Mixed 0-1 linear programming for an absolute value linear fractional programming with interval coefficients in the objective function

Borza, Mojtaba; Rambely, Azmin Sham; Saraj, Mansour

doi:10.12988/ams.2013.33196

Cited by 7 publications

(6 citation statements)

References 8 publications

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“…In the case when uncertainties are present, all quantities in (2) will be represented by intervals. The interval of possible values for chlorine concentration at node j, indicated by   ( ) [ ( ), ( )] j j j c k c k c k , is calculated by solving the following optimization problem: 12) is a linear fractional problem with interval coefficients which can be solved using the formulation described in (Borza et al, 2013).…”

Section: Function 3: Pipesjunction-chlorine Concentration and Bulk Reaction Rate At Pipe Junctionsmentioning

confidence: 99%

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Calculating Chlorine Concentration Bounds in Water Distribution Networks: A Backtracking Uncertainty Bounding Approach

Vrachimis

Ηλιάδης

Polycarpou

2021

Water Resources Research

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The most recent EU directive on the quality of water intended for human consumption (European Commission, 2018) emphasizes the importance of water-quality monitoring for reducing the risks to health from drinking water, with chlorine by-products being among the quality parameters recommended for monitoring. Chlorine is commonly used by water utilities as a disinfectant in Water Distribution Networks (WDN). According to the World Health Organization (WHO), a chlorine residual needs to be sustained throughout the drinking water network which should be sufficient to deactivate waterborne pathogens and, at the same time, small enough to reduce the formation of harmful chlorine by-products (Mouly et al., 2010). Additionally, due to the fact that certain contaminants will affect chlorine residuals in a specific way (e.g., a bacterial toxin may decrease the concentration of free chlorine due to its reaction dynamics) (Helbling & Van-Briesen, 2009), chlorine residuals can be used as key indicators of contamination events (Hall et al., 2007).The installation of online chlorine sensors can enhance monitoring capabilities of chlorine residuals and enable more timely control actions. For contamination event detection, water-quality sensors may be installed which can monitor multiple parameters (e.g., pH, free chlorine, total organic carbon) and detect changes in water-quality. The placement of such sensors in WDN in order to detect a contamination event has been a subject of research for years (Eliades & Polycarpou, 2010;Hart & Murray, 2010). The problem is posed as a multiobjective optimization, with one of the objectives being the minimization of the number of sensors due to their high capital and maintenance costs (Zeng et al., 2016), while addressing the uncertainty present in these real-world systems is also a crucial component of these methodologies (Sankary & Ostfeld, 2018). Single-parameter sensors (such as free chlorine concentration sensors) are cheaper than multiparameter sensors, and using them not only for chlorine residual monitoring but also for contamination event detection, could significantly reduce the health risks from contaminated drinking water. However, in order to determine whether a sensor reading is abnormal (e.g., due to a contamination), it needs to be compared with an estimate of the expected concentration at the sensor location. The estimated concentration can be calculated using water-quality models (Rossman & Boulos, 1996). These are mathematical representations

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Section: Function 3: Pipesjunction-chlorine Concentration and Bulk Reaction Rate At Pipe Junctionsmentioning

confidence: 99%

“…The interval

([], {\underset{c}{true}}_{i j} (k), {\overset{c}{true}}_{i j} (k))

is given by PipeContribution . Problem () is a linear fractional problem with interval coefficients which can be solved using the formulation described in (Borza et al., 2013).…”

Section: The Backtracking Uncertainty Bounding Algorithmmentioning

confidence: 99%

Calculating Chlorine Concentration Bounds in Water Distribution Networks: A Backtracking Uncertainty Bounding Approach

Vrachimis

Ηλιάδης

Polycarpou

2021

Water Resources Research

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“…As it is quite burdensome to solve fractional programming problems directly, Charnes and Cooper [4] derived an effective variable transformation method to equivalently convert LFP into LPP. By following this masterpiece, Borza et al [2] proposed a method to solve LFPs having interval coefficients. Dorn [9], Swarup [31], Wagner and Yuan [34], Sharma et al [29], Pandey and Punnen [26] derived some algorithms based on simplex method to optimise fractional linear programming problems.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear fuzzy fractional signomial programming problem: A fuzzy geometric programming solution approach

2023

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Fuzzy fractional signomial programming problem is a relatively new optimization problem. In real world problems, some variables may vacillate because of various reasons. To tackle these vacillating variables, vagueness is considered in form of fuzzy sets. In this paper, a nonlinear fuzzy fractional signomial programming problem is considered with all its coefficients in objective functions as well as constraints are fuzzy numbers. Two solution approaches are developed based on signomial geometric programming comprising nearest interval approximation with parametric interval valued functions and fuzzy α-cut with min-max approach. To demonstrate the proposed methods, two illustrative numerical examples are solved and the results are comparatively discussed showing its feasibility and effectiveness.

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“…The FP is applied to different disciplines such as engineering, business, finance, economics, health care, and hospital planning. In the recent years, we have seen many approaches to solve fractional programming problem [3,4,5,6,7,8,9,10].…”

Section: Introductionmentioning

confidence: 99%

A Parametric Approach for Solving Interval–Valued fractional Continuous Static Games

Elshafei¹

2019

JAM

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The aim of this paper is to show that a parametric approach can be used to solve fractional continuous static games with interval-valued in the objective function and in the constraints. In this game, cooperation among all the players is possible, and each player helps the others up to the point of disadvantage to himself, so we use the Pareto-minimal solution concept to solve this type of game. The Dinkelbach method is used to transform fractional continuous static games into non- fractional continuous static games. Moreover, an algorithm with the corresponding flowchart to explain the suggested approach is introduced. Finally, a numerical example to illustrate the algorithm’s steps is given.

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Mixed 0-1 linear programming for an absolute value linear fractional programming with interval coefficients in the objective function

Cited by 7 publications

References 8 publications

Calculating Chlorine Concentration Bounds in Water Distribution Networks: A Backtracking Uncertainty Bounding Approach

Calculating Chlorine Concentration Bounds in Water Distribution Networks: A Backtracking Uncertainty Bounding Approach

Nonlinear fuzzy fractional signomial programming problem: A fuzzy geometric programming solution approach

A Parametric Approach for Solving Interval–Valued fractional Continuous Static Games

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