Mathematics of Operations Research

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Efficient Algorithms for Solving Systems of Nonlinear Equations with a Block Diagonal Structure
Mathematics of Operations Research - Tập 16 Số 3 - Trang 566-579 - 1991
Kazuya Kamiya
The purpose of this paper is to present efficient algorithms for computing solutions to systems of nonlinear equations with a block diagonal structure. The special structure of the systems, which arises in economic models, allows us to use the decomposition of the problems.
Minimizing Total Tardiness on One Machine is NP-Hard
Mathematics of Operations Research - Tập 15 Số 3 - Trang 483-495 - 1990
Jianzhong Du, Joseph Y.‐T. Leung
The problem of minimizing the total tardiness for a set of independent jobs on one machine is considered. Lawler has given a pseudo-polynomial-time algorithm to solve this problem. In spite of extensive research efforts for more than a decade, the question of whether it can be solved in polynomial time or it is NP-hard (in the ordinary sense) remained open. In this paper the problem is shown to be... hiện toàn bộ
Computing Bounds for Stochastic Programming Problems by Means of a Generalized Moment Problem
Mathematics of Operations Research - Tập 12 Số 1 - Trang 149-162 - 1987
John R. Birge, Roger J.‐B. Wets
Bounds on the expected value of a convex function are obtained by means of an approximating generalized moment problem. Numerical implementation is discussed in the context of stochastic programming problems.
Robust Convex Optimization
Mathematics of Operations Research - Tập 23 Số 4 - Trang 769-805 - 1998
Aharon Ben‐Tal, Arkadi Nemirovski
We study convex optimization problems for which the data is not specified exactly and it is only known to belong to a given uncertainty set U, yet the constraints must hold for all possible values of the data from U. The ensuing optimization problem is called robust optimization. In this paper we lay the foundation of robust convex optimization. In the main part of the paper we show that if U is a... hiện toàn bộ
Models for Minimax Stochastic Linear Optimization Problems with Risk Aversion
Mathematics of Operations Research - Tập 35 Số 3 - Trang 580-602 - 2010
Dimitris Bertsimas, Xuan Vinh Doan, Karthik Natarajan, Chung‐Piaw Teo
We propose a semidefinite optimization (SDP) model for the class of minimax two-stage stochastic linear optimization problems with risk aversion. The distribution of second-stage random variables belongs to a set of multivariate distributions with known first and second moments. For the minimax stochastic problem with random objective, we provide a tight SDP formulation. The problem with random ri... hiện toàn bộ
A Distributional Interpretation of Robust Optimization
Mathematics of Operations Research - Tập 37 Số 1 - Trang 95-110 - 2012
Huan Xu, Constantine Caramanis, Shie Mannor
Motivated by data-driven decision making and sampling problems, we investigate probabilistic interpretations of robust optimization (RO). We establish a connection between RO and distributionally robust stochastic programming (DRSP), showing that the solution to any RO problem is also a solution to a DRSP problem. Specifically, we consider the case where multiple uncertain parameters belong to the... hiện toàn bộ
A Fluid EOQ Model of Perishable Items with Intermittent High and Low Demand Rates
Mathematics of Operations Research - Tập 40 Số 2 - Trang 390-402 - 2015
Onno Boxma, David Perry, Shelemyahu Zacks
We consider a stochastic fluid EOQ-type model with demand rates operating in a two-state random environment. This environment alternates between exponentially distributed periods of high demand and generally distributed periods of low demand. The inventory level starts at some level q, and decreases linearly at rate βH during the periods of high demand, and at rate βL < βH at periods of low demand... hiện toàn bộ
On Scheduling Fees to Prevent Merging, Splitting, and Transferring of Jobs
Mathematics of Operations Research - Tập 32 Số 2 - Trang 266-283 - 2007
Hervé Moulin
A deterministic server is shared by users with identical linear waiting costs, requesting jobs of arbitrary lengths. Shortest jobs are served first for efficiency. The server can monitor the length of a job but not the identity of the job’s user, thus merging, splitting, or partially transferring jobs offer cooperative strategic opportunities. Can we design cash transfers to neutralize such manipu... hiện toàn bộ
The Functional Equations of Undiscounted Markov Renewal Programming
Mathematics of Operations Research - Tập 3 Số 4 - Trang 308-321 - 1978
Paul J. Schweitzer, Awi Federgruen
This paper investigates the solutions to the functional equations that arise inter alia in Undiscounted Markov Renewal Programming. We show that the solution set is a connected, though possibily nonconvex set whose members are unique up to n* constants, characterize n* and show that some of these n* degrees of freedom are locally rather than globally independent. Our results generalize those obtai... hiện toàn bộ
A Greedy Heuristic for the Set-Covering Problem
Mathematics of Operations Research - Tập 4 Số 3 - Trang 233-235 - 1979
Vašek Chvátal
Let A be a binary matrix of size m × n, let cT be a positive row vector of length n and let e be the column vector, all of whose m components are ones. The set-covering problem is to minimize cTx subject to Ax ≥ e and x binary. We compare the value of the objective function at a feasible solution found by a simple greedy heuristic to the true optimum. It turns out that the ratio between the two gr... hiện toàn bộ
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