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THE network of suppliers, manufacturers, distributors and retailers constitutes a supply chain management system. Between interconnected entities, there are
two types of process flows: information flows, e.g., an order requesting goods, and material flows, i.e., the actual shipment of goods. Key elements to an efficient supply chain are accurate pinpointing of process flows and tim- ing of supply needs at each entity, both of which enable entities to request items as they are needed, thereby re- ducing safety stock levels to free space and capital. The operational planning and direct control of the network can in principle be addressed by a variety of methods, including deterministic analytical models and stochastic analytical models, and simulation models, coupled with the desired optimization objectives and network perfor- mance measures .
The significance of the basic idea implicit in the reced- ing horizon control (RHC) or RHC has been recognized a long time ago in the operations management literature as a tractable scheme for solving stochastic multi period op- timization problems, such as production planning and supply chain management, under the term receding hori- zon . In a recent paper , a RHC strategy was em- ployed for the optimization of production/distribution systems, including a simplified scheduling model for the manufacturing function. The suggested control strategy considers only deterministic type of demand, which re- duces the need for an inventory control mechanism [4,5].
For the purposes of our study and the time scales of in- terest, a discrete time difference model is developed .The model is applicable to multi echelon supply chain networks of arbitrary structure. To treat process uncer- tainty within the deterministic supply chain network model, a RHC approach is suggested [7,8].
Typically, RHC is implemented in a centralized fashion . The algorithm uses a receding horizon, to allow the incorporation of past and present control actions to future predictions [10,11,12,13].
In this paper, a centralized receding horizon controller applying to a supply chain management system consist of one plant (supplier), two distribution centers and three retailers.
2 DISCRETE TIME DIFFERENCE MODEL
In this work, a discrete time difference model is devel- oped. The model is applicable to multi echelon supply chain networks of arbitrary structure, that DP denote the set of desired products in the supply Chain and these can be manufactured at plants, P, by utilizing various re- sources, RS. The manufacturing function considers inde- pendent production lines for the distributed products. The products are subsequently transported to and stored at warehouses, W. Products from warehouses are trans- ported upon customer demand, either to distribution cen- ters, D, or directly to retailers, R. Retailers receive time varying orders from different customers for different products. Satisfaction of customer demand is the primary target in the supply chain management mechanism. Un- satisfied demand is recorded as backorders for the next time period. A discrete time difference model is used for description of the supply chain network dynamics. It is assumed that decisions are taken within equally spaced time periods (e.g. hours, days, or weeks). The duration of the base time period depends on the dynamic characteris- tics of the network. As a result, dynamics of higher fre- quency than that of the selected time scale are considered negligible and completely attenuated by the network [4,14].
Plants P, warehouses W, distribution centers D, and retailers R constitute the nodes of the system. For each
node, k, there is a set of upstream nodes and a set of downstream nodes, indexed by (k ‘, k ”) . Upstream nodes can supply node k and downstream nodes can be sup-not require a separate balance for customer orders at nodes other than the final retailer nodes [4,15].
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