Operations Research最新文献

Classical Bayesian mechanism design relies on the common prior assumption, but the common prior is often not available in practice. We study the design of prior-independent mechanisms that relax this assumption: The seller is selling an indivisible item to n buyers such that the buyers’ valuations are drawn from a joint distribution that is unknown to both the buyers and the seller, buyers do not need to form beliefs about competitors, and the seller assumes the distribution is adversarially chosen from a specified class. We measure performance through the worst-case regret, or the difference between the expected revenue achievable with perfect knowledge of buyers’ valuations and the actual mechanism revenue. We study a broad set of classes of valuation distributions that capture a wide spectrum of possible dependencies: independent and identically distributed (i.i.d.) distributions, mixtures of i.i.d. distributions, affiliated and exchangeable distributions, exchangeable distributions, and all joint distributions. We derive in quasi closed form the minimax values and the associated optimal mechanism. In particular, we show that the first three classes admit the same minimax regret value, which is decreasing with the number of competitors, whereas the last two have the same minimax regret equal to that of the case n = 1. Furthermore, we show that the minimax optimal mechanisms have a simple form across all settings: a second-price auction with random reserve prices, which shows its robustness in prior-independent mechanism design. En route to our results, we also develop a principled methodology to determine the form of the optimal mechanism and worst-case distribution via first-order conditions that should be of independent interest in other minimax problems.

Supplemental Material: The online appendices are available at https://doi.org/10.1287/opre.2022.0428.

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.