Production Planning under Uncertain Demands and Yields

The periodic demands of a single product are forecasted and given by a distribution function for each period. The product can be manufactured in n plants with heterogeneous characters. Each plant has its specific stochastic production capability. The expected capability and the standard deviation of each plant can be increased by allocation of additional budgets. The problem is to determine the total budget needed and its distribution among the n plants in order to ensure a complete fulfillment of the demands according to the due dates and the pre-given confidence levels.