On Stochastic Aspects of a Metal Cutting Problem

Dupačová, Jitka; Charamza, Pavel; Mádl, Jan

doi:10.1007/978-3-642-88272-2_11

Cited by 4 publications

(3 citation statements)

References 11 publications

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“…From Lemma C.1 (i), we get that there exist K 5.12 ∈ (K B.18 , ∞) and λ 5.12 ∈ (0, λ B. 18 ) such that 2|f λ (G)| ≤ K 5.12 λ ≤ K 5.12 λ q holds whenever λ ∈ (0, λ 5.12 ). Let λ ∈ (0, λ 5.12 ) and τ be an integrable stopping time.…”

Section: D19 Proof Of Theorem 512mentioning

confidence: 94%

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Almost log-optimal trading strategies for small transaction costs in model with stochastic coefficients

Dostál¹

2023

Kybernetika

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We consider a non-consuming agent investing in a stock and a money market interested in the portfolio market price far in the future. We derive a strategy which is almost log-optimal in the long run in the presence of small proportional transaction costs for the case when the rate of return and the volatility of the stock market price are bounded Itô processes with bounded coefficients and when the volatility is bounded away from zero.

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Section: D19 Proof Of Theorem 512mentioning

confidence: 94%

“…(Dominated convergence) If X ∈ CS(F ) and if Y, Y (n) t ∈ PM(F ) are such that |Y (n) t | ≤ Y, n ∈ N,and that Y dX is well-defined, then by[18, part III, 2.1.19] …”

mentioning

confidence: 99%

Almost log-optimal trading strategies for small transaction costs in model with stochastic coefficients

Dostál¹

2023

Kybernetika

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“…Based on the results of Kyparissis [22] for the geometric programming problems, Dupocova et al [23] have proposed statistical sensitivity analysis of the optimal machining conditions, the minimal value of the total machining costs in a single pass and single tool turning operation. Their study is concentrated on the case of random parameters only in the objective function, assuming that the only source of uncertainty stems from Taylor's equation.…”

Section: A Succinct Review On Probabilistic Optimization In Machiningmentioning

confidence: 99%

New approach for robust multi-objective optimization of turning parameters using probabilistic genetic algorithm

Sahali

Belaidi

Serra

2015

Int J Adv Manuf Technol

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In this paper, a contribution to the determination of reliable cutting parameters is presented, which is minimizing the expected machining cost and maximizing the expected production rate, with taking into account the uncertainties of uncontrollable factors. The concept of failure probability of stochastic production limitations is integrated into constrained and unconstrained formulations of multi-objective optimization problems. New probabilistic version of the nondominated sorting genetic algorithm P-NSGA-II, which incorporates the Monte Carlo simulations for accurate assessment of cumulative distribution functions, was developed and applied in two numerical examples based on similar and anterior work. In the first case, it is a question of the search space that is completely 'closed' by high natural variability related to the multi-pass roughing operation: in this case, the failure risk of technological limitations are considered as objectives to minimize with economic objectives. The second case is related to deformed search space due to the uncertainties specific to finishing operation; therefore, the economic objectives are minimized under imposed maximum probabilities of failure. In both situations, the efficiency and robustness of optimal solutions generated by the P-NSGA-II algorithm are analysed, discussed and compared with sequence of unconstrained minimization technique (SUMT) method. Keywords Failure probability . Monte Carlo simulations . Pareto optimal solutions . Optimization . NSGA-II . Reliable machining parameters Nomenclature R max The maximum roughness (μm) T max The maximum tool life (min) F max The maximum cutting force (kg) P max Power on the spindle (kW) L Length to be machined for a single pass (mm) d Diameter of workpiece (mm) t m Cutting time (min) t l Nonproductive and handling time (min) t r Tool changing time (min/edge) a Depth of cut (mm) t Total depth of metal to be cut in roughing operation (mm) n Number of passes in rough machining (an integer) p 0Direct labour cost added to overhead (paise/min) p 0 *t m Machining cost by actual time in cut (paise/pc) p 0 *t l Machine idle cost due to loading and unloading operations (paise) p l *(t m /T) Tool cost per unit piece (paise/pc) p lThe cost of a cutting edge (paise/edge) p 0 *(t r *t m / T) Tool replacement cost (paise/pc) r ε Nominal nose radius (mm) ηNominal machine efficiency (%) EThe expectation measurement

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Stochastic Geometric Programming

Avriel¹,

Wilde²

2015

Proceedings of the Princeton Symposium on Mathematical Programming

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On Stochastic Aspects of a Metal Cutting Problem

Cited by 4 publications

References 11 publications

Almost log-optimal trading strategies for small transaction costs in model with stochastic coefficients

Almost log-optimal trading strategies for small transaction costs in model with stochastic coefficients

New approach for robust multi-objective optimization of turning parameters using probabilistic genetic algorithm

Stochastic Geometric Programming

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