Newsvendor equations for production networks

Abstract We consider production networks with stochastic activity leadtimes. When activities finish early holding costs are incurred and when end products are delivered late penalty costs are incurred. Objective is to find the activity start and finish times that minimize the total cost. We introduce the concept of a tardy path and derive the optimality equations for each node in the network. We show that under the optimal solution, for a set of nodes the tardiness probability satisfies the Newsvendor equations.