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|PROGRAM||MASTER of business administration (MBA)|
|course CODE & NAME||DOMS304– APPLICATIONS OFOPERATIONS RESEARCH|
|nUMBER OF ASSIGNMENTS & Marks||02
30 Marks each
Assignment Set – 1
- Solve the given LPP using Big-M method:
Maximize Z = x1 + 2×2 +3×3-x4
Subject to: x1 + 2×2+3×3 = 15
2×1 + x2 + 5×3 = 20
x1 + 2×2+ x3 + x4 = 10
x1, x2, x3, x4 ≥ 0
The Big M method is a version of the Simplex Algorithm that first finds a feasible solution by adding artificial variables to the problem.
Maximize Z = x1 + 2×2 +3×3-x4
- x1 + 2×2 + 3×3 = 15
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2(a) What is Linear Programming Problem? Write its Assumptions and limitations.
Linear Programming Problem
Linear Programming (LP) is a mathematical method used to determine the best outcome or solution from a given set of requirements or constraints. The “linear” part comes from the fact that the problems are described using linear relationships. These problems involve optimizing (maximizing or minimizing) a linear objective function, subject to a set of linear equality or
2(b) Write in brief about the Sensitivity analysis.
Sensitivity analysis is a model model more leaning on financial side that determines how target variables are affected based on changes in input variables. It is a popular way to predict the outcome of a decision given a certain range of variables in the set of data analysis.
Now the question can be connected with operational efficiency which leans on Quality-Cost-
Assignment Set – 2
- What do you mean by Dynamic programming problem? Use Dynamic programming approach to solve the following problem:
Minimize Z = y12 + y22 + y32
Subject to constraints: y1 + y2 + y3 ≥ 15 and y1, y2, y3 ≥ 0
Dynamic programming is a method for solving complex problems by breaking them down into simpler subproblems. It is applicable to problems exhibiting the properties of overlapping subproblems and optimal substructure (described below).
- Overlapping subproblems: This means that subproblems may re-occur multiple times. Hence, the computations of these recurring subproblems can be stored and reused, leading to significant computational savings.
- Optimal substructure: This means that an optimal solution to the problem can be obtained by using optimal solutions to its subproblems.
- Solve the following integer programming problem using Gomory’s cutting plane method:
Maximize Z = 4×1 + 3×2
Subject to: x1 + 2×2 ≤ 4
2×1 + x2 ≤ 6
and x1, x2 are non-negative integers
Before we start, it’s important to note that the Gomory’s cutting plane method is for Integer Programming (IP) problems and involves two main steps:
- Solving the problem as a linear programming problem, i.e., without the integer restriction.
- Then, we add Gomory’s cutting planes to the LP relaxation in order to find an integer solution.
- Write short notes on the following:
- i) Quadratic Programming problem
- ii) Simulation Annealing Method
- i) Quadratic Programming Problem
Quadratic Programming (QP) is a specialized type of mathematical optimization problem, which falls under the broader category of nonlinear programming. As the name suggests, a quadratic programming problem involves the minimization or maximization of a quadratic function, subject to linear