On the counterintuitive behaviour of the economic order quantity in the presence of backorders

The basic deterministic stationary inventory problem, in which backorders are allowed, is analyzed. Instead of considering the backorder cost to be a cost per unit and per time, we also suppose the presence of a fixed backorder cost per unit. The latter generates a supplementary dependence of the economic order quantity on the demand, which happens to be of a different polynomial degree in the popular square root formula. Sensitivity analysis with respect to changes in the demand allows us to conclude that for some values of the holding cost, backorder cost, average yearly demand, etc. a counterintuitive behaviour might occur. This behaviour, being the decrease of the economic order quantity incurred by an increase of the demand, is due to the presence of multiple competing (nonlinear) dependencies of the economic order quantity on this demand.