Stability of inventory dynamics in supply chains with three delays

Distinctive delays accounting for lead time in manufacturing, transportation of products and decision-making are considered in a single link supply chain that is modeled by continuous-time differential equations via system thinking. As seen in the literature, behavior of inventory variations in the presence of delays can become undesirably oscillatory. The novelty of this work is the analytical characterization of these oscillations with respect to two intrinsic parameters of the supply chain and the three delays considered separately. Particularly, inventory dynamics is characterized on the so-called stability maps drawn in the space of three delays, displaying which combinations of each delay lead to (un)desirable inventory behavior. Arising from the characterization is also a novel ordering policy design with which the inventory variations can be rendered insensitive to detrimental effects of delays. Case studies are provided along with managerial interpretations.