The 0–1 linear knapsack problem with a single continuous variable (KPC) is an extension of the binary knapsack problem (KP). It is an NP‐hard problem. In this paper, we show that KPC can be reduced to KP and a pseudo‐knapsack problem (PKP), which is similar to the traditional knapsack problem except that the profits of items may be non‐positive, and the weight sum has two sided limits on capacity. We use the Dynamic Programming algorithm COMBO (Martello et al., Manag Sci 45(3):414–424, 1999) to solve KP, and modify the branch and bound method EXPKNAP (Pisinger, Eur J Oper Res 87:175–187, 1995) for KP to solve the PKP. Numerical experiments show the efficiency of our method.
