A mixed integer linear programming model applied in barge planning for Omya

This article presents a mathematical model for barge transport planning on the river Rhine, which is part of a decision support system (DSS) recently taken into use by the Swiss company Omya. The system is operated by Omya's regional office in Cologne, Germany, responsible for distribution planning at the regional distribution center (RDC) in Moerdijk, the Netherlands. The distribution planning is a vital part of supply chain management of Omya's production of Norwegian high quality calcium carbonate slurry, supplied to European paper manufacturers. The DSS operates within a vendor managed inventory (VMI) setting, where the customer inventories are monitored by Omya, who decides upon the refilling days and quantities delivered by barges. The barge planning problem falls into the category of inventory routing problems (IRP) and is further characterized with multiple products, heterogeneous fleet with availability restrictions (the fleet is owned by third party), vehicle compartments, dependency of barge capacity on water-level, multiple customer visits, bounded customer inventories and rolling planning horizon. There are additional modelling details which had to be considered to make it possible to employ the model in practice at a sufficient level of detail. To the best of our knowledge, we have not been able to find similar models covering all these aspects in barge planning. This article presents the developed mixed-integer programming model and discusses practical experience with its solution. Briefly, it also puts the model into the context of the entire business case of value chain optimization in Omya.