(496d) Improving Supply Chain Performance Using Game Theory, Cooperative MPC and Optimization

Subramanian, K. - Presenter, University of Wisconsin - Madison
Rawlings, J. B. - Presenter, University of Wisconsin-Madison
Maravelias, C. T. - Presenter, University of Wisconsin - Madison

A supply chain is a highly interconnected network of facilities and distribution options that performs the functions of procuring raw materials, transforming them into products and distributing the finished products to the customers. Many supply chains include the interactions between two or more companies which exchange raw materials, intermediate products etc. These agents in the supply chain, when belonging to two separate companies interact through the "contract" which governs the economics of order placement and production scheduling in the companies. Thus, the overall performance of the supply chain and the individual agents is dependent on the terms of the contract. Analysis of supply chain contracts is essential to identify opportunities to make the supply chain more efficient.

The centralized optimization of the supply chain, which seeks to minimize, for instance, the total production cost of the final product, is independent of the contracts as it treats all the entities of the supply chain in a single optimization problem. On the other hand, in practical applications, different agents belonging to different companies optimize their own objective function, which depends on the contract. In such cases, the solution converges to the Nash equilibrium which may or may not be close to the Pareto optimal identified by the centralized optimization. However, knowledge of the Pareto optimal can help practitioners design contracts such that the Nash equilibrium is close to the Pareto optimal. When the contract is designed such that the Nash equilibrium is the Pareto optimal, then the supply chain is said to be coordinated. To explore contracts that ensure coordinated supply chains, the agents have to cooperate with each other, for instance, by sharing their objective functions or demand forecasts etc.

In this paper, we first provide a simple example of a 2 firm supply chain. Firm-1 produces an intermediate product which it sells to firm-2. Firm-2 converts it into the final product and sells it to the customers. We study the benefits of firm-2, which directly interacts with the customers sharing its demand forecast with firm-1. Model predictive control (MPC) has been gaining popularity as an optimization tool for supply chains. MPC is a widely used multi-variable control technique capable of handling constraints and satisfying some optimal performance criteria. In this study, we model the supply chains from a systems-theory perspective and use MPC as our optimization tool for analyzing the contracts. We compare an existing contract, which requires no demand forecast sharing. In this contract firm-2 is required to order a minimum quantity every period at a fixed price. Orders above the minimum quantity is charged at a higher price. In the other contract, in which firm-2 is required to share forecasts, there is a single wholesale price for any order and no minimum order needs to be placed.

We discuss simulation results that show the benefits for cooperation in which firm-2 increases its profits by 20% while firm-1 increases its profit by 55% when using the second contract with information sharing. It is easy to notice that firm-1 will benefit by knowing the final customer demands. But, we have shown that it is easy to develop a contract in which firm-2 also has incentive to share the demands forecasts. In this case, firm-1 could provide some extra monetary incentives to firm-1 to adopt the new contract because of the massive advantage that knowing demand forecasts provide them.

Secondly, we discuss the application of the insights from the above analysis to an industrial supply chain consisting of a steel mill and an air separating unit (ASU). In achieving this, we develop models for the different players and generate gas demand information. We study the benefits of sharing this information and explore the effect of contracts in the supply chain.