Basics of inventory management (Part 4: The (s,S)-model)

Inventory Models;management science

Basics of inventory management (Part 6: The (R,s,S)-model)

Inventory Models;management science

Basics of inventory management (Part 5: The (R,b,Q)-model)

Inventory Models;management science

Comparison of supply chain planning concepts for general multi-item, multi-echelon systems

In this paper we present two alternative concepts to control general multi-item, multi-echelon systems under stochastic stationary demand for end items. Such systems consist of items that are assembled from other items and in turn are assembled into other items. Each assembly process involves a planned lead time. For such systems optimal control policies are unknown to-date. Therefore we resort to control concepts that at least enable an exact computation of the control parameters. The two alternative concepts represent two fundamentally different modeling concepts: an LP-based concept representing application of deterministic mathematical programming models in a rolling schedule context (the common practice in so-called Advanced Planning Systems), and modified base stock policies representing application of classical multi-echelon inventory models. The parameters of the LP-based concept can be detennined by discrete event simulation. The parameters of the modified base stock policies can be determined analytically. We compare the two concepts based on the required supply chain capital investment required to guarantee target end item service levels. Surprisingly, the modified base stock policies outperform the LP-based concept. We provide managerial insights as well as a deeper understanding into a number of fundamental issues related to supply chain planning and supply chain design

Stock control in practice: about incorrect formulas, infeasible solutions, and mathematics on quicksand

We introduce the concept of material coordination and formulate a basic model for this. That basic model makes it possible to formulate the objective of material coordination, and to indicate the mathematical hurdles to be overcome. The essence of these hurdles are the stochastic processes we face. Even for simple stock control situations, exact methods are already numerically complex and therefore time-intensive. This still makes large-scale application difficult, even though computers are getting faster and faster. We discuss the typical "short-cuts" that are currently used within the so-called Enterprise Resource Planning (ERP) systems, which are used at almost every company. Here the wrong formulas and infeasible solutions pop up. These have implications for the daily work of planners, schedulers and managers. We argue that there are essentially solutions available, which have been over for quite some time, but are still not commonplace. Next, we discuss a number of laws that are of use when looking for new results. And finally, the mathematical challenges that are worth exploring further