Interval linear fractional programming: optimal value range of the objective function
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Interval linear fractional programming: optimal value range of the objective function Fatemeh Salary Pour Sharif Abad1 · Mehdi Allahdadi1
· Hasan Mishmast Nehi1
Received: 28 November 2019 / Revised: 9 July 2020 / Accepted: 17 August 2020 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2020
Abstract In the real world, some problems can be modelled by linear fractional programming with uncertain data as an interval. Therefore, some methods have been proposed for solving interval linear fractional programming (ILFP) problems. In this research, we propose two new methods for solving ILFP problems. In each method, we use two sub-models to obtain the range of the objective function. In the first method, we introduce two sub-models in which the objective functions are non-linear and the two sub-models have the largest and smallest feasible regions; therefore, the optimal value range of the objective function has been obtained. In the second method, two sub-models have been proposed in which the objective functions are linear and the optimal value of the objective function lies in the range obtained from the first method. We use our approaches to maximize the ratio of the facilities optimal allocation to the non-return fund in a bank. Keywords Interval linear fractional programming · Fractional programming · Uncertainty · Optimality Mathematics Subject Classification 90C32 · 90C30
1 Introduction Linear fractional programming (LFP) is a particular category of mathematical programming such that the objective function is the ratio of two linear functions. Isbell and Marlow have used fractional programming (FP) problems in some real-world scenarios (Isbell and Marlow
Communicated by Anibal Tavares de Azevedo.
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Mehdi Allahdadi [email protected] Fatemeh Salary Pour Sharif Abad [email protected] Hasan Mishmast Nehi [email protected]
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Mathematics Faculty, University of Sistan and Baluchestan, Zahedan, Iran 0123456789().: V,-vol
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F. Salary Pour Sharif Abad et al.
1956). When we encounter a FP that deals with two contradictory objective functions on a common feasible region, we sometimes need to optimize the proficiency of some activities amongst maximum return on investment, minimum cost to time, minimum foreign loans to total loans and so forth. FP as an operation research technique is one of the most important tools of programming in length of the past 4 decades. Researchers have presented several methods for solving the LFP problem (Ghadle and Pawar 2015; Jiao and Liu 2014; Odior 2012; Soradi Zeid et al. 2017; Veeramani and Sumathi 2016; Zieniuk et al. 2016). Gilmore and Gomory (1963) used FP in the paper industry and showed that minimizing the ratio of waste to raw materials is more important than minimizing the amount of waste. Therefore, the most important reason for using this method is that the objective functions of the fractional are always generic certainty or uncertainty, which are important performance indicators. The interval linear frac
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