Problem Solving by using Quantitative Models and

Computers

?A real-world problem

Understand Problem thoroughly

Select an appropriate model

Formulate the problem into the model

Input into computer in a way that computer can understand

Scrutinize and interpret the computer result

Solve

Result

1 2 3

456

78

Sensitivity Analysis

9

Understanding Problem

• Step 2, understanding problem thoroughly:– Objective,– Conditions and restrictions,– Data needed,– What the result is like.

Formulate Problem

• Step 4, Formulate the problem into the selected model– Re-describe the problem in terms of the

model• In LP, objective function and constraints• In transportation model, sources and destinations.

Input into Computer

• Step 5, Input the problem into computer in a way that computer understands– Select software package for solving the model

(QM or Excel, for example)– Input the data into the proper model following

the data format.

Work with Results

• Step 8, Scrutinize and interpret the result from computer– Understand the output of computer.– Observe the result to see whether it is

reasonable, whether it makes sense.– Interpret the result from managerial point of

view.

Sensitivity Analysis

• Sensitivity analysis is to see how possible changes of parameters in the model would impact on the optimal solution.

Additional Restrictions

• Additional restrictions can be dealt with before or after the computer solves the problem.– Before. Re-formulate the model to

incorporate the additional restrictions.– After. Modify the computer result to reflect the

additional restrictions.

Manipulations

• The real-world problem usually does not fit a model perfectly, where manipulations are needed.– Manipulation is handling some conditions or

parameters in indirect but equivalent ways.– Examples:

• Prohibited route in the transportation model• Solving assignment problem by using

transportation model