Sensitivity of Pareto Solutions in Multiobjective Optimization

Balbás, Alejandro; Galperin, E. A.; Guerra, Pedro Jiménez

doi:10.1007/s10957-005-4713-3

Cited by 9 publications

(4 citation statements)

References 20 publications

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“…The difference could be expressed using the shadow price of respective objectives (Balbás, Galperin, & Guerra, 2005). For example in problem 'a' and from the TEC point of view, the shadow price of TEC when moving from schedule a10 to a9 is 0.0018 minutes per kilowatt hour.…”

Section: Tablementioning

confidence: 99%

Green scheduling of a two-machine flowshop: Trade-off between makespan and energy consumption

Mansouri

Aktaş

Beşikçi³

2016

European Journal of Operational Research

247

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a b s t r a c tSustainability considerations in manufacturing scheduling, which is traditionally influenced by service oriented performance metrics, have rarely been adopted in the literature. This paper aims to address this gap by incorporating energy consumption as an explicit criterion in shop floor scheduling. Leveraging the variable speed of machining operations leading to different energy consumption levels, we explore the potential for energy saving in manufacturing. We analyze the trade-off between minimizing makespan, a measure of service level and total energy consumption, an indicator for environmental sustainability of a two-machine sequence dependent permutation flowshop. We develop a mixed integer linear multi-objective optimization model to find the Pareto frontier comprised of makespan and total energy consumption. To cope with combinatorial complexity, we also develop a constructive heuristic for fast trade-off analysis between makespan and energy consumption. We define lower bounds for the two objectives under some non-restrictive conditions and compare the performance of the constructive heuristic with CPLEX through design of experiments. The lower bounds that we develop are valid under realistic assumptions since they are conditional on speed factors. The Pareto frontier includes solutions ranging from expedited, energy intensive schedules to prolonged, energy efficient schedules. It can serve as a visual aid for production and sales planners to consider energy consumption explicitly in making quick decisions while negotiating with customers on due dates. We provide managerial insights by analyzing the areas along the Pareto frontier where energy saving can be justified at the expense of reduced service level and vice versa.

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Section: Tablementioning

confidence: 99%

Green scheduling of a two-machine flowshop: Trade-off between makespan and energy consumption

Mansouri

Aktaş

Beşikçi³

2016

European Journal of Operational Research

247

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“…Both P and Q are similar so let us analyze the partial derivatives of Q. The latter lemma guarantees that the envelope theorem applies (see for instance [21] or [22]' where the result is also called "envolvent theorem"). Accordingly, g~ = ~, j E l¡, and g~ = ~,j E 12, where .c2 (PjO' (Xj)j.¡.jo' (Yj)j'¡'jo,p"A, (Vj)j'¡'jo' (Vj)j.¡.jo)…”

Section: Shadow Prices and Strong-ps-arbitragementioning

confidence: 99%

“…It may be done by drawing on a procedure quite parallel to that used when proving Theorem 6. In fact, these effects may be analyzed by sensitivities that may be measured by applying a general envelope (or envolvent) theorem for balance points that was established ín [22].…”

Section: Efficiency Weak-ps-arbitrage and Coalitionsmentioning

confidence: 99%

“…In order to ensure that the Pareto solution (45) exists we will impose the following. There exists a balance point of (43) in the direction of d. IA possible way to detect the balance point in the direction of preferential deviations d (or the Pareto solution (45» is to solve (see[21] or[22] for further details) min,L zjVj(k) -¿ zjWj(k) + L xjVj(k) -L yj Wj (k):2: 0, zJl'0,xJ 3 ) (0,ZJ2,YJ3» + ¿ "TrjZj -¿ PjZj + ¿(qjXj -PjYj)::; 0,…”

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confidence: 99%

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Nonconvex optimization for pricing and hedging in imperfect markets

Balbás

Mayoral

2006

Computers & Mathematics with Applications

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The paper deals with imperfect financial markets and provides new methods to overcome many inefficiencies caused by frictions. Transaction costs are quite general and far from linear or convexo The concepts of pseudoarbitrage and efficiency are introduced and deeply analyzed by means of both scalar and vector optimization problems. Their optimality conditions and solutions yield strategies to invest and hedging portfolios, as well as bid-ask spread improvements. They also point out the role of coalitions when dealing with these markets. Several sensitivity results will permit us to show that a significant transaction costs reduction is very often feasible in practice, as well as to measure its effect on the general efficiency of the market. AII these findings may be especially important for many emerging and still illiquid spot or derivative markets (electricity markets, com odity markets, markets related to weather, infiation-linked or insurance-linked derivatives, etc.).

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Nonlinear Multiobjective Programming

Engau

2011

Wiley Encyclopedia of Operations Research and Management Science

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This introductory treatment of the theory and methodology of nonlinear multiobjective programming offers an annotated bibliographic overview of various concepts and approaches to solve continuous deterministic multicriteria optimization problems. First, the notions of Pareto optimality, efficiency, and nondominance are discussed and then related to approximate, epsilon, and proper efficiency. Second, after highlighting similarities and pointing out differences to first‐ and second‐order optimality conditions in classical nonlinear programming, several other topics including duality and sensitivity are also mentioned. Third, a number of solution approaches and generating methods are described with a particular focus on scalarizations using objective aggregation, prioritization, and norm or distance minimization to some utopian reference point.

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Sensitivity of Pareto Solutions in Multiobjective Optimization

Cited by 9 publications

References 20 publications

Green scheduling of a two-machine flowshop: Trade-off between makespan and energy consumption

Green scheduling of a two-machine flowshop: Trade-off between makespan and energy consumption

Nonconvex optimization for pricing and hedging in imperfect markets

Nonlinear Multiobjective Programming

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