A technique to develop simplified and linearised models of complex dynamic supply chain systems

Abstract

Please note: Changes made as a result of publishing processes such as copy-editing, formatting and page numbers may not be reflected in this version. For the definitive version of this publication, please refer to the published source. You are advised to consult the publisher's version if you wish to cite this paper.This version is being made available in accordance with publisher policies. See http://orca.cf.ac.uk/policies.html for usage policies. Copyright and moral rights for publications made available in ORCA are retained by the copyright holders.At e c h n i q u et od e v e l o ps i m p l i fi e da n dl i n e a r i s e dm od e l so fc o m p l e x dynamic supply chain systems AbstractThere is a need to identify and categorise different types of nonlinearities that commonly appear in supply chain dynamics models, as well as establishing suitable methods for linearising and analysing each type of nonlinearity. In this paper simplification methods to reduce model complexity and to assist in gaining system dynamics insights are suggested. Hence, an outcome is the development of more accurate simplified linear representations of complex nonlinear supply chain models.We use the highly cited Forrester production-distribution model as a benchmark supply chain system to study nonlinear control structures and apply appropriate analytical control theory methods. We then compare performances of the linearised model with numerical solutions of the original nonlinear model and with other previous research on the same model.Findings suggest that more accurate linear approximations can be found. These simplified and linearised models enhance the understanding of the system dynamics and transient responses, especially for inventory and shipment responses.A systematic method is provided for the rigorous analysis and design of nonlinear supply chain dynamics models, especially when overly simplistic linear relationship assumptions are not possible or appropriate. This is a precursor to robust control system optimisation.

Identifying dynamical instabilities in supply networks using generalized modeling

“…These studies use variations of the inventory‐ and order‐based production control system (IOBPCS) (Towill, ), which are based on linear fractional control rules and constitute generalizations of the standard “inventory order up to level” models (Dejonckheere et al, ). Although the models in the literature are predominantly linear, some studies have sought to consider nonlinearities due to the nonnegativity of flows (Laugesen & Mosekilde, ; Wang, Disney & Wang, ; Warburton, ) and the strain on the system due to limited capacity and/or product availability (Spiegler & Naim, ; Spiegler, Naim, Towill, & Wikner, ; Venkateswaran & Son, ). These studies show that nonlinearities greatly influence the stability and the dynamics, leading for instance to chaotic behavior (Laugesen & Mosekilde, ).…”

“…If the inventory level of parts is insufficient to meet a desired production rate, which may be the case when external demand far exceeds the supply for a popular product, the production rate needs to be adjusted according to the inventory level of parts, thus f S > 0. Such strain due to limited material availability is considered by Spiegler et al (). If all parts available in stock are used directly for production, then f S = 1.…”

A Simulation Model for the Closed-Loop Control of a Multi-Workstation Production System

“…Other applications based on model predictive control or robust optimal control are not listed here, but can be found in (Sarimveis et al, 2008). Also, there are some alterna- (Towell, 1982;Zhou et al, 2006;Spiegler et al, 2016) productioninventory models with single and multiple-machines (with or without additional constraints) dynamic programming and optimal control (Scarf, 1960;Boukas and Liu, 2001;Gharbi and Kenne, 2003) multi-echelon productioninventory models using bills of material as input input-output analysis, Laplace or z-transform, probability distributions, NPV (Axsäter, 1976;Grubbström and Molinder, 1994;Grubbström et al, 2010) Schukraft et al, 2016) tive formulations out of the control theory area, based, for instance, in queueing systems, which are out of the scope of this paper.…”

Modeling and analyzing the chaotic behavior in supply chain networks: a control theoretic approach

“…In the chaotic SCN, when the market demand increases, suppliers are often unable to support manufacturers; while market demand is slowdown, the suppliers often continue to overproduction, which resulting in overstock. Spiegler et al [28] developed more accurate simplified linear representations of complex nonlinear supply chain models and reduced the complexity. The synchronization of two identical chaotic supply chain management systems based on their mathematical model is presented in [11].…”