Kinetic and Fluid Model Hierarchies for Supply Chains

Abstract

We present a model hierarchy for queuing networks and supply chains, analogous to the hierarchy leading from the many body problem to the equations of gas dynamics. Various possible mean field models for the interaction of individual parts in the chain are presented. For the case of linearly ordered queues the mean field models and fluid approximations are verified numerically.

Existence of Solutions for Supply Chain Models Based on Partial Differential Equations

“…Supply chain modeling is characterized by different mathematical approaches : on the one hand there are discrete event simulations based on considerations of individual parts; on the other hand, continuous models like [1,2,3] using partial differential equations have been introduced. We consider supply chain modeling based on the latter -the continuous models.…”

Optimization of order policies in supply networks

“…The inventory model used here essentially corresponds to replacing the inventory by a processor with a very short cycle time ε, and then using a version of the model for a production unit developed in [2] and [10]. Similar simple inventory models have been used in [1] and [3] in a different context.…”

A level set approach to modeling general service rules in supply chains

“…The left panel in Figure 4.6 shows result for the FIFO policy, and the right panel for the policy corresponding to the priority function (4.11). The top row shows the cycle time Y (1) k (x = 40,t), k = 1 : 2 at exit, i.e. the total time parts have spent in the system.…”

“…Their evolution through the stages is described by a conservation law. The flux function governing this law can either be derived from heuristic considerations [1], elementary queueing theory (using so called clearing functions [9], [12]) or from microscopic models describing the individual behavior of each part (i.e. from a kinetic theory) [5], [2], [8].…”