The problem of scheduling n jobs with a single machine where each job has a differentiable cost function and the total cost being minimized is studied. A heuristic solution procedure is proposed. The algorithm is also applicable when the cost functions are piecewise differentiable. Running time of the algorithm is O(n2). The effectiveness of the algorithm is evaluated and is shown that in many cases the algorithm picks an optimal order. The algorithm proposed here empirically is compared with linearized algorithm by Fisher and Kreiger.
