FLOW CONTROL IN TIME-VARYING, RANDOM SUPPLY CHAINS
Ion Matei and Assane Gueye
Supply chains can be defined as the movement of materials as they flow from their source to the end customer including purchasing, manufacturing, warehousing, transportation, customer service, demand planning, supply planning. All these are made up of the people, activities, information, and resources involved in moving a product from its supplier to customer. Today’s supply chains are more and more complex, forming a network of independent, yet interconnected, moving parts and relying on critical infrastructure; they need roads, railways, and airports to move goods. Supply chains also need effective communication systems to transmit information between trading partners. The global supply chain, consisting of multiple activities covering the design, procurement, manufacturing, distribution, and consumption of goods, repeatedly demonstrates the co-existence of operational optimization with operational vulnerability.
Until recently, stakeholders have focused mainly on operational optimization, but recent events that had caused disruptions in the supply chains have commanded stakeholders to recognize operational vulnerabilities and to underline the time-varying and random nature of the supply chains. Due to the increasingly globalized economy, supply chains disruptions may have impacts that propagate not only locally but globally and hence, a holistic, system-wide approach to supply chain network modeling and analysis is essential in order to be able to capture the complex interactions among decision-makers. Indeed, rigorous modeling and analysis of supply chain networks, in the presence of possible disruptions is imperative since disruptions may have lasting major financial consequences.
In this work we focus on the logistics of the supply chain, i.e., that part of supply chain management that plans, implements and controls the flow and storage of goods, and the services between the point of origin and the point of consumption, necessary to meet customers’ requirements. We propose a randomized control algorithm for the flow of products in a time varying, random supply chain aimed at maximizing the profit of a firm. The algorithm, based on queue theory and stochastic analysis concepts is designed to get arbitrarily close to the maximum of the profit function in terms of the long-run time averages of the flows. The proposed algorithm is dynamic, adapts to the current state of the supply chain and results as a solution of a stochastic optimization problem. The solution of the stochastic optimization problem is derived in a distributed manner using a drift analysis technique. The algorithm deals with both supply changes and demand variability.