We study stable and strongly stable matchings in the marriage market with indifference in their *** characterize the stable matchings as integer extreme points of a convex *** give an alternative proof for the integri...
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We study stable and strongly stable matchings in the marriage market with indifference in their *** characterize the stable matchings as integer extreme points of a convex *** give an alternative proof for the integrity of the strongly stable matching ***,we compute men-optimal(women-optimal)stable and strongly stable matchings using linear *** preferences are strict,we find the men-optimal(women-optimal)stable matching.
Cassava starch production is a key industrial production of Tay Ninh province, Vietnam. However, this production chain has also caused many negative impacts on the environment. This study applied the principles of cir...
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Cassava starch production is a key industrial production of Tay Ninh province, Vietnam. However, this production chain has also caused many negative impacts on the environment. This study applied the principles of circular economy to analyze the waste streams via linear programming method for cassava starch circular production chain towards zero waste emission. The results show that the cassava starch indutry can achieve the goals of zero electricity, zero waste, and zero fossil energy by re-planning the production chain. The chain's output products are 517.5 tons of bio-oil/year, 206.7 thousand tons of biochar/year, 190.0 thousand tons of dry pulp/year, 10 million m3/year of liquid fertilizer. In order to increase further the value of the chain in the circular economy, future research needs to study the feasibility of a solution to reuse wastewater to produce microalgae, as well as evaluate the effectiveness of these methods. The optimization method applied in this study can also be extended to similar agricultural chains properties such as rice processing, sugar cane, etc.
We introduce a class of specially structured linear programming (LP) problems, which has favorable modeling capability for important application problems in different areas such as optimal transport, discrete tomograp...
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We introduce a class of specially structured linear programming (LP) problems, which has favorable modeling capability for important application problems in different areas such as optimal transport, discrete tomography, and economics. To solve these generally large-scale LP problems efficiently, we design an implementable inexact entropic proximal point algorithm (iEPPA) combined with an easy-to-implement dual block coordinate descent method as a subsolver. Unlike existing entropy-type proximal point algorithms, our iEPPA employs a more practically checkable stopping condition for solving the associated subproblems while achieving provable convergence. Moreover, when solving the capacity constrained multi-marginal optimal transport (CMOT) problem (a special case of our LP problem), our iEPPA is able to bypass the underlying numerical instability issues that often appear in the popular entropic regularization approach, since our algorithm does not require the proximal parameter to be very small in order to obtain an accurate approximate solution. Numerous numerical experiments show that our iEPPA is efficient and robust for solving some large-scale CMOT problems on synthetic data. The preliminary experiments on the discrete tomography problem also highlight the potential modeling capability of our model.
During the energy transition, the electricity supply in the isolated island should change from fossil fuel to renewable energy. Since the renewable energy sources on the island are limited and have unique characterist...
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We present a general version of bundle trust region method for minimizing convex functions. The trust region is constructed by generic p-norm with p is an element of [1, +infinity]. In each iteration the algorithm sol...
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We present a general version of bundle trust region method for minimizing convex functions. The trust region is constructed by generic p-norm with p is an element of [1, +infinity]. In each iteration the algorithm solves a subproblem with a constraint involving p-norm. We show the convergence of the generic bundle trust region algorithm. In implementation, the infinity norm is chosen so that a linear programming subproblem is solved in each iteration. Preliminary numerical experiments show that our algorithm performs comparably with the traditional bundle trust region method and has advantages in solving large-scale problems.
A high generation of solar panels and wind turbines is able to increase voltage magnitudes of electricity grids, whereas uncoordinated procedures of recharging several plug-in electric vehicles (PEV) have capability t...
