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1

Optimizing electricity costs during integrated scheduling of jobs and stochastic preventive maintenanceunder time-of-use electricity tariffs

Sadiqi Assia, El Abbassi Ikram, El Barkany Abdellah, Darcherif Moumen, El Biyaali Ahmed

Management and Production Engineering Review

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2019

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Vol. 10, No. 4

123--132

EN

Time-of-use (TOU) electricity pricing has been applied in many countries around the world to encourage manufacturers to reduce their electricity consumption from peak periods to oﬀ-peak periods. This paper investigates a new model of Optimizing Electricity costs during Integrated Scheduling of Jobs and Stochastic Preventive Maintenance under time of-use (TOU) electricity pricing scheme in unrelated parallel machine, in which the electricity price varies throughout a day. The problem lies in assigning a group of jobs, the ﬂexible intervals of preventive maintenance to a set of unrelated parallel machines and then scheduling of jobs and ﬂexible preventive maintenance on each separate machine so as to minimize the total electricity cost. We build an improved continuous-time mixed-integer linear programming (MILP) model for the problem. To the best of our knowledge, no papers considering both production scheduling and Stochastic Preventive Maintenance under time of-use (TOU) electricity pricing scheme with minimization total Electricity costs in unrelated parallel machine. To evaluate the performance of this model, computational experiments are presented, and numerical results are given using the software CPLEX and MATLAB with then discussed.

2

The comparison study for the models of reservoir release rule for irrigation. Case study: Sutami Reservoir

Soetopo W., Suhardjono, Andawayanti U., Sayekti R. W., Ismoyo J.

Journal of Water and Land Development

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2018

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no. 36

153--160

EN

Three models of release rule for operating a large reservoir for irrigation water supply are discussed in this paper. The models are a 50-grid storage continuous line restricted release rule, a single rule curve release rule, and a multi 4 rule curves release rule. These three models are to be optimized by stochastic simulation using 30 year inflow data with the maximization of the average monetary annual production in the irrigation area as the objective function. The purpose of this study is to look for the proper release rule for operating the Sutami Reservoir. The optimization is done first by the random search stochastic simulation model to generate a number of alternative solutions. Using these solutions as a generation of solutions, the genetic algorithm model is the applied to improve the solution. Afterward the best of solutions are checked by the Add-Ins Solver of MS-Excel 2010 to see if they can still be improved further. The results show that the 4 rule curves model gives the best solution with the average monetary annual production in the irrigation area of USD 72.248 million.

PL

W pracy omówiono trzy modele zasad eksploatacji dużego zbiornika, którego wody są wykorzystywane do nawodnień. Są to: zasada pięćdziesięcioelementowej ciągłej linii pojemności zbiornika, zasada pojedynczej krzywej i zasada czterech krzywych pojemności zbiornika. Wymienione trzy modele były optymalizowane przez losową symulację z użyciem danych o dopływie z 30 lat z zastosowaniem maksymalizacji wartości średniej rocznej produkcji w nawadnianym obszarze jako funkcji obiektywnej. Celem prezentowanych badań było poszukiwanie odpowiednich zasad eksploatacji zbiornika Sutami. Optymalizację realizowano wstępnie poprzez losowe poszukiwanie stochastycznego modelu symulacji dla uzyskania szeregu alternatywnych rozwiązań. Rozwiązania te ulepszano, stosując model genetycznego algorytmu. Następnie najlepsze rozwiązania sprawdzano, stosując Add-Ins Solver programu MS-Excel 2010, by sprawdzić, czy można je jeszcze usprawnić. Wyniki dowiodły, że model czterech krzywych dawał najlepsze rozwiązania przy rocznej produkcji w nawadnianym obszarze o wartości 72,248 miliona dolarów.

3

The effect of the safety stock on the occurrence probability of the stock shortage

Korponai J., Tóth Á. B., Illés B.

Management and Production Engineering Review

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2017

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Vol. 8, No. 1

69--77

EN

The objective of the logistics management is to guarantee the stock level required for the adequate handling of production at the lowest possible level of costs and risks. The main purpose of the paper is to present the relations between stock level and risk of shortages. As a result of the research, the introduction of the safety stock is the solution to cover the effects of the uncertain factors in the supply chain. The theoretical approach of the model assumes a deterministic operational environment, in practice, however, there are several unpredictable factors influencing the operation of the production company. By using the periodic and continuous review models, the paper presents the effects of demand changes and stochastic length of replenishment time on the risk of stock availability. We need to quantify a service level which determines the accepted probability of the shortage occurrence.

4

Critical infrastructure preparedness : cascading of disruptions considering vulnerability and Dependency

Eid M., Hakkarainen T., Terhi K., Souza-Cursi-de E., El-Hami A.

