Optimization Method Xi Chen Department of Management Science and Engineering International Business School Beijing Foreign Studies University 4口48+4三4至，至)只0 Xi Chen (chenxi0109@bfsu.edu.cn) Optimization Method 1/41
Optimization Method Xi Chen Department of Management Science and Engineering International Business School Beijing Foreign Studies University Xi Chen (chenxi0109@bfsu.edu.cn) Optimization Method 1 / 41
General Procedure General Procedure Modeling ③Solution Approach Linear Programming o Sensitivity Analysis Duality Theory o Commercial Softwares o Integer Programming Dynamic Programming o Game Theory OLTEX 4口4+4三4至，至)只0 Xi Chen (chenxi0109@bfsu.edu.cn) Optimization Method 2/41
General Procedure 1 General Procedure 2 Modeling 3 Solution Approach Linear Programming Sensitivity Analysis Duality Theory Commercial Softwares Integer Programming Dynamic Programming Game Theory 4 LATEX Xi Chen (chenxi0109@bfsu.edu.cn) Optimization Method 2 / 41
General Procedure o Problem Description 。Modeling ●Solution Approach o Computational Experiments and Analysis 4口40+4三4至，至)只0 Xi Chen (chenxi0109@bfsu.edu.cn) Optimization Method 3/41
General Procedure Problem Description Modeling Solution Approach Computational Experiments and Analysis Xi Chen (chenxi0109@bfsu.edu.cn) Optimization Method 3 / 41
Modeling General Procedure Modeling Solution Approach Linear Programming o Sensitivity Analysis Duality Theory o Commercial Softwares o Integer Programming Dynamic Programming o Game Theory OLTEX 4口4+4三4至，至)只0 Xi Chen (chenxi0109@bfsu.edu.cn) Optimization Method 4/41
Modeling 1 General Procedure 2 Modeling 3 Solution Approach Linear Programming Sensitivity Analysis Duality Theory Commercial Softwares Integer Programming Dynamic Programming Game Theory 4 LATEX Xi Chen (chenxi0109@bfsu.edu.cn) Optimization Method 4 / 41
Modeling Example 1 Giapetto's Woodcarving,Inc.,manufactures two types of wooden toys: soldiers and trains.Demand for trains is unlimited,but at most 40 soldiers are bought each week. A soldier sells for $27 and uses $10 worth of raw materials.Each soldier that is manufactured increases Giapetto's variable labor and overhead costs by $14.A train sells for $21 and uses $9 worth of raw materials.Each train built increases Giapetto's variable labor and overhead costs by $10. The manufacture of wooden soldiers and trains requires two types of skilled labor:carpentry and finishing.A soldier requires 2 hours of finishing labor and 1 hour of carpentry labor.A train requires 1 hour of finishing and 1 hour of carpentry labor.Each week,Giapetto can obtain all the needed raw material but only 100 finishing hours and 80 carpentry hours. How to maximize Giapetto's weekly profit? Xi Chen (chenxi0109@bfsu.edu.cn) Optimization Method 5/41
Modeling Example 1 Giapetto’s Woodcarving, Inc., manufactures two types of wooden toys: soldiers and trains. Demand for trains is unlimited, but at most 40 soldiers are bought each week. A soldier sells for $27 and uses $10 worth of raw materials. Each soldier that is manufactured increases Giapetto’s variable labor and overhead costs by $14. A train sells for $21 and uses $9 worth of raw materials. Each train built increases Giapetto’s variable labor and overhead costs by $10. The manufacture of wooden soldiers and trains requires two types of skilled labor: carpentry and finishing. A soldier requires 2 hours of finishing labor and 1 hour of carpentry labor. A train requires 1 hour of finishing and 1 hour of carpentry labor. Each week, Giapetto can obtain all the needed raw material but only 100 finishing hours and 80 carpentry hours. How to maximize Giapetto’s weekly profit? Xi Chen (chenxi0109@bfsu.edu.cn) Optimization Method 5 / 41