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A high generation of solar panels and wind turbines is able to increase voltage magnitudes of electricity grids, whereas uncoordinated procedures of recharging several plug-in electric vehicles (PEV) have capability to decrease them. Accordingly, this paper proposes a novel decentralized algorithm of power management to reschedule charging and discharging events of PEV over appropriate time slots of energy generation and consumption to maintain voltage profiles within their limits. A linear programming model of optimization is utilized to coordinate bi-directional power flows of charging and discharging PEV batteries, while considering solar panels and wind turbines in smart grids. Simulation results of 7 scenarios show that the proposed strategy is able to maintain voltage profiles of power grids within their margins by charging and discharging PEV batteries over specific hours of energy generation and consumption. The proposed algorithm of power management prevents PEV batteries from being overcharged or deeply discharged by keeping their state of charge between upper and lower boundaries. Therefore, the proposed technique has capability to increase PEV hosting capacity of distribution networks without significant upgrading requirements.
This paper investigates the fault detection filter and consensus control of positive multi-Agent systems with disturbances and faults. First, a kind of positive fault detection filter is designed by virtue of the posi...
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After the 1950s, operations research (OR) moved from military applications of scientific methods to a distinct academic discipline, applying mainly mathematical models to complex systems in the public and private sect...
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After the 1950s, operations research (OR) moved from military applications of scientific methods to a distinct academic discipline, applying mainly mathematical models to complex systems in the public and private sectors. linear programming (LP) with its simplex algorithm, developed by George Dantzig in 1949, is the first method that marked OR as a new academic discipline. The purpose of this article is to examine the evolution of OR through linear programming, its leading methodology, and some of its derivatives, concentrating on one of them-data envelopment analysis (DEA)-developed by Charnes, Cooper, and Rhodes in 1978. We focus on DEA and its derivatives, as this article is the most cited in a search performed using the main OR journals. Although we found LP to be mentioned much more than DEA in our search of Google Scholar and beyond, DEA is still well represented in the OR literature. Fur-thermore, based on insights gained from examining DEA vis-a-vis LP and the "secret" of their spread, we conclude with suggestions to further enhance OR's visibility, implementing ideas from OR founders and others over the years. Thus, future directions include combining hard and soft OR, involving interdisci-plinary teams, consulting of OR academic researchers, and more.(c) 2022 Elsevier B.V. All rights reserved.
A one step ahead optimal strategy is proposed for the inventory control and management problem, and rewritten as a linear programming problem, permitting practical implementation. Important novel aspects of the propos...
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A one step ahead optimal strategy is proposed for the inventory control and management problem, and rewritten as a linear programming problem, permitting practical implementation. Important novel aspects of the proposed solution are that it uses economic value added (EVA), a comprehensive performance index commonly used in business management, instead of regulation to a set point or to a interval of stock values;it does not require knowledge or prediction of the demand distribution;it achieves good efficiency with respect to a globally optimal value, defined in this paper, and no significant bullwhip effect, while being robust to demand and lead time variations. The proposed one step ahead optimal controller is compared with the classical (s, S) controller, as well as with a representative of the inventory and order-based production controller family. In order to make a fair comparison, this paper also proposes a tuning method for the latter two controllers. Numerical experiments based on average performance of the three controllers for a set of normally distributed demands show the superiority of the proposed one step ahead optimal controller, in terms of EVA as well as in terms of other measures proposed in the paper.
One of the oldest results in scheduling theory is that the Shortest Processing Time (SPT) rule finds an optimal solution to the problem of scheduling jobs on identical parallel machines to minimize average job complet...
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One of the oldest results in scheduling theory is that the Shortest Processing Time (SPT) rule finds an optimal solution to the problem of scheduling jobs on identical parallel machines to minimize average job completion times. We present a new proof of correctness of SPT based on linear programming (LP). Our proof relies on a generalization of a single-machine result that yields an equivalence between two scheduling problems. We first identify and solve an appropriate variant of our problem, then map its solutions to solutions for our original problem to establish SPT optimality. Geometric insights used therein may find further uses;we demonstrate two applications of the same principle in generalized settings. (c) 2022 Elsevier B.V. All rights reserved.
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