Transportation delays in reverse logistics

In this paper we extend and apply MRP theory towards reverse logistics including the considerations of transportation consequences. Our aim is to demonstrate the versatility obtained from using MRP theory when combining Input–Output Analysis and Laplace transforms. This enables an analysis of a supply chain including four sub-systems, namely manufacturing, distribution, consumption and reverse logistics, where the geographical distance between the activities play an important role. The main focus in this paper is on reverse logistics (recycling, remanufacturing). Especially we wish to model the evaluation of disposal and reverse activities far away from agglomerations, which often means an improved environment for nearby inhabitants. This is also illustrated in a numerical example. We use the Net Present Value as a measure of the economic performance. Our ambition is to show that supply chain sub-systems may accurately be described using input and output matrices collected together in corresponding matrices for the system as a whole. Activity levels in each sub-system govern the speed of the respective processes, and these activity levels, in general, will be considered as decision variables. We now analyse reverse logistics activities in which the flows of materials and goods are typically divergent (arborescent processes), similar to properties of the distribution sub-system, and recent results on the extensions of basic MRP theory introducing the concepts of output delays and the generalised output matrix are also introduced here, when modelling the reverse logistics sub-system. & 2011 Elsevier B.V. All rights reserved.