# Capital Budgeting Problem with Combinatorial Allocation Constraints by Column Generation Method

## Authors

• Rataphol Sangkhasuk Faculty of Industrial Technology, Phranakhon Rajabhat University
• Titirat Vivithkeyoonvong Faculty of Engineering, Thai-Nichi Institute of Technology
• Benchaporn Phuangchampee Faculty of Engineering, Kasetsart University
• Sarintip Anurak Faculty of Science and Industrial Technology, Prince of Songkla University, Surat Thani Campus
• Sahachat Leartsiriphesaj Faculty of Agro-Industry, Kasetsart University
• Peerayuth Charnsetthikul Faculty of Engineering, Kasetsart University

## Keywords:

Capital Budgeting Problem, Combinatorial Allocation, Column-generation, Optimization

## Abstract

This research studied the method to solve the problem of capital allocation in order to reach the optimal profit by Column Generation technique with 3 methodologies; Full model of Linear programming, Row Generation and Column Generation. The study compare between performance and number of projects to do operate in qualities and time. The result showed that the small size of problem solution by Column Generation gave the same answer to the solution by full model of linear programming and Row Generation. The method of Column Generation is supported the solutions that are larger than by Full model of linear programming Row Generation. Due as Column Generation is a method that using variable increment in each column decision. In the other hand, the solution by Full model of linear programming considers to solve every possibility and Row Generation is a method that using constraints increment. Therefore, the processing program which creating Row Generation use more processing resources and resulting in a shorter processing time in the method of Column Generation.

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