This dissertation consolidates previous research on an optimal strategy to reduce the running risk in hedging a long-term supply commitment with short-dated futures contracts. By introducing a cap function, this dissertation defines scenarios of running risk over the hedging horizon. We introduce a linear cap function and wish to find a hedging strategy G with the smallest constant F such that the variance of the cumulative cash flow is less than or equal the multiplication of a cap function and the constant F. The objective is to seek the best function G(s) to cap the variance of cash flow under a given non-negative cap function. We also implement the result in MATLAB by creating a Graphical User Interface application that enables the user to see the various results of the variance of cash flow of the best hedging scenario.