Determining profit-maximizing production/shipping policies in a one-to-one direct shipping, stochastic demand environment

The problem of manufacturing and shipping a product from an origin to a destination facing stochastic demands with a known probability distribution is considered. The production rate and shipment size are treated as decision variables. Profit per unit produced is derived as a function of the production rate and shipment size. An iterative methodology is developed based on the concavity of the profit function on the production rate for the uniform demand distribution case to generate the optimum production/shipping policy. These assumptions are tested via Monte Carlo experiments.