Knapsack constraint reformulation: A new approach that significantly reduces the number of sub-problems in the branch and bound algorithm

The paper presents a new approach to significantly reduce the number of sub-problems required to verify optimality in the branch and bound algorithm. The branch and bound algorithm is used to solve linear integer models and these models have application in areas such as scheduling, resource allocation, transportation, facility allocation and capital budgeting. The single constraint of the knapsack linear integer problem (KLIP) is reformulated in such a way that the number of standard branch and bound sub-problems required to verify optimality is significantly reduced. Computational results of the proposed approach on randomly generated KLIPs are also presented.