Inventory Control in Supply Chains: An Internal Model Control Approach

Student thesis: Doctoral thesis


This thesis relies on the design of inventory management strategies in supply chain systems by using control theory approaches. The main objective is to propose a control scheme to solve the principal problems appearing in the inventory control of the supply chain (uncertainty in the lead time, the bullwhip effect and the inventory drift). This objective is divided in two particular objectives: 1. On the one hand, the counteraction of effects caused by the existing delay between the time at which an order is placed on the immediate supplier and the moment at which the petition is satisfied. 2. On the other hand, the design of inventory policies allowing a trade-off between the disturbance (demand) rejection and the inventory target tracking. Since the internal model control scheme (IMC) allows to tackle the objectives (1) and (2) under the same paradigm of control but in a decoupled way, the IMC scheme is presented in this thesis as a novel inventory replenishment policy for the entire supply chain. Nevertheless, the IMC requires the perfect knowledge of the lead time to compensate its effects. This situation is not viable when the delay changes during the process which is a common situation in supply chains. Hence, first of all, the research is focused on the identification of the lead time. As a result of this part of the research, an identification algorithm that allows to estimate the actual delay values of the entire supply chain at each time interval is formulated. The estimated delay values are used to adapt the delay block in the control scheme. Thereby, the particular objective (1) is finalised. The objective (2) relies on the design of the IMC scheme controllers. The aim of the IMC controllers is to keep the inventory levels of the supply chain close to the inventory target mitigating the bullwhip effect. Each echelon of the supply chain may operate under several working modes during the time: Infinite Supply and High stock, (ISHS), Infinite Supply and Low Stock, (ISLS), Limited Supply, (LS). When the lead time is too long and there exist uncertainty in the demand level, many companies choose to use a safety stock strategy to assure the customer demand satisfaction. Under this strategy the supply chain is always in the (ISHS) working mode. When the stock is insufficient, the supply chain may work under any of (ISHS), (ISLS) or (LS) working modes. Therefore, we start proposing the design of the control scheme for supply chain under safety stock strategy (ISHS). The design is based on the IMC guidelines where a trade-off between the bullwhip effect avoidance and inventory tracking is carried out, which is the second objective of the research. After that, the control scheme is designed for a supply chain working without safety stock (i.e. under any working mode (ISHS), (ISLS) or (LS)). Therefore, we propose a switched inventory control system for a serial multivariable supply chain under decentralized control strategy. This consists in a bank of controllers designed for each possible operation case of each echelon and a switching logic that selects the best controller at each instant time. Thus, the objective (2) is finalised.
Date of Award1 Mar 2013
Original languageEnglish
SupervisorAsier Ibeas Hernandez (Director) & Ramon Vilanova Arbos (Director)


  • coontrol theory
  • supply chain
  • bullwhip effect

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