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Proceeding of the 4 rd International Symposium“NEW RESEARCH IN BIOTECHNOLOGY” USAMV Bucharest, Romania, 20112. MATERIALS AND METHODSWe will try to apply the mathematical optimization for two refrigeration processes,in order to improve product quality and increase food safety. We used for this, the studiesindicated in references with [2] and [4].The first problem that we want to optimize applying mathematical modeling is "howto completely thaw blocks of meat in a given time while minimizing surface temperature inorder to minimize microbial growth, by varying the air temperature in a suitable way ", alsoknowing that when the air temperature is too high, the surface will heat up and increase thenumber of microbes, while if it is too low the centre will not thaw in time.The second problem that what we study is "beef carcass chilling optimization." Wewant to model a system of temperature, given the constraints and maximizing thetenderness of the loin muscle and reducing microbial growth rate.Before presenting solutions, we see that we have analyzed a phenomenon occurringin certain variables (air temperature at the surface and the center block of meat) andrestrictions (increasing the number of microbes to be minimal), that have the general data ofa problem optimization. It is necessary to introduce some features of mathematicalmodeling and optimization that we subsequently apply the above mentioned problems. Weused in this order [1], [3] and [7].2.1. The mathematical modelingThe mathematical modeling has an important role in modern scientific research. Inconstruction of a mathematical model, those characteristics of the object modeling arehighlight on one hand and on the other hand for the informative characteristics we considerthe mathematical formalization. The mathematical model is a mathematical relationshipdescribing the essential properties of the original. So, solving a real problem can be reducedto solving a mathematical problem.The general mathematical modeling steps are formulation of the problem,developing a model, computer experimentation (simulation) and analysis of modelingresults (satisfactory or unsatisfactory).Depending on the sizes involved in models, they can be deterministic (the precisesize value) or stochastic (a part of all sizes take random values, for example occurs intemperature, humidity, etc.).The stochastic modeling is a relatively new branch in mathematical programming, inwhich the results and methods of deterministic programming and the theory of probabilityare used. The stochastic programming aims to study the problems of determining the bestdecision possible solutions when the crowd is not completely known (in the deterministicsense) but predictable, due to the presence of random factors specified, and the objectivefunction is a function defined on the set of random possible solutions [5]. In such problemsit is considered as random factors involved in defining possible solutions crowd and theobjective function (status parameters) to form a single multi-dimensional random variable,whose distribution law is unknown. An important feature of stochastic methods is that theytend to imitate natural phenomena.106
Proceeding of the 4 rd International Symposium“NEW RESEARCH IN BIOTECHNOLOGY” USAMV Bucharest, Romania, 2011There are two principles in addressing stochastic programming:a) the principle of "wait and see" is intended that the knowledge of probabilisticinformation about n-dimensional random vector, and distribution function, or somemoments (mean, variance), stochastic problem is then treated as a deterministic problem,characterized by a probability distribution.b) The 'here and now "means choosing a solution from the set of possible solutions thatmeet a certain criterion of optimality, before studying random variables involved in theproblem.2.2. General formulation of optimization problemsThe optimization process is divided in three stages:- Problem definition, in which one define the system (process) to be optimized, thevariables that can be changed, the objective function to calculate the minimum ormaximum, and limitations to be observed;- Construction of a mathematical model to be used to calculate the objective function;- Choosing of mathematical methods for finding the minimum or maximum objectivefunction.2.2.1. Problem definitionThe objective function is what we seek to maximize or minimize. This is usually aneconomic function (e.g.: energy consumption, equipment size, production costs, capitalcosts, total cost, the duration of the recovery of money or the internal rate of return) or noneconomic(safety and reliability, product quality or dependence work or often acombination of these factors, weighted in some way reflecting our priorities). Often, thegoal is to minimize costs, therefore the objective function is called the "cost".The variables can be modeled - design variables such as number, size and structuretypes of equipment or plants, or operational variables such as freezers and coolersprogramming, how to rotate refrigeration compressors or number of laps in a day. Thevariables can also be classified as continuous variables (or simple) and structural variables.The former tend to be more easily optimized, while structural variables (those which cannotconveniently be made in figures) are the most difficult to represent mathematically andtherefore most uncomfortable for optimization.The constrains of optimization problems are: physical (laws of conservation ofenergy or materials, laws of thermodynamics), economical (capital available, the rate ofreturn or recovery time), technological (materials and technology available), and others arelegal and sociological.Basically a mathematical optimization problem (linear or nonlinear programming) isto determinate maximum or minimum (optimum) of a function that depends on certainvariables, that respect the restrictions given.2.2.2. Construction of a mathematical modelThe optimization process is performed on a mathematical model. It must establish aset of equations that expect the objective function (cost) and a set of variable valuestogether with a method of solving these equations. The equations are generally solved by anumerical procedure.107
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