Adaptive Production and Inventory Control in Supply Chains against Changing Demand Uncertainty
We applied an adaptive controller to the general model of a replenishment rule. The replenishment rule is the “automatic pipeline, variable inventory and order based production control system”. In the current literature the possibility to reduce the bullw
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Department of Planning and Control of Production Systems, BIBA, University of Bremen, Germany 2 Institute for Microsensors, -actuators and -systems, University of Bremen, Germany
Abstract We applied an adaptive controller to the general model of a replenishment rule. The replenishment rule is the “automatic pipeline, variable inventory and order based production control system”. In the current literature the possibility to reduce the bullwhip effect and demand fluctuations by setting the right smoothing parameters to this replenishment rule was shown for independently and identically distributed stationary stochastic demand. In the real world the demand uncertainties are changing (e.g. along the product life cycle). On this account we developed a gain scheduling adaptive control mechanism, which is able to adjust the parameter based on states of the system and demand uncertainties. With the adaptive controller the system can be adapted to uncertainties in demand by holding the production fluctuations stable and adjust smoothly to a new appropriate inventory coverage level by setting the right inventory adjustment parameter, the right target inventory level and the right forecast time.
1 Introduction The design of the production and inventory control (PIC) policy is an important factor for effective supply chain. This rule determines the dynamics in the supply chain and the costs for production and inventory holding. Inventory costs rises based on inventory holding increase which is created by uncertainties in demand, supply, production and control policy. Production costs increase with ramp-up and phase out of production and capacity holding, caused by changing order and production rate. Furthermore fluctuations in order quantity build up along the supply chain from the point of origin to the point of consumption. This effect called “Bullwhip Effect” (Lee et al. 1997) and was shown in many real-world supply chains (e.g. Holmström 1997). The main causes for the bullwhip effect are “non-zero lead times”, “demand signal forecasting”, “order batching”, “gaming” and “promotions” (Lee et al. 1997). We focus on “non-zero lead times” and “demand signal forecasting” as core prob-
H.-D. Haasis et al., Dynamics in Logistics DOI: 10.1007/978-3-540-76862-3, © Springer 2008
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lems of the supply chain and neglect the other effects. The similar bound are used by Chen et al. (2000) and Lalwani (2006). The bullwhip effect is measured by the “variance ratio” based on Chen et al. (2000). The variance ratio is the long term ratio between the variance of orders (OR) over the variance of demand (D). The ratio can be applied for single order decision (e.g. Disney and Towill 2003) or order decision in each echelon over the whole supply chain (e.g. Hosoda 2006). In order to measure the effectiveness of the policy in terms of inventory holding the variance ratio of the inventory is used. The variance inventory ratio is defined as the variance of inventory (I) over the variance of demand. The aim is the dev
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