A new supply chain model and its synchronization behaviour. (June 2019) - Mondal, Sayantani
Highlights: A new supply chain model is proposed assuming inventory dependent demand. Bifurcation diagram with respect to the demand saturation parameter is presented. Synchronization under unidirectional and bidirectional coupling are discussed. It is shown that chaos to order transition is possible with the variation of demand. Abstract: Marketing researchers and practitioners have noticed that the demand of many retail items are proportional to the amount of inventory displayed. In this paper, a new supply chain model is proposed assuming that demand of a product does not increase monotonically with the increase of inventory. In this model it is assumed that the demand has a saturation level and it does not increase monotonically with the inventory. The stationary solutions (fixed points) of the model are determined and their stability natures are determined using Routh–Hurwitz criteria. The variation of the model dynamics for different parameter values are presented numerically by drawing time evolution diagrams and phase diagrams. Bifurcation diagram of the model with respect to the demand saturation parameter is presented to note the importance of the parameter. Next, synchronization behavior of two coupled identical supply chain models under both unidirectional and bidirectional coupling are discussed. Sufficient conditions for synchronization in case of bidirectional coupling are derived. Numerical simulation results are presented to validate the analytical findings.