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

The paper considers the problem of producing and transporting a unqiue product directly from an origin (e.g., a production plant) to a destination (e.g., its retail outlet) where demands are stochastic and follow a known probability distribution. It first derives the expected profit per unit produced and shipped as a function of the production rate and shipment size for a general demand distribution. Then, an iterative procedure is designed to obtain the optimal production/shipping policies by exploiting the concavity of the expected profit function on the production rate for the Uniform demand distribution case. Monte Carlo experiments and sensitivity analyses are also performed to validate the model and give further insights into the effect of changes in parameter values on the optimal policies and the expected profit function. This research extends the classic Newsboy Model by combining the production and logistical decision into an integrated framework, and provides optimal production/ shipping policies for profit-oriented organizations that own both the production and retail entities and face demand uncertainties.