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Unit 5: Modeling and Analysis
The most common optimization models can be solved by a variety of mathematical programming Notes
methods, including the following:
Assignment (best matching of objects)
Dynamic programming
Goal programming
Investment (maximizing rate of return)
Linear and integer programming
Network models for planning and scheduling
Non-linear programming
Replacement (capital budgeting)
Simple inventory models (e.g., economic order quantity)
Transportation (minimize cost of shipments)
Self Assessment
Fill in the blanks:
14. ....................... is the best-know technique in family of optimization tools called mathematical
programming in which all relationships among the LP variables are linear.
15. ....................... is a family of tools designed to help solve managerial problems in which the
decision maker must allocate scarce resources among competing activities to optimize a
measurable goal.
Case Study Multi-objectives Mathematical Programming using
“Payoff Technique” for Andhra Pradesh
An Approximation of the Multi-objective Programming Problem
Multi-Objective Programing of vector optimization technique tackle the problem of
simultaneous optimization of several objectives subject to a set of constraints, usually
linear. As an optimum solution is undefined for several simultaneous objectives, MOP
seeks to identify the set that contains efficient (non-dominated or Pareto optimal) solutions.
The elements of this efficient set are feasible solutions such that there are no other feasible
solutions that can achieve the same or better performance for all the objectives and strictly
better for at least one objective.
Given that the purpose of MOP is to generate the efficient set, the general nature of
problem can be stated as:
Eff z(x) – [z (x),z (x)...z (x)]
1
2
q
Subject to: x ∈ F
Where Eff means the search for the efficient solutions (in a minimizing or maximizing
sense) and F represents the feasible set.
Contd....
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