Improving Branch-And-Price Algorithms For Solving One Dimensional Cutting

Column Generation is a technique for solving linear programming problems with larger number of variables or columns. This technique was first applied to large real life cutting stock problem by Gilmore and Gomory. Since then several researchers have applied the column generation technique to many real life applications. Subsequently the technique is combined with the standard branch-and-bound method to solve integer programming problems with huge number of variables. This combined method is commonly known as branch-and-price. In this report, we discuss the work undertaken in our project on how to improve the branch-andprice method to solve industrial 1D cutting stock problem which requires integer programming formulation with huge number of columns. In the first stage and the initial part of second stage, we explored the details of branch-and-price method. In the second stage we exprimented to improve one subtask of the branch-and-price. We provide an outline of the next stage of our work.