A first order approach to a class of multi-time-period stochastic programming problems

There are many types of multi-time-period stochastic programming problems. In particular, there are problems where activities in one time period provide inventories or new capacities of uncertain magnitude for use in the next time period. One approach is then to ignore the uncertainties and solve a deterministic model using mean values. A slightly more sophisticated approach is to make first-order corrections to allow for the uncertainty. This paper suggests a strategy for computing such corrections. The problem of implementing this strategy is then studied by considering some very simple examples. These examples suggest that it may be seriously misleading to assume that all the relevant random variables are normally distributed unless the variance is small compared with the mean. This is because in reality the random variables are nonnegative. Fortunately the approach also works if the variables are assumed to have Gamma distributions.