Dynamics of a risk-averse newsvendor model with continuous-time delay in supply chain financing

Abstract

In this paper, delay differential equations are adopted to describe the ordering performance of the risk-averse newsvendor with supply chain financing. Firstly, authors theoretically explore the local asymptotical stability for equilibrium point, and also the conditions and directions for Hopf bifurcation of the ordering quantity for risk-averse retailer. Secondly, they investigate the influence of important parameters on the bifurcation, and find that the initial capital, risk aversion and friction coefficient can make the Hopf bifurcation undergo a long time, but the adjustment speed induces the inverse effect. Then phase diagram, stable region, bifurcation to chaos, time series and CVaR profit are illustrated by means of numerical simulation. It is found that the upstream supplier can share the risk from market uncertain with stochastic demand under supply chain financing. The results also indicate that the optimal ordering quantity placed by risk-averse newsvendor is smaller than the risk-neutral ordering quantity. Furthermore, the less initial capital may cause the CVaR profit to increase steadily or drop sharply, which exhibits complex dynamical behaviour in the presence of the time delay. Finally, the stability and bifurcation analysis of a fractional delay ordering model has also been proposed and studied. It is worth pointing out that in this study authors assume there is only one retailer who is risk-averse. Therefore, it will be more interesting and meaningful to consider the scenario having multiple retailers and to incorporate the upstream supplier’s optimal decision into the dynamical decision model.