Question

you will find out a real-life problem which can be formulated as a linear programming model. After determining and understanding the problem on hand, you will collect the necessary data and develop the linear programming model. Then, you will solve the proposed mathematical model by using GAMS optimization software. After obtaining the optimal solution, you also need to perform sensitivity analysis on this problem. Finally, you will prepare

a report as described below.

Chapter 1 – Problem Definition

Give the detailed problem definition by explaining the following items:

• Motivation of the study.

• Known parameters of the problem.

• Restrictions of the problem.

• Objective of the study.

• Values that should be determined.

Chapter 2 – Linear Programming Model

Give the details of developed linear programming model by explaining the following items: • Indices

Page 1

• Parameters

• Decision Variables

• Objective Function

• Constraints

• Explain the objective function and constraints by words.

Chapter 3 – Implementation & Results

In this chapter, please give the information related to your input data. Give the values of parameters (table representation is preferred). Give brief information about the optimization software (GAMS) that you are using. Give the optimal results of your problem (table representation is preferred). Optimal solution and optimal values of decision variables should be explained in detail.

Chapter 4 – Scenario Analysis

For the parameters on hand, you should perform sensitivity analysis. You have to perform sensitivity analysis on at least two parameters of the problem.

For example, you can analyze the effect of increase in the cost to the optimal solution (objective function and values of decision variables). For different increase rates (such as %5, %10, %15, %20, %25, etc.), you can run the model and obtain the results for those increased values. Do the necessary comparisons. Please explain all results and comparisons in detail.

Chapter 5 – Conclusion & Suggestions

Please provide a general conclusion of your project. Do not forget to write some recommendations related to the problem you have studied

Answer 1

Now we will formulate the LP

}After all it’s a linear programme!

}Simplex method for LP

}Using Excel Solver