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In this paper, a reformulation that was proposed for a knapsack problem has been extended to single and bi-objective linear integer programs. A further reformulation by adding an upper bound constraint for a knapsack problem is also proposed and extended to the bi-objective case. These reformulations significantly reduce the number of branch and bound iterations with respect to these models. Numerical illustrations have been presented and computational experiments have been carried out todoi:10.33889/ijmems.2019.4.5-090 fatcat:yvz5vxlo2zdobpl2kar64themy