Food-Processing-Plant-Design-layout

Food Processing Plant Design & layout
mathematical analysis. Whereas PERT (statistical tool) is designed to analyse and
represent the tasks involved in completing a given project.
Game Theory (Competitive Models).It is a study of strategic decision making.
Specifically, it is "the study of mathematical models of conflict and cooperation
between intelligent rational decision-makers". It has been used to study a wide
variety of human and animal behaviours. It was initially developed in economics to
understand a large collection of economic behaviours, including behaviours of firms,
markets, and consumers.
14.4 Introduction to linear programming:
Linear programming is one of the commonly used operations research techniques. It has its
early use for military applications but now employed widely for various business/industry
problems.
Definition: Linear programming is a mathematical technique for the purpose of allocating
the limited resources in an optimum manner (i.e., either maximum or minimum) to achieve
the objectives of the business, which may be maximum overall profit or minimum overall
cost. The word "linear" means that the relationships handled are those which can be
represented by straight lines, i.e., the relationships are of the form y = ax + b and the word
"programming" means "taking decisions systematically".
In other words, linear programming is the optimization (either maximization or
minimization) of a linear function of variables subject to constraint of linear inequalities.
Thus, linear programming involves the planning of activities to obtain an "optimal"
result i.e., a result that reaches the specified goal best (according to the mathematical model)
among all feasible alternatives.
(i) It attempts to maximize .or minimize a linear function of decision variables.
(ii) The values of the decision variables are selected in such a way that they satisfy a set of
constraints, which are in the form of linear inequality.
Linear programming is based on the following basic concepts:
1. Decision Variables (Activities). Decision variables are the variables whose quantitative
values are to be found from the solution of the model so as to minimize or maximize the
objective function. For example, decision variables in a product mix manufacturing,
represents the quantities of the different products to be manufactured by using its limited
resources, such as men, machines, materials, money etc. The decision variables are usually
denoted by x1, x2,……,xn.
2. Objective Functions. It states the determinants of the quantity either to be maximized or
to be minimized. For instance, profit is a function to be maximized or cost is a function to be
minimized. An objective function must include all the possibilities with profit or cost
coefficient per unit of output. For example, for a firm which produces four different
products A, B, C and D in quantities Q1, Q2, Q3 and Q4 respectively, the objective function
can be stated as:
Minimise C = Q1 C1 + Q2 C2 + Q3 C3 + Q4 C4,
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