We study a general version of this setting, in which the functions determining the joint processing speed of machines for a given job follow different discrete concavity assumptions (subadditivity, fractional subadditivity, submodularity, and matroid ranks). We show that under these assumptions, the problem of scheduling malleable jobs at minimum makespan can be approximated by a considerably simpler assignment problem. Moreover, we provide efficient approximation algorithms for both the scheduling and the assignment problem, with increasingly stronger guarantees for increasingly stronger concavity assumptions, including a logarithmic approximation factor for the case of submodular processing speeds and a constant approximation factor when processing speeds are determined by matroid rank functions. Computational experiments indicate that our algorithms outperform the theoretical worst-case guarantees.

Funding: D. Fotakis received financial support from the Hellenic Foundation for Research and Innovation (H.F.R.I.) [“First Call for H.F.R.I. Research Projects to Support Faculty Members and Researchers and the Procurement of High-Cost Research Equipment Grant,” Project BALSAM, HFRI-FM17-1424]. J. Matuschke received financial support from the Fonds Wetenschappelijk Onderzoek-Vlanderen [Research Project G072520N “Optimization and Analytics for Stochastic and Robust Project Scheduling”]. O. Papadigenopoulos received financial support from the National Science Foundation Institute for Machine Learning [Award 2019844].

Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2022.0168.

Consider a mechanism run by an auctioneer who can use both payment and inspection instruments to incentivize agents. The timeline of the events is as follows. Based on a prespecified allocation rule and the reported values of agents, the auctioneer allocates the item and secures the reported values as deposits. The auctioneer then inspects the values of agents and, using a prespecified reward rule, rewards the ones who have reported truthfully. Using techniques from convex analysis and calculus of variations, for any distribution of values, we fully characterize the optimal mechanism for a single agent. Using Border’s theorem and duality, we find conditions under which our characterization extends to multiple agents. Interestingly, the optimal allocation function, unlike the classic settings without inspection, is not a threshold strategy and instead is an increasing and continuous function of the types. We also present an implementation of our optimal auction and show that it achieves a higher revenue than auctions in classic settings without inspection. This is because the inspection enables the auctioneer to charge payments closer to the agents’ true values without creating incentives for them to deviate to lower types.

Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2020.0651.

We introduce the framework of slowly varying regression under sparsity, which allows sparse regression models to vary slowly and sparsely. We formulate the problem of parameter estimation as a mixed-integer optimization problem and demonstrate that it can be reformulated exactly as a binary convex optimization problem through a novel relaxation. The relaxation utilizes a new equality on Moore-Penrose inverses that convexifies the nonconvex objective function while coinciding with the original objective on all feasible binary points. This allows us to solve the problem significantly more efficiently and to provable optimality using a cutting plane–type algorithm. We develop a highly optimized implementation of such algorithm, which substantially improves upon the asymptotic computational complexity of a straightforward implementation. We further develop a fast heuristic method that is guaranteed to produce a feasible solution and, as we empirically illustrate, generates high-quality warm-start solutions for the binary optimization problem. To tune the framework’s hyperparameters, we propose a practical procedure relying on binary search that, under certain assumptions, is guaranteed to recover the true model parameters. We show, on both synthetic and real-world data sets, that the resulting algorithm outperforms competing formulations in comparable times across a variety of metrics, including estimation accuracy, predictive power, and computational time, and is highly scalable, enabling us to train models with tens of thousands of parameters.

Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2022.0330.

This study proposes two new dynamic assignment algorithms to match refugees and asylum seekers to geographic localities within a host country. The first, currently implemented in a multiyear randomized control trial in Switzerland, seeks to maximize the average predicted employment level (or any measured outcome of interest) of refugees through a minimum-discord online assignment algorithm. The performance of this algorithm is tested on real refugee resettlement data from both the United States and Switzerland, where we find that it is able to achieve near-optimal expected employment, compared with the hindsight-optimal solution, and is able to improve upon the status quo procedure by 40%–50%. However, pure outcome maximization can result in a periodically imbalanced allocation to the localities over time, leading to implementation difficulties and an undesirable workflow for resettlement resources and agents. To address these problems, the second algorithm balances the goal of improving refugee outcomes with the desire for an even allocation over time. We find that this algorithm can achieve near-perfect balance over time with only a small loss in expected employment compared with the employment-maximizing algorithm. In addition, the allocation balancing algorithm offers a number of ancillary benefits compared with pure outcome maximization, including robustness to unknown arrival flows and greater exploration.

Funding: Financial support from the Charles Koch Foundation, Stanford Impact Labs, the Rockefeller Foundation, Google.org, Schmidt Futures, the Stanford Institute for Human-Centered Artificial Intelligence, and Stanford University is gratefully acknowledged.

Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2022.0445.