A max plus algebra approach for modeling and control of lots delivery: application to a supply chain case study

Timed event graphs in lots are introduced as a new tool for modeling and control of the lots delivery problem in freight transportation systems. The model is developed by enhancing timed event graphs with transitions in lots that have particular dynamic. We develop a linear mathematical model under constraints in the (max,+) algebra. This leads us to develop a just-in-time control for the lots delivery using the residuation theory. The proposed approach is illustrated with a supply chain subject to a non constant logistic demand. The modeling and simulation-based optimization approach allows evaluating the just-in-time control and the model performances in term of respecting the time criterion.