Operations Research

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The Theory and Computation of Knapsack Functions
Operations Research - Tập 14 Số 6 - Trang 1045-1074 - 1966
Paul C. Gilmore, Ralph E. Gomory
In earlier papers on the cutting stock problem we indicated the desirability of developing fast methods for computing knapsack functions. A one-dimensional knapsack function is defined by: [Formula: see text] where Πi and li are given constants, i = 1, …, m. Two-dimensional knapsack functions can also be defined. In this paper we give a characteri...... hiện toàn bộ
Multistage Cutting Stock Problems of Two and More Dimensions
Operations Research - Tập 13 Số 1 - Trang 94-120 - 1965
Paul C. Gilmore, Ralph E. Gomory
In earlier papers [Opns. Res. 9, 849–859 (1961), and 11, 863–888 (1963)] the one-dimensional cutting stock problem was discussed as a linear programming problem. There it was shown how the difficulty of the enormous number of columns occurring in the linear programming formulation could be overcome by solving a knapsack problem at every pivot step. In this paper higher dimensional cutting...... hiện toàn bộ
A Minimal Algorithm for the 0-1 Knapsack Problem
Operations Research - Tập 45 Số 5 - Trang 758-767 - 1997
David Pisinger
Several types of large-sized 0-1 Knapsack Problems (KP) may be easily solved, but in such cases most of the computational effort is used for sorting and reduction. In order to avoid this problem it has been proposed to solve the so-called core of the problem: a Knapsack Problem defined on a small subset of the variables. The exact core cannot, however, be identified before KP is solved to...... hiện toàn bộ
Single Facility Sequencing with Random Execution Times
Operations Research - Tập 13 Số 3 - Trang 358-364 - 1965
Bonny Banerjee
A single facility sequencing problem where the execution time for each job at the facility is random with known probability distribution, is formulated and solved. The solution is shown to be easily extended to situations where further jobs arrive while the program is in operation. Further extensions are discussed, where (a) the facility is taken to consist of multiple (identical or other...... hiện toàn bộ
Stochastic Scheduling with Release Dates and Due Dates
Operations Research - Tập 31 Số 3 - Trang 559-572 - 1983
Yuqian Xu
We consider stochastic scheduling problems in which the processing times of jobs are independent exponentially distributed random variables, the release dates are random variables with an arbitrary joint distribution, and the due dates are random variables with a joint distribution that satisfies certain conditions. Our development establishes simple policies that minimize such criteria a...... hiện toàn bộ
Stochastic Network Interdiction
Operations Research - Tập 46 Số 2 - Trang 184-197 - 1998
Kelly J. Cormican, David P. Morton, R. Kevin Wood
Using limited assets, an interdictor attempts to destroy parts of a capacitated network through which an adversary will subsequently maximize flow. We formulate and solve a stochastic version of the interdictor's problem: Minimize the expected maximum flow through the network when interdiction successes are binary random variables. Extensions are made to handle uncertain arc capacities an...... hiện toàn bộ
Balancing Terrorism and Natural Disasters—Defensive Strategy with Endogenous Attacker Effort
Operations Research - Tập 55 Số 5 - Trang 976-991 - 2007
Jun Zhuang, Vicki M. Bier
In this paper, we apply game theory to identify equilibrium strategies for both attacker and defender in a fully endogenous model of resource allocation for countering terrorism and natural disasters. The key features of our model include balancing protection from terrorism and natural disasters, and describing the attacker choice by a continuous level of effort rather than a discrete cho...... hiện toàn bộ
Bounds on the Effect of Aggregating Variables in Linear Programs
Operations Research - Tập 28 Số 2 - Trang 403-418 - 1980
Paul Zipkin
This paper explores the effects of aggregating variables in large linear programs. We define a reasonable criterion for the resulting loss in accuracy, and derive bounds on this quantity. A posteriori bounds may be calculated after solving the aggregated problem, and a priori bounds before. Also, we show that standard iterative methods can be used to improve the accuracy of a given aggreg...... hiện toàn bộ
Jointly Optimal Inventory and Maintenance Policies for Stochastically Failing Equipment
Operations Research - Tập 16 Số 3 - Trang 587-601 - 1968
Charles H. Falkner
A dynamic programming problem is formulated to find the inventory, x, of a spare component and a sequence of maintenance intervals r= (r1,…,rx + 1) that minimize the expected cost of operating an equipment for a finite planning horizon, T. It is assumed that the component fails according to a life distribution function, F(⋯), with an increasing ha...... hiện toàn bộ
Production and Inventory Model Using Net Present Value
Operations Research - Tập 50 Số 3 - Trang 528-537 - 2002
Daning Sun, Maurice Queyranne
Using the net present value is the standard methodology in theoretical analysis, and the most frequently used method for making financial decisions. However, net present value is rarely used in production and inventory decisions. The main reasons appear to be the complexity of the formulae and the robustness of the EOQ model. We investigate the general multiproduct, multistage production ...... hiện toàn bộ
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