Operations Research Letters最新文献

Many Markov chain expectations and probabilities can be computed as solutions to systems of linear equations, by applying “first transition analysis” (FTA). When the state space is infinite or very large, these linear systems become too large for exact computation. In such settings, one must truncate the FTA linear system. This paper is the first to discuss such FTA truncation issues, and to provide computable a posteriori error bounds.

Quadratically constrained quadratic programs (QCQPs) are a highly expressive class of nonconvex optimization problems. While QCQPs are NP-hard in general, they admit a natural convex relaxation via the standard semidefinite program (SDP) relaxation. In this paper we study when the convex hull of the epigraph of a QCQP coincides with the projected epigraph of the SDP relaxation. We present a sufficient condition for convex hull exactness and show that this condition is further necessary under an additional geometric assumption. The sufficient condition is based on geometric properties of Γ, the cone of convex Lagrange multipliers, and its relatives ${\Gamma }_1$ and ${\Gamma }^{\circ }$.

It has been shown that any 9 by 9 Sudoku puzzle must contain at least 17 clues to have a unique solution. This paper investigates the more specific question: given a particular completed Sudoku grid, what is the minimum number of clues in any puzzle whose unique solution is the given grid? We call this problem the Minimum Sudoku Clue Problem (MSCP). We formulate MSCP as a binary bilevel linear program, present a class of globally valid inequalities, and provide a computational study on 50 MSCP instances of 9 by 9 Sudoku grids. Using a general bilevel solver, we solve 95% of instances to optimality, and show that the solution process benefits from the addition of a moderate amount of inequalities. Finally, we extend the proposed model to other combinatorial problems in which uniqueness of the solution is of interest.

The Multiple Knapsack Assignment Problem is a strongly $\mathrm{NP}$-hard combinatorial optimisation problem, with several applications. We show that an upper bound for the problem, due to Kataoka and Yamada, can be computed in linear time. We then show that some bounds due to Martello and Monaci dominate the Kataoka-Yamada bound. Finally, we define an even stronger bound, which turns out to be particularly effective when the number of knapsacks is not a multiple of the number of item classes.

The problem of constrained Markov decision process (CMDP) is investigated, where an agent aims to maximize the expected accumulated reward subject to constraints on its utilities/costs. We propose a new primal-dual approach with a novel integration of entropy regularization and Nesterov's accelerated gradient method. The proposed approach is shown to converge to the global optimum with a complexity of $\tilde{O}(1/ϵ)$ in terms of the optimality gap and the constraint violation, which improves the complexity of the existing primal-dual approaches by a factor of $O(1/ϵ)$.

Consider a newly developed system sold under a performance based contract (PBC), and subject to failures following various failure modes. Redesign may address certain failure modes. To trade-off redesign costs and costs associated with the PBC, we find the optimal failure modes to redesign based on the current beliefs on the failure rate per failure mode, and the amount of time remaining under the PBC. We develop analytic insights into the structure of the optimal policy.

House allocation refers to the problem where m houses are to be allocated to n agents so that each agent receives one house. Since an envy-free house allocation does not always exist, we consider finding such an allocation in the presence of subsidy. We show that computing an envy-free allocation with minimum subsidy is NP-hard in general, but can be done efficiently if m differs from n by an additive constant or if the agents have identical utilities.

We consider the problem of optimally designing a system for repeated use under uncertainty. We develop a modeling framework that integrates the design and operational phases, which are represented by a mixed-integer program and discounted-cost infinite-horizon Markov decision processes, respectively. We seek to simultaneously minimize the design costs and the subsequent expected operational costs. This problem setting arises naturally in several application areas, as we illustrate through examples. We derive a bilevel mixed-integer linear programming formulation for the problem and perform a computational study to demonstrate that realistic instances can be solved numerically.

Refining and extending works by Ye and Kitahara-Mizuno, this paper presents new results on the number of pivots of simplex-type methods for solving linear programs of the Leontief kind, certain linear complementarity problems of the P kind, and nonnegatively constrained convex quadratic programs. Our results contribute to the further understanding of the complexity and efficiency of simplex-type methods for solving these problems. Two applications of the quadratic programming results are presented.

In this paper, we demonstrate that non-convex multiobjective optimization problems have nonempty and compact weakly efficient solution sets if and only if finite scalar optimization problems have nonempty and compact solution sets under mild conditions, which partially reduces the gap between non-convex and convex multiobjective problems in characterizing the nonemptiness and compactness of weakly efficient solution sets. Two examples are provided to support the findings.