Spatio-temporal economic properties of multi-product supply chains

•Presents a graph-structured dynamical market coordination framework.•Captures spatiotemporal behavior of product prices through market clearing.•Draws insights from primal, dual, and Lagrangian formulations.•Presents case study based on Wisconsin dairy farming and MISO electricity prices. In this work we present a generalization of market coordination to multi-product supply chains and use this framework to analyze their spatio-temporal economic properties. We interpret a supply chain as a market consisting of independent stakeholders (suppliers, consumers, transportation, and technology providers) who bid into a coordination system that is managed and cleared by an independent entity to obtain product allocations and prices. The proposed model provides a general graph representation of spatio-temporal product transport that helps capture geographical transport, time delays, and storage (temporal transport) in a unified and compact manner. This representation allows us to establish fundamental economic properties for the supply chain (revenue adequacy, cost recovery, and competitiveness) and to establish bounds for space-time prices. To illustrate these concepts, we consider a case study in which organic waste is used for producing biogas and electricity. Our market model shows that incentives for waste storage emerge from electricity demand dynamics and illustrates how space-time price dynamics for waste and derived products emerge from geographical transport and storage.