The Effect of Computer Simulation, Linear Programming for Industrial Projects

Using the effect of computer simulation linear programming models with many objectives in operations research. The maximum profits were calculated for companies in the ministry of Industry in Iraq accurate. The Dual Model method was used for the conflicting objectives of the model. This is done by using the corresponding model and then finding the optimal solution for each objective function, which represents the profits and under the same restrictions. Then extracting the average of the optimal solution for the multiple objective functions. And by building a linear model with one objective that achieves maximizing profits for the factory. Also we used modern computer simulation using WIN QSB programs to built according in Steps to solving a multi-objective model.


Introduction
Using mathematical methods to calculate the profits of a group of companies with the highest accuracy through linear programming and the formation of a linear model for the objective function and constraints. It gives efficiency and accuracy in calculating profits [1].

Objective Functions Models
The goal function is the mathematical formula or the mathematical equation that shows the measurement of the total impact of profit if it is a goal function of type max or cost if the goal function is of type min for the variables related to decision-making, which determines the amount of total profit or the amount of total cost [2].

Linear Programming Simplex Method
The simplex method is based on the property that the optimal solution to a linear programming problem, if it exists, can always be found in one of the basic feasible solutions. The simplex method is quite simple and mechanical in nature. The iterative steps of the simplex method are repeated until a finite optimal solution, if exists, is found. If there is no optimal solution, the method indicates that no finite solution exists [1].In the simplex method, the number of corner points to be tested is greatly reduced by using a very efficient algorithm which leads us to the optimal solution point in only a few iterations [1]. This process stops when we reach one of the following cases: 1. Obtaining a final solution, which is the optimal solution and includes the case of multiple solutions and the case of dissolution.
2. Determine an infinite number of solutions.
3. The problem has infeasible solution.

Big -M Method
The big m method is a modified version of the simplex method in linear programming (LP) in which we assign a very large value (M) to each of the artificial variables. Define the principle of Big M (simple form method) After adding the artificial variables to the constraints of the linear programming system, the considered term M or a parameter needs to be added to the objective function accordingly. In the maximization problem, a synthetic variable M is assigned as its parameter; In the minimization problem, a synthetic variable M is set as a parameter, and M is an arbitrarily large (not infinite) positive number. Regarding M as an algebraic symbol to participate in the process, it is solved by the simplex method, so this method is called the big M method, which can also be called the penalty factor method.

Artificial Variable Method
Using this method is simpler than big (M) method in finding the optimal solution for linear programming (L.P) in the case of minimization, as it is possible to obtain the optimal solution for the model after making sure that there is a solution to the model, by obtaining the value of a function. The new target is equal to zero [4]. That is, (r = 0) and without it, there is no solution to the model, and the solution is carried out according to this method in two basic stages, as follows: a. The first stage Includes the following steps:

Mathematical Model
To seek to take the optimal decision to achieve a set of goals facing the decision maker, these goals should be formulated in a way that works to find effective results, and the general formula for linear multi-objective programming is as follows: = is the number of goal functions to be maximized. = the number of goal functions to be minimized and maximized. = is the vector of the decision variables. = is the vector of the right-hand side (the constants). ( − ) = is the number of goal functions to be reduced, A = is an array (m x n) of operator.

The corresponding model (equivalent) The Dual Model
Sometimes it is necessary to convert the linear programming model to the standard form and to convert the objective functions or constraints to go with the solution and to get the optimal solution to the problem, as it is possible to convert the objective function to any model Linear programming from type Max to type Min and vice versa, as the conversion is by multiplying the function by (-1), that is, if the function is of type (Max (z), then converting it to the corresponding function or its equivalent will be in the form (Min) -z and any solution to the function Of type Max, it will in turn be a solution to its equivalent function, which is Min. The same method is used for constraints, as it can be converted according to the requirements of the model and according to the nature of the constraint, where if the constraint is of a type greater or equal to (k), it can be converted to the other type which is less or equal to (2) by multiplying it by (-1) [8].

Applied side
A cotton factory is one of the factories of the General Company for Textile and Leather Industries, and the factory consists of several from factory (Baghdad textile, medical bandage, plastic bag factory), as the last factory is the latest factory of the factory, as it produces two types of plastic bags, which are (standard plastic bags, standard plastic lined bags), and the medical bandage factory produces several products. The most important of them are (medical cotton, gauze and bandage rolls of different sizes, masks), and the Baghdad Textile Factory produces (cotton fabrics of all kinds).

Building the multi-objective linear model
Maximizing profits for the factory, achieving the (expected) annual demand, reducing the total cost of production and reducing working hours based on the current conditions. It also shows the time taken to produce one of the mentioned products.  The constraints will also be the constraints of raw materials, as the factory faces a challenge in providing the raw materials needed to produce the products and meet the demand. Table (2) shows the design capacity and available for each product according to the factory data. Table  (3) shows the raw materials involved in making the products and the quantity of available materials one of the raw materials in factories. 0.02 6 ≤ 3400 The constraints represent the available raw materials and the proportion of the material needed by each product after building the model. The problem is solved using Win QSB program, as the results will be as follows: The function of maximizing profits amounted to (214,67720) thousand dinars compared to the profits of the company, which amounted to (19043881) thousand dinars, while the function of reducing costs amounted to (175572919) thousand dinars compared to the manufacturing costs of the company, which amounted to (178430700) thousand dinars, and the total time of the time reduction function was (10) hours per day The average work was 12 hours per day, and the optimal product production amount was as follows: When using the method of unifying the objectives and following the mentioned steps, the optimal rate was determined, as its value amounted to (45318.745) and after building the model and solving it using the Win QSB program, the total profits of the company under the same