Problem statement: One-Dimensional Cutting Stock Problem with discrete demands and capacitated planning objective is an NP hard problem. Objectives: The objectives of this study are 1) to propose a mathematical programming with column-generation technique for solving the stochastic one-dimensional cutting stock problem with discrete random demands, 2) to propose a heuristic for solving the stochastic one-dimensional cutting stock problem with discrete random demands, and 3) comparing two algorithms in computation times, and upperbound value. Approach: The mathematical model with column generation technique by a branch-and-bound procedure and the heuristic based on the first fit decreasing method are proposed. Then, both approaches were compared and some characteristics were investigated such as upperbound value, percentage above lowerbound value, computation time, and number of patterns. Results: The 24 instances were examined. The proposed heuristic provides the upperbound value above the lowerbound around 0-13.16%. All upperbound values from column-generation and integer programming are better than the proposed heuristic but all computation times are higher. Conclusion: The proposed heuristic has consistently high performance in computation times. This particular information is worth for making decision to closely meet the appropriate planning of the One-Dimensional Cutting Stock problem with discrete demands. Next research: A heuristic on random fit decreasing method is interested to study in next step