LP relaxation of the two dimensional knapsack problem with box and GUB constraints

In the present paper we derive an O(n² log n) algorithm for the linear programming (LP) relaxation of the two dimensional knapsack problem with box and generalized upper bound (GUB) constraints. The two dimensional linear knapsack problem with box constraints and GUBs generalizes the multiple choice linear knapsack problem considered by Dyer and others. The problem arose in an application in a steel tube rolling mill in India.