Fractal strategy is an important tool in manufacturing proposals, including computer design, conserving, power supplies and decorations. In this work, a parametric programming, analysis is proposed to mitigate an optimization problem. By employing a fractal difference equation of the spread functions (local fractional calculus operator) in linear programming, we aim to analyze the restraints and the objective function. This work proposes a new technique of fractal fuzzy linear programming (FFLP) model based on the symmetric triangular fuzzy number. The parameter fuzzy number is selected from the fractal power of the difference equation. Note that this number indicates the fractal parameter, denoting by λ ε [0, 1]. Accordingly, we specify the objective function to the fractional case, utilizing the fractal difference equation. We apply the suggested model in an application under the oil market. Based on the fractal fuzzy set theory, the fuzzy demand, transportations, management, inventory and buying cost are explained and formulated in a unique fractal fuzzy linear programming model. This model is presented to obtain a maximal profit production approach with an evaluation. The costs indicate that the proposed model can bring valued solutions for developing profit-effective oil refinery methods in a fuzzy fractal situation. Some examples are illustrated in the sequel.

The idea of a fuzzy linear programming (FLP) problem is the most important method for decision making [

Recently, researchers have explored the FLP by utilizing the parametric analysis and parametric spaces. Payan et al. [

In this work, we utilize the concept of fractal derivative to present a parametric set for solving a fuzzy linear system. A fractal derivative [

One or more of the following uncertainties can occur in the refinery industry: the cost of oils alternates depending on the international oil reserve. In such cases, the factors that may increase the oil price include global political issues, military pressure, periodic demand, and/or cold (or hot) issues. Similarly, environmental security problems have tempted dogmatic discussions on valuing rules for oil, which has led to additional uncertainties [

Here, we consider a fuzzy demand

where

(for some constants

We proceed to define another item in the parametric space, which is the fuzzy buying cost, as follows:

where

where

Yang presented the local fractional derivative (fractal) of the function

where

Now, by using the concept of a fractal, we introduce a generalization of the spread function

where

where

Under a fuzzy economic situation and constraints on manufacturing ability, inventory and operations, we propose a mathematical model to sustain a master buying and manufacturing proposal such that when the fluctuating demand is achieved, the maximum gain can be attained at an acceptable flat value.

The aim is to maximize the

where

We have the following list of constraints inequalities:

• Invention of manufacturing in a month plus the previous manufacturing inventory must be larger than or equal to the fluctuating demand (variation demand) for the manufacturing. Therefore, we suggest the average by using

• The invention of every manufacturing at all refineries should be no less than the economical manufacture quantity of every manufacture at all refineries. Consequently, we obtain the following inequality

• The manufacturing at all refineries is controlled by the maximum production capability. Thus, we conclude the following inequality

• The quantity of every category of oil produced should be greater than or equal to the minimum monthly buying amount of every category of oil by agreements. Hence, we obtain the next inequality

• The total sum of oil purchases rendering to agreements is at least a positive fraction

• The total of manufactured material transported from a refinery by any type of transportation (trains, pipelines or trucks) is less than or equal to the maximum permissible amount of the transportation

• The overall sum of manufactured material transported from refineries ought to be less than or equal to the refineries’ overall manufacturing output. Hence, we get the inequality

• The overall sum of manufactured material transported from refineries has to be greater than or equal to the fluctuating (changing) demand for the manufacturing process. Connected to what has been mentioned above, we have the following constrain

• Overall, the variables must be non-negative

The following steps represent our technique, respectively:

We aim to maximize the objective function

Based on the 3-D parametric space, we represent the objective function by the 3-multi-objective system, as follows:

where

and the following system for the upper bound

Following the membership function of

where we aim to maximize

where

We formulate the multiple objective functions

where

Next, we proceed to convert the fuzzy inequality constraints as it is implied by

and

Finally, we combine the multi-objective functions to maximize the following:

taking in account that inequalities

We applied the above mentioned model in the Iraqi Patrol Company (IPC). IPC is the major oil manufacturing firm in Iraq. This company has one part located in Kirkuk city in northern Iraq, and another in Basrah city in southern Iraq. While there are four sub-companies in the middle of Iraq: Al-Doura, Al-Samawa, Al-Najaf and Al-Diwaniya (all have four yields) correspondingly. In this study, we dealt with the primary materials, specifically Gasoline (Ga), Kerosene (Tk), Gas oil (Go) and Fuel oil (Fo). The types of plain oils were limited to the four types mentioned above, and the planning and manufacturing period was set to

To ensure an acceptable oil source, the IPC must come to an agreement with industrial oil countries. Relevant to our work, each group of basic oil

To find the optimal solution, we collected our data as in Appendix A from its sources.

For

• Step 1: we obtained the upper bounds

• Step 2: we determine the vector

• Step 3: Using the vector in step two, we estimate the interval or the value of

• Step 4: By employing the vector in step two, we calculate the interval or the value of

Since the hypotheses and incomes are time irregular, several mathematical tests can describe the impact of uncertainty of the recent model. By shifting both demand and the price factors, as well as the estimate of the systems (see

We point out the following facts for our data that is collected in Appendix A.

•

•

The authors would like to express their thanks to the Iraqi Patrol Company to provide us with all the data under document number 783 in 2018-2019. The authors also would like to acknowledge Prince Sultan University for paying the Article Processing Charges (APC) of this publication. Finally, we would like to thank the editor and reviewers for their valuable comments.