A continuum-discrete model for supply chains dynamics

Abstract

This paper is focused on continuum-discrete models for supply\ud chains. In particular, we consider the model introduced in [10], where a system\ud of conservation laws describe the evolution of the supply chain status on\ud sub-chains, while at some nodes solutions are determined by Riemann solvers.\ud Fixing the rule of flux maximization, two new Riemann Solvers are defined. We\ud study the equilibria of the resulting dynamics, moreover some numerical experiments\ud on sample supply chains are reported. We provide also a comparison,\ud both of equilibria and experiments, with the model of [15]

Continuum-Discrete Models for Supply Chains and Networks

“…The model of D' Apice & Manzo (2006), on the other hand, is useful when there is the possibility to reorganize the supply chain: in particular, the productive capacity can be readapted for some contingent necessity. Starting from the model introduced in D' Apice & Manzo (2006) and fixing the rule that the objects are processed in order to maximize the flux, two different Riemann Solvers are defined and equilibria at a node are discussed in Bretti et al (2007). Moreover, discretization algorithms to find approximated solution to the problem are described, numerical experiments on sample supply chains are reported and discussed for both the Riemann Solvers.…”

“…Probably the first paper for supply chains in continuous direction was Armbruster et al (2006b) where the authors, taking the limit on the number of parts and suppliers, have obtained a conservation law, whose flux is described by the minimum among the parts density and the maximal productive capacity. Due to the difficulty of finding solution for the general equation proposed in Armbruster et al (2006b), other fluid dynamic models for supply chains were introduced in Göttlich et al (2005 and Bretti et al (2007).…”

Time-varying Riemann solvers for conservation laws on networks

“…One of the main motivation is the wide range of different applications covered by the research theme: vehicular traffic, data networks, irrigation channels, gas pipelines, supply chains, blood circulation and others (see [4,6,7,11,13,18,22]). It is then natural to consider control problems for such systems.…”

Existence of solutions to Cauchy problems for a mixed continuum-discrete model for supply chains and networks

“…In order to solve this problem, Riemann Solvers according to rules SC2 and SC3, allowing more rich dynamics, have been considered in [7]: SC2 The objects are processed in order to maximize the flux with the minimal value of the processing rate. SC3 The objects are processed in order to maximize the flux.…”