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Techniques of Optimisation and Uses : Assignment

   

Added on  2020-01-23

8 Pages2112 Words108 Views
STUDENT NAME:STUDENT ID:SUBJECT CODE:ASSIGNMENT TITLE: TECHNIQUES OF OPTIMISATION ANDITS USES

TABLE OF CONTENTSFormulating optimization problem in terms of decision variables, constraints and objectivefunction............................................................................................................................................3Stochastic programming problem of demand uncertainty to minimize expected total cost............5Expected value of perfect information............................................................................................5Markowitz’s mean-variance optimization model............................................................................5Imposing restrictions on the maximum number of assets included in a portfolio for monitoringand controlling purposes..................................................................................................................6Dynamic programming model.........................................................................................................6Linear integer programming model.................................................................................................7Reference List..................................................................................................................................82

Formulating optimization problem in terms of decision variables, constraints and objective function.Deterministic optimisation is a division of a numerical optimisation which focuses on findingglobal solution to an optimisation problem while providing theoretical guarantee for it, withsome predefined tolerances. The terms of deterministic optimisation typically refers to acomplete or rigorous optimisation methods. Rigours methods converge to a global optimum in adefinite time frame state are described by mathematical model. In cases of finding a globalminimum of an optimisation problem it is extremely difficult to find a feasible solution.The variables in a linear program are a set of quantities that needs to be determined while solvingthe problem. The problem is solved by the identification of the best values of the variables; suchvariables are called decision variables because the problem is to decide on what value eachvariable should take. Typically, the variables represent the amount of a resource to be used.Defining the variables for the problem is the most crucial step in formulating the problem as alinear program. Here creative variable definition can be used to reduce the size of the problem ormake a non-linear problem linear. The variables are represented in an abstract manner as X1, X2, .. ., Xn . (As there are n variables in this list.)Constrained optimization is the process of optimizing an objective function with respect to somevariables or values in the presence of constraints on those variables or values. In determining theconstraints the constraints can either be hard constraints for which there are set conditions for thevariables which are required to be satisfied, or soft constraints which have some variable valuesthat are penalized in the objective function based on the extent that, the conditions on thevariables are not satisfied (Graham et al. 1979, p.125 ).Objective function of a linear programming model is to maximise or minimise a value. Theobjective function indicates how much each variable contributes to the value that is to beoptimized in the problem. The objective function takes the following general form:WhereCi - the objective function coefficient corresponding to the ith variable, andXi - the ith decision variable.The coefficients of the objective function are to indicate the contribution to the value of theobjective function of one unit of the corresponding variable. As for example, if the objective3

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