“Multi-echelon inventory theory and practice: some ideas for alignment”
by Ton De Kok
Eindhoven University of Technology
Multi-echelon inventory theory has developed over six decades from concepts like echelon base stock policies to software for “optimizing” real-world supply chains. Multi-echelon inventory theory is a field in which the same problem is modelled differently, whereby optimal solutions may be different. Thus it is important to validate modelling assumptions. We have done so for a large number of real-life cases by using data on Bills of Materials, lead times, mean and average of independent demand for items, mean inventory on-hand, and mean order sizes as inputs, after which we used the model analysis to compute the end-item fill rates or ready rates as outputs. These model service levels we compared with the actual service levels, finding on aggregate level model outputs and actual values were close. This provided solid ground to continue modelling real-world supply chains assuming i.i.d. independent demand for items, constant item lead times, and explicit modelling of material constraints that imply the need for allocation over time of child item availability to parent items.
Though the concept of so-called Synchronized Base Stock policies has been successful in modelling real-world supply chains, many challenges remain, such as multi-sourcing, finite capacity, and integration of forecasting and inventory management. In practice, inventory management is supported by ERP and APS systems that are based on the rolling scheduling principle. As many of the underlying models are MILP formulations, it is feasible to include many types of constraints and options into these models, such as material and capacity availability constraints, and multi-sourcing. However, it is not obvious how to set safety stock parameters that ensure service level targets are met under rolling scheduling.
In this presentation we discuss a number of building blocks that may allow to set safety stock parameters in rolling schedule mode formulations for multi-item multi-echelon inventory systems. These building blocks comprise the so-called _net stock translation property, _the _safety stock adjustment procedure_, and _quadratic programming_.
We discuss the issue of degeneracy of MILP formulations that negatively impacts the performance of such formulations under uncertainty. As the research conducted so far is primarily explorative, we expect that the modelling approach presented is promising for both theoretical and applied research.
Ton de Kok received his PhD from the Free University of Amsterdam in 1985, after which he joined the Philips Electronics Centre for Quantitative Methods (CQM. In 1990, he became Manager Logistics Innovation of Philips and a Certified Fellow in Production and Inventory Management (CFPIM) of the American Production and Inventory Control Society (APICS). In 1991 he was appointed part-time professor in Industrial Mathematics at TU/e and he has been a full time professor Operations Management since 1992. Previously, he was also head of Operations Planning, Accounting, and Control at TU/e.