Operations Research最新文献

We propose a new stochastic emergency network design model that uses a fleet of drones to quickly deliver naloxone in response to opioid overdoses. The network is represented as a collection of $M/G/K$ queueing systems in which the capacity K of each system is a decision variable, and the service time is modeled as a decision-dependent random variable. The model is a queuing-based optimization problem which locates fixed (drone bases) and mobile (drones) servers and determines the drone dispatching decisions and takes the form of a nonlinear integer problem intractable in its original form. We develop an efficient reformulation and algorithmic framework. Our approach reformulates the multiple nonlinearities (fractional, polynomial, exponential, factorial terms) to give a mixed-integer linear programming (MILP) formulation. We demonstrate its generalizability and show that the problem of minimizing the average response time of a collection of $M/G/K$ queueing systems with unknown capacity K is always MILP-representable. We design an outer approximation branch-and-cut algorithmic framework that is computationally efficient and scales well. The analysis based on real-life data reveals that drones can in Virginia Beach: (1) decrease the response time by 82%, (2) increase the survival chance by more than 273%, (3) save up to 33 additional lives per year, and (4) provide annually up to 279 additional quality-adjusted life years.

Funding: M. A. Lejeune acknowledges the support of the National Science Foundation [Grant ECCS-2114100] and the Office of Naval Research [Grant N00014-22-1-2649].

Supplemental Material: The online appendices are available at https://doi.org/10.1287/opre.2022.0489.

We consider the problem of determining the optimal prices and product configurations of horizontally differentiated products when customers purchase according to a locational (Hotelling) choice model and where the problem parameters are initially unknown to the decision maker. Both for the single-product and multiple-product setting, we propose a data-driven algorithm that learns the optimal prices and product configurations from accumulating sales data, and we show that their regret—the expected cumulative loss caused by not using optimal decisions—after T time periods is $O(T^{1/2+o(1)})$. We accompany this result by showing that, even in the single-product setting, the regret of any algorithm is bounded from below by a constant time $T^{1/2}$, implying that our algorithms are asymptotically near optimal. In an extension, we show how our algorithm can be adapted for the case of fixed locations. A numerical study that compares our algorithms with three benchmarks shows that our algorithm is also competitive on a finite time horizon.

Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2021.0093.

We consider a three-stage game in which, first, a large number of potential firms make entry decisions, then those who choose to stay in the market decide on the investment (quality) level in each product, and last, customers with heterogeneous preferences arrive sequentially to make (random) purchase decisions based on product quality and historical sales under the network effect according to a discrete choice model. We characterize such a random purchase process and show that a growing network effect always contributes to more sales concentration ex post on a small number of products. Perhaps surprisingly, we further show several phase-changing phenomena regarding equilibrium outcomes with respect to the network effect’s strength. In particular, the equilibrium product variety (respectively, quality investment) first decreases (respectively, increases) and then increases (respectively, decreases) as the network effect grows. Specifically, when the strength of the network effect is below a threshold, an increasing network effect would shift more sales toward those products with higher quality, preventing more products from entering the market ex ante and inducing firms to adopt the high-budget equilibrium strategy by making a small number of high-quality products, which is consistent with the blockbuster phenomenon. When the strength of the network effect is above the threshold, the network effect would easily cause the market to be concentrated on a few products ex post; even some low-quality products may have a chance to become a “hit.” Interestingly, in this case, when the network effect is growing, the ex ante equilibrium product variety will be wider, and firms adopt the low-budget equilibrium strategy by making a (relatively) large number of low-quality products, a finding consistent with the long tail theory. We then establish the robustness of the previous main insights by accounting for endogenized pricing and multiproducts carried by each firm.

Funding: Y. Feng was financially supported by the Major Program of National Natural Science Foundation of China [Grants 72192830 and 7219283X], Fundamental Research Funds for the Central Universities, and Program for Innovative Research of Shanghai University of Finance and Economics. M. Hu was supported by the Natural Sciences and Engineering Research Council of Canada [Grants RGPIN-2015-06757 and RGPIN-2021-04295].

Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2022.0275.

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.

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.