Journal of Polish Safety and Reliability Association

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2016

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Vol. 7, No. 1

61--66

EN

Critical Infrastructures’ disruptions may result in crises of unacceptable outcomes in modern societies. Thus, it is important to develop models that allow describing CIs’ disruptions and their propagation characteristics. CI disruptions depend on both the type of the threat and on the nature of the CIs’ mutual dependencies. A model describing the cascade of disruptions should, then, be able to consider the CI-threat vulnerability and the CI-CI dependency. The paper presents a model where cascades are exactly described using an integral equation. The integral equation admits an analytical solution if the occurrence probability distribution functions (pdf) of the disruptions obey Stochastic Poisson Processes (SPP). The introduction of the “vulnerability to the threat” and the “CIs’ (inter)dependencies” is carried out with the help of time constant factors called: “vulnerability strain factor” and “disruption strain factor”, respectively. An academic case is presented in order to demonstrate the applicability of the model and illustrate some interesting features of the model. A complete set of numerical applications will be published separately.

5

Stochastic impulsive pressure calculations for time dependent human hip joint lubrication

Wierzcholski K.

Acta of Bioengineering and Biomechanics

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2012

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Vol. 14, no. 4

81-100

EN

The present paper is concerned with the calculation of the stochastic unsteady, impulsive pressure distributions and load carrying capacities in human hip joint for unsteady stochastic conditions, various standard deviations and Gaussian probability density function. The total changes of hydrodynamic pressure caused by viscoelastic synovial fluid properties are completely estimated. Calculations are performed in a super thin layer of biological synovial fluid inside the slide hip joint gap limited by a spherical bone head. Using a new unified operator of summation (UOS) method, the numerical topology of pressure calculation for a difference method is applied. From numerical standpoint the proposed method of solving modified hydrodynamic equations reduces this problem to resolving the partial recurrence non-homogeneous equation of second order with variable coefficients.

6

Identification of stochastic material properties in multiscale modelling

Kuś W., Burczyński T.

Computer Methods in Materials Science

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2011

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Vol. 11, No. 4

524-530

EN

The paper is devoted to identification problems in multiscale modeling in stochastic conditions. The multiscale modeling is able to take into account materials or geometrical effects which occur in microscale and obtain more precise results in macroscale analysis. The identification allows to evaluate materials or geometrical parameters of a structure in microscale on the basis of statistical measurements in macroscale. The methodology presented in the paper takes into account stochastic nature of parameters in the microscale and the identification problem is formulated as minimization of a certain stochastic objective function. The problem is transformed into deterministic one in which a new objective functional dependent on mean values and variances is minimized with respect to moments of stochastic parameters. An approach based on evolutionary computing is presented in the minimization problem. The main advantage of the presented approach consists in the fact that a gradient of the objective functional is no needed and moreover there is a great probability of finding the global minimum. The computational homogenization is used to multiscale modelling of the structures. The problem formulation, description of optimization algorithm and a numerical example are shown in the paper.

PL

Artykuł jest poświęcony zagadnieniom identyfikacji parametrów modelu w skali mikro w ujęciu wieloskalowym. Pozwala to uwzględnić wpływ parametrów materiałowych oraz geometrycznych w skali mikro na rozwiązania w skali makro. Rozwiązanie zagadnienia identyfikacji umożliwia określenie parametrów struktury w skali mikro na podstawie pomiarów przeprowadzonych dla skali makro. Przedstawiona w pracy metodologia oparta jest na założeniu, że parametry w skali mikro mają naturę stochastyczną i można je wyznaczyć dysponując wynikami statystycznych pomiarów eksperymentalnych przemieszczeń i odkształceń w skali makro. Zagadnienie sprowadzono do minimalizacji różnicy między charakterystykami probabilistycznymi przemieszczeń i odkształceń obliczonych dla modelu stochastycznego oraz obiektu rzeczywistego. W tym celu zastosowano koncepcję homogenizacji komputerowej, metodę Monte Carlo oraz algorytm ewolucyjny. Opracowaną koncepcję identyfikacji w warunkach stochastycznych zweryfikowano pozytywnie na przykładzie numerycznym.

7

The recourse to evolutionary strategies for the limit calculation of voussoir arches in heritage buildings

Van Parys L., Descamps T., Lamblin D., Guerlement G.

Foundations of Civil and Environmental Engineering

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2008

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No. 12

73-86

EN

In the past centuries, masonry arches were the unique option for builders having to carry heavy loads over large spans. They were later neglected as the advantages of other solutions had been discovered. Today they represent a contemporary challenge for people engaged in heritage preservation. In accordance with international guidelines, the interventions that are avoidable should be avoided and an important responsibility is in the hands of civil engineers and architects. As the continuation of preliminary research published in the present journal, this paper proposes an innovative approach in the wellknown field of the Limit Analysis theory. After a short presentation of the context, the arch limit behavior is formulated as a constrained optimization problem solved through evolutionary strategies. A tool, implementing this approach in the Matlab environment, has been described and its validation has been proposed by a comparison with numerical results (ABAQUS) obtained on different morphologies.

