Complexity Analysis and Control in Time-Delay Vaccine Supply Chain considering Cold Chain Transportation

• Published in: Mathematical problems in engineering Vol. 2020; no. 2020; pp. 1 - 15
• Main Authors: Dai, Daoming, Si, Fengshan, Wu, Xuanyu
• Format: Journal Article
• Language: English
• Published: Cairo, Egypt Hindawi Publishing Corporation 2020; Hindawi; Hindawi Limited
• Subjects: Bifurcations; Chaos theory; Control methods; Critical point; Decision analysis; Decision making; Delay; Distributors; Entropy; Immunization; Infectious diseases; Influenza; Liapunov exponents; Mathematical models; Measles; Neural networks; Order quantity; Profits; Retail stores; Social responsibility; Suppliers; Supply chains; Systems stability; Transportation; Two dimensional models; Vaccines
• ISSN: 1024-123X; 1563-5147
• DOI: 10.1155/2020/4392708

Due to the important role of the vaccines in the prevention of global epidemics, this paper focuses on a vaccine transportation supply chain composed of one distributor and one retailer. Based on the assumption that the decision-maker does not make a decision instantaneously, we present a decision-making time-delay model. Firstly, we captured some sufficient conditions of delay-induced bifurcation for the model by regarding different combinations of the decision delay periods as the bifurcation parameters and analyzed how the speed of decision-making adjustment of distributor or retailer affects the critical point of system stability. Secondly, we made a numerical simulation on the model by using a two-dimensional bifurcation diagram, largest Lyapunov exponent, and entropy and chaotic attractor, respectively. Finally, we used two coordination methods to control chaos and compared them. The results show that when the decision delay exceeds a certain threshold, the system will lose stability or go into chaos. The precipitous speed of decision variable adjustment of the distributor or retailer will increase the entropy of the system and lead the system into a chaotic state. When the vaccine supply chain is in chaos, the effect of external control on chaos is better than that of internal control on chaos.