Cash demand for a cash dispensing device is forecasted for individual days, weeks and multi-day load periods. In one embodiment, an expected value of withdrawal for any particular period, as well as an upper limit on expected withdrawals for a given confidence level, are computed. The technique facilitates the creation of a daily and multi-day withdrawal forecast for a given ATM. The forecasts are also used to compute an optimum load amount for a given load period (the period between loading operations) for a given ATM, subject to given parameters (such as courier cost, interest rate, transit time, desired confidence level, cost of run-out, and the like) and given constraints (bundle size, maximum capacity, possible delivery days, and the like). The forecasts are also used to determine an optimal load period length and schedule.