Efficient near-optimal procedures for some inventory models with backorders-lost sales mixture and controllable lead time, under continuous or periodic review

This paper considers a number of inventory models with backorders-lost sales mixture, stockout costs, and controllable lead time. The lead time is a linear function of the lot size and includes a constant term that is made of several components. These lot-size-independent components are assumed to be controllable. Both single- and double-echelon inventory systems, under periodic or continuous review, are considered. To authors knowledge, these models have never been previously studied in literature. The purpose of this paper is to analyse and optimise these novel inventory models. The optimisation is carried out by means of heuristics that work on an ad hoc approximation of the cost functions. This peculiarity permits to exploit closed-form expressions that make the optimisation procedure simpler and more readily applicable in practice than standard approaches. Finally, numerical experiments investigate the efficiency of the proposed heuristics and the sensitivity of the developed models.