8

Slack due date assignment and scheduling stochastic jobs on a single machine

Soroush H. M.

Foundations of Computing and Decision Sciences

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2007

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Vol. 32, No. 2

153-181

EN

This paper solves the general case of the stochastic single machine scheduling problem where processing times are random variables and due dates are assigned using the slack method. Its objective is to identify the optimal sequence and optimal due dates which minimize the expected total weighted cost of assigning and missing due dates, with no restriction imposed on either cost. The paper presents an exact two-stage algorithm. The first stage (i) utilizes an adjacent precedence relation structure to determine an initial ordering of jobs, (ii) investigates the optimality of the initial job ordering, and (iii) when it cannot prove optimality. it tries to improve the initial ordering by moving jobs from their current positions to any other positions that ensure the precedence relations hold; thus, obtains an incumbent solution. The second stage, which uses the incumbent to show its optimality or search for the optimal solution, is a branch and bound. It utilizes the expected cost of the incumbent as an initial upper bound. It avoids investigating dominated branches by using the job precedence relations; thus, greatly reduces the size of the tree. Extensive computational results show that the incumbent solution obtained in the first stage of the algorithm provides a very tight upper bound cost which fathoms a significant number of non-dominated solutions in the second stage; thus, the proposed algorithm can solve large problems quickly on PC.

9

Effect of subsurface heterogeneous correlated hydraulic properties on the stochastic behavior of the unsteady well drawdown in a confined aquifer

Abdeen M, A. M., Abdin A. E.

Engineering Transactions

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2006

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Vol. 54, iss. 2

125-142

EN

Groundwater is considered to be one of the most important water resources especially in areas where surface water resource, is not sufficient. However, utilizing this important groundwater resource requires a complete understanding of the groundwater flow behavior within the subsurface formations. The assumption of considering the subsurface formation as homogeneous media has been proven to be un-realistic. Therefore, the subsurface formation has to be considered as a heterogeneous structure in investigating the groundwater flow behavior. In addition, full understanding of the impact of the subsurface heterogeneous formation on the groundwater flow behavior is very essential in safe utilization of this important water resource. The current study investigates the impact of two subsurface heterogeneous correlated hydraulic properties on the stochastic behavior of a two-dimensional unsteady well drawdown in a confined aquifer. In addition, the presented study compares the impact of two subsurface heterogeneous cases. The first case considers two subsurface correlated hydraulic properties (current study), while the second case considers the heterogeneous subsurface hydraulic conductivity only. The two hydraulic properties considered in the current study are the subsurface hydraulic conductivity and storativity. The Monte Carlo stochastic approach is used in this study to perform various numerical computations required to assess the investigated problem. The results obtained from this study showed how important it was to consider and understand the heterogeneous subsurface formation and its impact on the groundwater flow behavior, since the two-dimensional unsteady well draw-down was greatly affected by the degree of heterogeneity and the correlation structure of the subsurface hydraulic properties.

10

Pomiar ryzyka finansowego w warunkach niepewności

Trzpiot G.

Badania Operacyjne i Decyzje

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2006

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nr 2

81-88

EN

Coping with the uncertainties of future outcomes is a fundamental theme in finance in a stochastic environment. In the field of stochastic programming, which has grown from the traditions of linear and quadratic programming, constrains on future outcomes have commonly been relaxed to the penalty expressions. Probabilistic constrains, requiring that a condition only to be satisfied up to a given probability. Objectives have usually taken the form of maximizing expected utility or minimizing expected cost. In financial optimization, where uncertainties are likewise unavoidable, approaches of stochastic programming have prevailed. An important example is constraint and objective based notion of the value-at-risk, which is closely related to probabilistic one; unfortunately it suffers from similar mathematical shortcomings. Value-at-risk suffers from financial inconsistencies, which have led to axiomatic development of coherent risk measures, so we also add the robust alternative called conditional value-at-risk. We also cope with some connection between CVaR and stochastic dominance.

PL

Zarządzanie losowymi przyszłymi stopami zwrotu jest podstawowym zadaniem finansów w otoczeniu, które ma charakter stochastyczny. W metodologii programowania stochastycznego, które wyrosło z tradycji programowania liniowego i kwadratowego, ograniczenia, co do przyszłych wartości, są często zamieniane na funkcję kary. Probabilistyczne ograniczenia w zadaniu wymagają jedynie, aby zdarzenia zachodziły z pewnym prawdopodobieństwem. Funkcja celu zazwyczaj maksymalizuje oczekiwaną użyteczność albo minimalizuje koszty. W finansach zadania optymalizacji stochastycznej mają, zatem uprzywilejowane miejsce. Ważne są zadania bazujące na optymalizacji VaR, które są podejściem probabilistycznym do zagadnienia. Rozwój aksjomatycznej teorii związanej z koherentnymi miarami ryzyka, wskazał na odporny odpowiednik VaR nazywany CVaR. W pracy omówiono związek tej miary z dominacjami stochastycznymi.