DFG-SGSM-DP – how can demand propagation be added to safety-stock placement models?

DFG-SGSM-DP: The Stochastic Guaranteed Service Model with Demand Propagation

Project Leader: Prof. Dr. Jörg Rambau
Contact: Prof. Dr. Jörg Rambau

Project start: 2019/10/15 Project end: 2022/10/14

Project team: External partners:

Deutsche Forschungsgemeinschaft (DFG)

Project description:

Application Background

One important aspect of Supply Chain Management is how to distribute stock in a network of inventories. A prominent way of organizing replenishment orders is by the specification of safety stocks (the inventory level up to which we replenish) and reorder points (the inventory level at which an order is triggered). The (Stochastic) Guaranteed Service Model (S)GSM provides a mathematical-programming framework to optimize safety-stock placement in supply chain networks. See also the MODUS project MEIO.

Our main objective in this project is to incorporate explicit demand propagation into the GSM and the SGSM. With this enhancement the following will be possible to model correctly a system where a stock point can decide to choose where to get its supply from. This is important for the GSM and the SGSM, e.g., in the following situations:

  • Outsourcing is a decision option.
  • Lateral transshipments are a decision option.
  • The choice between several regular suppliers in the network is a decision option.

In all these cases, a decision of a policy can influence the demand propagation in the multi-echelon network. Thus, the demand upstream cannot be taken as input data but must be derived from the downstream decision variables of the model. Although a first modeling approach has already been presented (SGSM-DP), it is not clear that the SGSM-DP represents the best possible approach with respect to scalability and generalizablility.

The Lehrstuhl Wirtschaftsmathematik (Prof. Dr. Jörg Rambau) cooperates in this project with Prof. Dr. Stefan Minner (TU München), Prof. Dr. A.G. de Kok (TU Eindhoven, The Netherlands), and Dr. Konrad Schade (Volkswagen AG, Baunatal).

Contribution to the Mission of MODUS

The logically correct formal modeling of demand propagation makes modeling for safety-stock placement more realistic. Such modeling efforts must keep in mind that the resulting models can be solved algorithmically. We aim at solution methods from Mixed Integer Linear Programming (MILP).


A first model with demand propagation was already developed. The model, however, does not yet scale well with respect to the number of stockpoints in the network. Thus, alternative models and improved solution methods are investigated.

University of Bayreuth -