A COMBINING GENETIC LEARNING ALGORITHM AND RISK MATRIX MODEL USING IN OPTIMAL PRODUCTION PROGRAM

One of the important issues for any enterprises is the compromise optimal solution between inverse of multi objective functions. The prediction of the production cost and/or pro ﬁ t per unit of a product and deal with two obverse functions at same time can be extremely dif ﬁ cult, especially if there is a lot of con ﬂ ict information about production parameters. But the most important is how much risk of this compromise solution. For this reason, the research intrduce and developed a strong and cab-able model of genatic algorithim combinding with risk mamagement mtrix to increase the quality of decisions as it is based on quantitive indicators, not on qualititive evaluation. Research results show that integration of genetic algorithim and risk mamagement matrix model has strong signi ﬁ cant in the decision making where it power and time to make the right decesion and improve the quality of the decision making as well.


INTRODUCTION
The analysis of the production program of enterprises is an important and complex segment of managing the enterprise, considering the fact that it infl uences all elements or resources, such as planning of the material, human resources, machinery resources, research and development, marketing etc.All of these resources infl uence in multi-criteria optimization of production program.To reduce and improve the decesion making quality, it is important and necessary to evaluate them to minimize the risk of operating losses.
In investigations carried out to date the production program optimization was based on multicriteria approach using linear functions [01,09].Using nonlinear functions in multi-objective optimization enables the application of genetic algorithms and is a step forward in the analysis of the product optimal quantities to maximize production resources utilization [06,10,07].On the other hand, economic calculation of the product cost price is a complex procedure, so that the analysis of optimal production program most commonly employed direct costs to determine the cost price and to defi ne the cost function.However, cost functions based only on product variable costs cannot provide real optimal product quantities but are more suitable for ranking products that should be given priority in manufacturing.Introducing overhead costs in the function of cost price is a complex calculation procedure most often diffi cult to understand by the user in a concrete enterprise, considering that it is not easy to classify individual expenses.It is thought that in metalworking companies, roughly assessing, direct costs account for about 60% of total unit costs, while the share of overhead costs is 40% [03].
In business of enterprises, there are several categories of risk: risk of equipment failure (estimated in relation to human safety, to evironment, to business losses, ect.), risk management as a security measure, fi nacial risk assessment in cases of loan approval, quality management risk, ect.Generally, Enterprise Risk Management is relatively new concept, Fraser and Simskins [05] distinguish following risk categories: Shareholder  The risk is defi ned as product of probability and consequence of certain events, which can be expressed in formula: R = P*Q P -Probability a particular event.
Q -Consequences of particular event.
For any enterprises, there are external and internal of n-sources of risk.The total risk will represented by high-risk, medium-risk and low-risk sources of operating losses.The based approach of applying risk are risk identifi cation -what can affect the implementation of production program, risk analysis -defi ning the probability of occurrence of that, and risk assessment -determining the consequences, expressed in the form of operating losses.The most low-risk sources of operating losses refer to good quality decision.Figure 2 shows the map for identifying Business risks.
Glover at all [9] states that the most real life optimization and scheduling problems are too complex to be solved completely and that the complexity of real life problems often exceeds the ability of classic methods.Miettinen [08] considered that a key challenge in the real-life design is to simultaneously optimize different objectives through taking into account different criteria low cost, manufacturability, long life and good performance, which cannot be satisfi ed at the same time.
Profi t maximization is the main objective of business enterprises and as such the subject of numerous investigations.Profi t is defi ned as the difference between the total revenue generated by selling products on the market and the overall costs, i.e.:

