Review of stochastic cost functions for production and inventory control


We review a dozen cost functions that could be used to assign capacity related costs to a stochastic production rate. These cost functions compose of linear, step-wise and quadratic components. We assume demand is a normally distributed random variable. In some of the cases we are able to completely characterise the cost function and optimise the decision variables to minimise the defined cost function. In one instance there are no endogenous variables, so there is nothing to optimise. In all of the other cases we obtain insights into the convexity and limit behaviour of the cost function. This allows us to gain knowledge of the number of minimums and, in some cases, upper and lower bounds on optimal parameter setting and costs incurred.

Pre-prints of the 17th International Working Seminar of Production Economics, Innsbruck, Austria, February 20th – 24th, Volume 1, 117-128