Operations Research Letters最新文献

The classical Kullback-Leibler distance is known to enjoy desirable statistical properties in the context of decision-making with noiseless data. However, in most practical situations data is subject to a certain amount of measurement noise. We hence study here data-driven prescription problems in which the data is corrupted by a known noise source. We derive efficient data-driven formulations in this noisy regime and indicate that they enjoy an entropic optimal transport interpretation.

In this paper we design cost allocation rules for inventory games with private information. First, we design incentive-compatible cost allocation rules for inventory games with private information via Vickrey-Clarke-Groves (VCG) rules. Then, we propose incentive-compatible and approximate budget-balanced cost allocations via polynomial approximations such as the Chebyshev approximation and the Taylor approximation. In addition, we propose an incentive-compatible cost allocation with individual rationality. Finally, we conduct numerical experiments to compare the performance of the proposed cost allocations.

This paper aims to formulate scalar representations and stability conditions for parametric set optimization problems involving set less order relations. We first introduce new nonlinear scalarization functions for sets and discuss their properties, and then they are utilized to establish scalar representations for solutions to such problems. Finally, we study sufficient conditions for the Hausdorff continuity of approximate solution mappings to the reference problems.

Presolving is a critical component in modern mixed integer programming (MIP ) solvers. In this paper, we propose a new and effective presolving method named inequation-based variable aggregation and develop a combined variable aggregation (VA ) technique with the advantage of significantly reducing the scales of MIP problems. This technique is particularly effective for problems involving semi-continuous variables, such as unit commitment problems. Extensive numerical experiments demonstrate that the combined VA technique can substantially accelerate the solution process of MIP problems.

We propose a novel adaptive stepsize for the gradient descent scheme to solve unconstrained nonlinear optimization problems. With the convex and smooth objective satisfying locally Lipschitz gradient we obtain the complexity $O\left(\frac{1}{k}\right)$ of $f\left(x^k\right)-f_{⁎}$ at most. By using the idea of the new stepsize, we propose another new algorithm based on the projected gradient for solving a class of nonconvex optimization problems over a closed convex set. The computational experiments show the efficiency of the new method.

The random consideration set choice model is a recently proposed choice model that can capture the stochastic choice behavior of consumers. One advantage of the random consideration set choice model is that it can accommodate some phenomena that cannot be explained by the multinomial logit model. In this paper, we prove revenue bounds when the attention probabilities and preference order over products change for the random consideration set model. The bounds proposed can be used to control revenue differences when consumers' preference over product changes and can be useful for settings like online assortment optimization with a non-stationary environment.

This paper considers the relationship between semidefinite programs (SDPs), matrix rank, and maximum cuts of graphs. Utilizing complementary slackness conditions for SDPs, we investigate when the rank 1 feasible solution corresponding to a max cut is the unique optimal solution to the Goemans-Williamson max cut SDP by showing the existence of an optimal dual solution with rank $n-1$. Our results consider connected bipartite graphs and graphs with multiple max cuts. We conclude with a conjecture for general graphs.

We consider a Cournot-Bertrand competition with uncertain demand where firms receive private information about it. We prove that sharing information is a dominant strategy for the quantity-setting firm and not sharing is a dominant strategy for the price-setting firm. We uncover that the quantity-setting firm enjoys higher expected profits with more precise information and pools the information, whereas the price-setting firm's decision to pool the information depends on competition levels and a side payment. Consumers benefit from higher accuracy and pooling of information.

This paper studies the welfare effects of the abatement cost burden of a supplier in a multi-echelon supply chain. We theoretically show that the profits of all echelons other than the supplier become lower when the supplier contributes more to the abatement. Also, we computationally show that the profit of the supplier may be higher when it makes a small amount of contribution to the abatement provided that the demand curve faced by the retailer is sufficiently linear.

In this paper, we study the mixed-integer nonlinear set given by a separable quadratic constraint on continuous variables, where each continuous variable is controlled by an additional indicator. This set occurs pervasively in optimization problems with uncertainty and in machine learning. We show that optimization over this set is NP-hard. Despite this negative result, we discover links between the convex hull of the set under study, and a family of polyhedral sets studied in the literature. Moreover, we show that although perspective relaxation in the literature for this set fails to match the structure of its convex hull, it is guaranteed to be a close approximation.