MIP models for production lot sizing problems with distribution costs and cargo arrangement

Abstract

This study presents mixed integer programming (MIP) models for production lot sizing problems with distribution costs using unit load devices such as pallets and containers. Problems that integrate production lot sizing decisions and loading of the products in vehicles (bins) are also modelled, in which constraints such as weight limits, volume restrictions or the value of the cargo loaded in the bins are considered. In general, these problems involve a trade-off between production, inventory and distribution costs. Lot sizing decisions should take into account production capacity and product demand constraints. Distribution decisions are related to the loading and transport of products in unit load devices. The MIP models are solved by the branch-and-cut method of an optimization package and the results show that these approaches have the potential to address different practical situations.

Keywords:

• lot sizing
• distribution costs
• cargo unitization
• bin packing
• integrated problems

Acknowledgements

The authors thank the two anonymous reviewers for their useful comments and suggestions. This research had the financial support of CNPq and FAPESP (Process number 2010/10133-0, 2014/01203-5 and 474782/2013-1).