Modelling Nonlinear Supply Chains Using Methods of System Dynamics / Modeliranje nelinearnih oskrbovalnih verig z metodami dinamike sistemov

Rudolf Pušenjak, Maks Oblak
 
ANALI PAZU, 3 (2013), št./ No. 2, strani/ pages 87-93
Celotno besedilo/ Full text (PDF)
 
Abstract: This paper treats a three level nonlinear supply chain, which consists from a manufacturer, a distributor and a retailer as a dynamical system. The dynamic behavior of supply chain is modelled by using the continuous Lorenz-like model with disturbances. The Lorenz model is known from physics in the study of dissipative hydrodynamical systems with excitation and represents a paradigmatic example of the deterministic system, which is able to exhibit chaotic motions. Very complex supply chain relationships are modelled due to the information flow distortion at the distributor, caused by disturbances, which appear at the retailer. By using the proposed nonlinear supply chain model, the steady state, the saturation and the chaotic state of the supply chain are analyzed,  respectively. The range of parameter values, which are characteristic for the appearance of such states are determined. In the paper, the meaning of the regular state in which the supply chain cannot keep due to the disturbances and the risk of the saturation state are explained. In the analysis of such states, the multistage homotopic perturbation method is used.  The gained results are checked analyticaly or by the help of standard numerical integration, such as the Runge-Kutta method.
Key words:  Nonlinear supply chains, dynamics of Lorenz-like model, characteristic states, multistage homotopic perturbation method.

Povzetek: Članek  obravnava trinivojsko nelinearno oskrbovalno verigo, ki sestoji iz proizvajalca, distributerja in trgovca na drobno kot dinamični sistem. Dinamično obnašanje oskrbovalne verige je modelirano z zveznim  modelom z motnjami, ki je podoben Lorenzovemu sistemu. Lorenzov system je znan iz fizike v študiju disipativnih hidrodinamičnih sistemov z vzbujanjem in velja za enega izmed tipičnih determinističnih sistemov, ki lahko izvajajo kaotična nihanja. V oskrbovalni verigi modeliramo kompleksne razmere zaradi popačenja informacijskega toka pri distributerju, ki jih izzovejo motnje, s katerimi se sooča trgovec. S pomočjo modela je izvedena analiza ustaljenega stanja, stanja nasičenja in kaotičnega stanja oskrbovalne verige. Določena so območja vrednosti parametrov oskrbovalne verige za nastanek posameznih stanj. V članku je pojasnjen pomen regularnega stanja oskrbovalne verige, v katerem oskrbovalna veriga zaradi motenj v splošnem ne more vztrajati in stanje nasičenja kot enega najnevarnejših stanj oskrbovalne verige. V analizi teh stanj je v članku uporabljena večstopenjska homotopsko perturbacijska metoda. Dobljeni rezultati so preverjeni analitično oziroma s pomočjo standardne numerične metode Runge-Kutta.
Ključne besede: Nelinearne oskrbovalne verige, dinamika sistema, karakteristična stanja, večstopenjska homotopsko perturbacijska metoda.
 
 
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