P = TR -TC
Where: P -Total profi t TR -Total revenue TC -Total cost When analyzing the possibilities of profi t maximization, it is important to consider the fl uctuation of the TR and the TC.The TR depends on supply and market demands for particular types of goods, while the TC depends on different constraints faced by the company, such as the mechanical facilities, number and structure of employees, possibility of providing necessary specifi c materials for the manufacturing process implementation, delivery etc.For the company, to be competitive on the market means to produce a product at an appropriate price and quantity with the use of capital and labor in the appropriate volume and costs.Therefore, profi t maximization refers to the optimization of variable parameters in the observed model, with given production constraints. Where: In real life, the functions of dependence of production quantity and the TR and the TC are nonlinear.The maximum profi t is the maximum difference between the total profi t curve and the total cost curve, as represented in the Figure 3. Where: 149 Dr Mirjana Misita -A combining genetic learning algorithm and risk matrix model using in optimal production program , 232

METHODOLOGY
Methodological steps in developing model for risk management integration methodology and GA is shown on Figure 3.The functions of criteria for profi t maximization will have the form:   From the Pareto front diagram, it is evident that optimum solution for production quantity and profi t maximization under given constraints is a set [2312; 219; 944], where the maximum profi t is 5,950,340 RSD calculated as max (f1-f2).
After getting the optimum solution, the second step is Identify and analysis of risk sources for the observed optimum product program.In our case, we have focused on the internal resources only.Identifi cation, evaluations, and determination of trend are shown in the table 2.
This fi gure 5 shows a two-dimension risk map.The vertical axis represents loss likelihood and the horizontal axis represents loss impact.The four quarter panels stand for different combinations of likelihood and impact.Risk matrix indicates a small number of highrisky, a small number of low-risk risk sources, but the largest number risk sources with medium probability and consequences for business losses, namely: Over all research results indicate that at these restrict conditions of production, there is comparatively high risk of production losses.Therefore, it is necessary to resolve our problem to fi nd another optimal solution and repeat analysis until achieved an optimal production program.

CONCLUSIONS
A strong and cabable model of genatic algorithim combinding with risk mamagement mtrix is intrduced and developed to get optimal production program and increase the quality of decisions.
Applying genatic algorithm as a technique deals with huge confl ect constrains to create one or altrenative optimal solusions.On ther hand, applying risk mamagement mtrix for choice of optimal production program reduces the risk of operating losses and affects the effi ciency of management.Furthermore, qualitative aspects that are defi ned trough risk sources and by its identifi cation and evaluation, more realistic production program evaluation can be taking into account.Integrated both of them, genetic algorithim and risk mamagement mtrix guide to optimal production program.
value risk, Financial reporting risk, Governance risk, Customer and market risk, Operations risk, Innovation risk, Brand risk, Partnering risk, Communications risk.Risk management consisit of strategic risk, operational risk, fi nancial risk and risk acceptance.Strategic risk deal with competition, market position and economic conditions.Operational risk daily operations, precisely, to the consequences of daily decisions made in the company.The fi nancial risks are related to relations with banks and stockholders, etc.The types of risk and process steps itroduced by Risk Management Committee 2003 [11].

Figure 2 :
Figure 2: Graphic representation of profi t maximizationIn real enterprise's operating conditions the functions of the TR and the TC are nonlinear and to determine them two different approaches must be applied.The TR function consists of the sum of variable and fi xed costs, therefore, the sum of linear mathematical form by applying the Lagrange interpolation polynomial based on the values of variable costs from the previous period.It is possible to determine the nonlinear function of fi xed costs in a Lagrange interpolation polynomial is, in our case, a function of production quantity P (Q) with ≤(n-1) level if we have n data points on the value of costs from the previous period.

Figure 3 :
Figure 3: Steps in developing model for risk management integration methodology and GA we consider the production capacity as a key constraint in the production quantity of some products, temporarily ignoring the structure of demand for mentioned products on the market, the restrictions are: ***Employees and raw material in the observed company are not of limiting character.The Pareto front and values of the functions f1 and Figure 1 are shown in Figure 4.

Figure 4 :
Figure 4: The Pareto front of optimum solution

Figure 5 :
Figure 5: A Two-Dimensional Risk Map

Table 2 :
Evaluation of risk sources and determination of trend