Supply Chain Simulation with Switching Adaptive Model Predictive Control Methodology

An adaptive multiple model predictive control (MMPC) method for an uncertain input-constrained neutrally stable supply chains system with control-relevant switching is presented. By employing an input-to-state stabilizing MPC as the multi-controller, switching adaptive MMPC is proposed for the system. Unlike previous methods for handling uncertainties on the basis of minimal MPC laws or techniques for linear parameter varying systems, the proposed MPC scheme employs model switching to deal with modeling uncertainties through adaptation; a best model is selected for the MPC law from time to time. The proposed scheme using finite prediction horizon guarantees global stability. Simulation results are given to show the effectiveness of the scheme. Introduction In recent years, the supply chain network structure is ever-changing, Firms are obliged to maintain high customer service levels while at the same time they are forced to reduce cost and maintain profit margins. Traditionally, firms can operate and coordinate their marketing, distribution, planning, manufacturing, and purchasing along their own single supply chain. But, in real business world, there are likely to be a couple of related single supply chains nearby. Not only these single supply chains compete with one another, but cooperation happens among them. Where does it occur? With the further development of industrial and specialization division, industrial cluster provide an environment to makeup multi-chains and promote their member cooperation between them in order to implement legality strategy for sharpening their edge of competitive advantages. Moreover, uncertain market demand also forces firms to adopt coordination policy from firm-wide cooperation to chain-wide cooperation, and even to a cross-chain cooperation so that firms can survive and thrive. On this basis, we refer to multiple of single supply chains located in industrial cluster as cluster supply chains.Researches regarding inventory management of supply chain mainly focused on a single supply chain, which only take into account inventory management and bullwhip effect at two or more than two tiers and ignore inventory transshipment from the other adjacent related single supply chain. Although some literatures refer to their studies in the context of supply chain networks, which looks like multi-chains, this ‘networks’ basically contain just one focal firm who is dominant in whole supply chain and superior to other upstream and downstream firms, due to fan-shaped structure formed by subordinating, this supply chain calls as chain networks firms (Chopra & Meindl, 2004), but the one focal firm, rather more than one, plays a leadership role in making decision regarding as facility location, production capacity, inventory policy, transportation mode and batch size etc, in this way, this kind of chain network is indeed a single supply chain rather than multi-chains system. Model predictive control (MPC) is a receding horizon strategy, where the control is computed via an optimization procedure at every sampling instant. It is therefore possible to handle physical constraints on the input and/or state variables through the optimization. Over the last decade, there have been many stability and robustness results on constrained MPC. Because of this, MPC is recognized as one of the most successful control schemes in both theory and practice. Perea-Ló PEZ et al. (2003) proposed a SCM model based on the reasonable hypothesis from the 6th International Conference on Sensor Network and Computer Engineering (ICSNCE 2016) © 2016. The authors Published by Atlantis Press 644 raw materials suppliers to the consumers, and parameters of the various nodes were analyzed by the policy of overall optimization target. Box et al. (1978) proposed a time series forecasting method in details, and under a series of white noise in demand, an autoregressive moving average model ( ARIMA ) was employed, which is based on the past experience obtained. In this paper, a switching adaptive MPC for input-constrained neurally stable linear plant is presented. As the controller in the proposed switching adaptive control scheme, the input-to-state stabilising MPC is employed. As seen later, employing such a robust MPC against the estimation error is the key to design the adaptive MPC. For the switching logic, the control-relevant switching logic recently devised is employed. MPC Model for a Class of Supply Chains System In recent years numerous articles in supply chain modeling have addressed the issue of inventory coordination. Goyal and Gupta (1989) classified the literature dealing with the integrated models into four main classes. And Houqe and Goyal (2000) extended the idea of producing a single product in a multi-stage serial production system with equal and unequal sized batch shipments between stages. Khouja (2003) considered the case a three-stage non-serial supply chain and developed the model to deal with three inventory coordination mechanisms between the chain members. Cárdenas-Barrón (2007) formulated and solved an n-stage-multi-customer supply chain inventory model where there is a company that can supply products to several customers. Chung and Wee (2007) considered an integrated three-stage inventory system with backorders. They formulated the problem to derive the replenishment policies with four-decision-variables algebraically. As mentioned earlier numerous articles in inventory modeling have been written under a single supply chain. Therefore, there is a need to analyze models that relax the usual assumptions to allow for multiple supply chains network inventory coordination with the across-chain transshipment. Suppose the supply chain upstream node always satisfy the demand from downstream node. This paper considers two models: inventory model and demand model. Inventory model is used to maintain inventory balance of supply chain knods, demand model used to forecast future demand. System parameters are stated as follows: ) (t I Product inventory of a node at time t ) (t in M Product quantity from the upstream node ) (t out M Product quantity to a downstream node in O Order quantity from the upstream node out O Order quantity of the downstream node L Delay time of arrival order in P The purchase price of the product from the upstream node out P The price of the product to a downstream node stock P Products inventory cost pur C Products procurement cost ) (t R The total product yield stock C Inventory cost Inventory Model. In order to simplify the analysis of supply chains, suppose there are three nodes in every supply chain: supplier, manufacturer, and retailer. Income is from the downstream nodes, and the cost contains purchasing cost and maintain inventory cost from an upstream node. Assume that each node proceeds from the difference between income and cost. Fig. 1 shows the structure diagram of two supply chains (where, across-chain mutual replenishment is included.).