‎fuzzy programming‎

In the real world, the parameters of a problem may not be the crisp values. The fuzzy theory among the theories in which uncertainty plays a crucial role. Type-2 fuzzy sets generalize fuzzy sets. We consider a special type of such sets here. In this paper, we consider two issues. First, we review the method proposed by Javanmard and Mishmast Nehi for solving an interval type-2 triangular fuzzy linear programming problem, and improve it. Then, we express a bilevel linear programming problem, that, to the best of our knowledge, has not been investigated so far. We consider the bilevel linear programming problem with uncertainty where all the coefficients in the problem are interval type-2 triangular fuzzy numbers. We convert an interval type-2 triangular fuzzy bilevel linear programming problem into an interval bilevel linear programming problem using Grzegorzewski's nearest interval approximation method. Finally, we obtain five problems, and by solving them, we achieve the solution of interval type-2 triangular fuzzy bilevel linear programming problem as an interval type-2 triangular fuzzy number.

Data envelopment analysis (DEA) is a method to estimate a relative efficiency of decision making units (DMUs) performing similar tasks in a production system that consumes multiple inputs to produce multiple outputs. The original DEA model does not include a decision maker’s (DM’s) preference structure while measuring relative efficiency. Regarding to relationship between DEA and multiple objective linear programming (MOLP) this paper propose a method based on fuzzy goal programming to incorporate DM’s wishes in evaluation of DMUs then it analyzes the situations that the input-output levels of the estimated benchmark will not or may worsen. A compromised method is suggested that not only considers DM’s wishes in target setting but also improve the efficiency of DMUs while none of input-output levels deteriorate.

Due to the nature of activities and processes, the petrochemical industry causes the production of industrial effluents, emissions and wastes that have adverse effects on the environment. The purpose of this study is to investigate the effect of petrochemical economic activities on environmental factors. In this paper, in order to minimize the costs and the amount of pollution caused by the emission of harmful gases, the closed-loop green supply chain model has been used, in which direct and reverse logistics networks have been considered. As a result, a fuzzy mathematical programming model has been developed for when the data are not definitively known. After the demand parameters and the amount of pollution are considered fuzzy, the maximum and bisector mean methods of the area are considered as methods (diffusion) of comparison and ranking of fuzzy definite numbers, and by adding Limitations of these two methods, the model was developed. To solve the model with real data, a plant from the petrochemical industry was selected and the data were prepared for a solution with very good estimates. Finally, the colonial competition algorithm was used to solve it. According to the model, its applicability was shown to reduce the number of environmental pollutants along with the reduction of transportation and waste, and the model for the closed-loop supply chain, which simultaneously considers two direct and inverse logistics networks. It is appropriate.

Appointment scheduling for outpatient services is a challenge in the healthcare sector. For addressing this challenge, most studies assumed that patients’ unpunctuality and the duration of service have constant values or a specific probability distribution function. Consequently, there is a research gap to consider the uncertainty of both patients’ unpunctuality and the duration of service in terms of fuzzy sets. Therefore, this research aims to consider fuzzy values for both unpunctuality and duration of service have to improve an outpatient appointment scheduling (the time interval between two patients) in a referral clinic with the objective of reducing the total weight of waiting time, idle time, and overtime. Four different fuzzy linear programming models and 36 scenarios have been developed based on the show, no-show of patients, single-book, and double-book by using GAMS software. These four models are as follows: (1) probability of no-show equal to zero, (2) probability of no-show equal to 20%, (3) probability of no-show equal to zero and with double-book factor, and (4) probability of no-show equal to 20% and with double-book factor. The results of the first, second, third, and fourth models, respectively, present the scenarios considering 10, 5, 15, and 15 minutes for the time interval between two patients that have the minimum total weight of patient waiting times, physician idle times, and physician overtime. By considering these findings, the investigated referral clinic can improve its appointment system’s performance. Moreover, other similar clinics can apply the proposed model for improving their appointment systems' performance.

Probabilistic or stochastic programming is a framework for modeling optimization problems that involve uncertainty.In this paper, we focus on multi-objective linear programmingproblems in which the coefficients of constraints and the righthand side vector are fuzzy random variables. There are several methodsin the literature that convert this problem to a stochastic orfuzzy problem. By using a special type of fuzzy inequality, wetransform the problem into a convenient stochastic problem. Thensome known methods are applied to obtain the optimal solution.Finally, the equivalent multi-objective problem is solved by aninteractive approach. A numerical example is provided to illustrate the procedure.