In this paper, a production scheduling model with constraint resources and parallel machines has been investigated. This problem is proposed as a multi-product production problem. Shortage is not allowed and the production horizon is indefinite. The objective is to maximize the level of resource usage and support the management’s standpoint (delays reduction). In this paper, this problem is modeled as the popular Knapsack problem in 0 and 1 programming. Then due to being NP-hard type for this kind of problems to obtain an optimal solution, A heuristic approach has been used to obtain the acceptable solution. By using the branch-and bound method, a near optimal solution is provided. Finally, resultant solutions by the proposed approach have been compared with the optimal solutions of some real-world problems and it has been observed that deviation from the optimal solution is negligible that indicates the accuracy of the proposed approach.