Question

(a) What are the different types of spreadsheet modeling? Give a real world example for each type where spreadsheet modeling and analysis is useful.

(b) What is an infeasible linear optimization problem? How do we find if a given linear optimization problem is infeasible? Give a real world example of an infeasible linear optimization problem.

Answer 1

Answer:

Ans a)

Spreadsheet modelling means : Computer models of mathematical data, such as budgets which are usually done using a spreadsheet application that processes and performs calculations on the data entered by the user.

Distinct types of spreadsheets are defined by their format. For example, Microsoft Excel has three options for spreadsheet format: Simple tables, Excel tables and Pivot tables.

Simple spreadsheets are the most commonly used type, and you have to make most changes manually. For example, if you set up a simple table and want to refer to the table as a whole in a formula or instruction, you need to define border columns and rows and make sure any additional data is added between those cells.

The most distinct type of spreadsheet, though, is the Pivot table. This looks similar to a normal table, but each column has a drop-down menu you can use to filter or sort the results to suit your needs. For example, if you have a spreadsheet table listing sales volumes by product, you can easily sort the table from most sales to least. You can also filter results so that you only see one type of product – say, cell phones – by checking a box beside each eligible product.

Spreadsheets are used in

1) Financial Tracking: they allow the clear presentation of expenditures and incomes related to different departments and can be set up to display negative numbers in red. Templates for budget spreadsheets are included with spreadsheet programs to reduce the amount of setup work required.

2) Research Work/ Data Analysis and Statistics: For example, applying a formula to hundreds of data points would be a tedious, time-consuming process without some form of automation, and programs like Microsoft Excel offer just this capability.

3)Graphing and Presenting Data: Spreadsheet programs are valuable tools when you're looking to present data in the form of graphs or tables. The spreadsheet itself contains the data to be included on the graph, and spreadsheet programs have many types of graphs built in.

Ans b)

A problem is said to be infeasible if no solution exists which satisfies all the constraints. The FICO Xpress Optimizer provides functionality for diagnosing the cause of infeasibility in the user's problem.

Before we discuss the infeasibility diagnostics of the Optimizer we will, firstly, define some types of infeasibility in terms of the type of problem it relates to and how the infeasibility is detected by the Optimizer.

We will consider two basic types of infeasibility. The first we will call continuous infeasibility and the second discrete or integer infeasibility. Continuous infeasibility is where a non–MIP problem is infeasible. In this case the feasible region defined by the intersecting constraints is empty. Discrete or integer infeasibility is where a MIP problem has a feasible relaxation (note that a relaxation of a MIP is the problem we get when we drop the discreteness requirement on the variables) but the feasible region of the relaxation contains no solution that satisfies the discreteness requirement.

Either type of infeasibility can be detected at the presolve phase of an optimization run. Presolve is the analysis and processing of the problem before the problem is run through the optimization algorithm. If continuous infeasibility is not detected in presolve then the optimization algorithm will detect the infeasibility. If integer infeasibility is not detected in presolve then, in the rare occasion where this happens, a branch and bound search will be necessary to detect the infeasibility.

Example:Diagnosis in Presolve

The presolve processing, if activated, provides a variety of checks for infeasibility. When presolve detects infeasibility, it is possible to "trace" back the implications that determined an inconsistency and identify a particular cause. This diagnosis is carried out whenever the control parameterTRACE is set to 1 before the optimization routine

XPRSlpoptimize (LPOPTIMIZE) is called. In such a situation, the cause of the infeasibility is then reported as part of the output from the optimization routine.

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