Branch-and-bound approach for a stochastic production planning problem with capacity constraints

A stochastic production planning problem with a finite number of planning periods is analyzed where cumulative demands up to each period are independent random variables with continuous probability distributions. In the problem, backlogging is permitted and production is restricted by its capacity. Dynamic but linear costs of inventory holding and backlogging, and of production with setup charge are considered. A branch-and-bound algorithm is developed to find an optimal plan within finite searching steps, and its computational effectiveness is evaluated.