Systems approach in civil engineering

Simulation : Stochastic Programming  DEFINITION Simulation is a representation of reality through the use of model or other device, which will react in the same manner as reality under a given set of conditions. CLASSIFICATION OF SIMULATION MODELS Simulation models are classified as: (a) Simulation of Deterministic models: In the case of these models, the input and output variables are not permitted to be random variables and models are described by exact functional relationship. (b) Simulation of Probabilistic models: In such cases method of random sampling is used. The techniques used for solving these models are termed as Monte-Carlo technique. (c) Simulation of Static Models: These models do not take variable time into consideration. (d) Simulation of Dynamic Models: These models deal with time varying interaction. ADVANTAGES OF SIMULATION Simulation is a widely accepted technique of operations research due to the following reasons: *

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Seqencing: Stochastic programming  let us look to a problem, where we have to determine the order or sequence in which the jobs are to be processed through machines so as to minimize the total processing time. Here the total effectiveness, which may be the time or cost that is to be minimized is the function of the order of sequence. Such type of problem is known as SEQUENCING PROBLEM. In case there are three or four jobs are to be processed on two machines, it may be done by trial and error method to decide the optimal sequence (i.e. by method of enumeration). In the method of enumeration for each sequence, we calculate the total time or cost and search for that sequence, which consumes the minimum time and select that sequence. This is possible when we have small number of jobs and machines. But if the number of jobs and machines increases, then the problem becomes complicated. It cannot be done by method of enumeration. Consider a problem, where we have ‘n‘ machines and ‘m’

Transportation Model and it's variants  The transportation model deals with a special class of linear programming problem in which the objective is to transport a homogeneous commodity from various origins or factories to different destinations or markets at a total minimum cost. To understand the problem more clearly, let us take an example and discuss the rationale of transportation problem. Three factories A, B and C manufactures sugar and are located in different regions. Factory A manufactures, b1 tons of sugar per year and B manufactures b2 tons of sugar per year and C manufactures b3 tons of sugar. The sugar is required by four markets W, X, Y and Z. The requirement of the four markets is as follows: Demand for sugar in Markets W, X, Yand Z is d1, d2, d3 and d4 tons respectively. The transportation cost of one ton of sugar from each factory to market is given in the matrix below. The objective is to transport sugar from factories to the markets at a minimum total tran

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