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 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