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This paper examines a supply planning problem for multilevel serial production systems under lead time uncertainties. The techniques used in industry are often based on the assumption that the lead times are known. However, in a supply chain the lead times are often random variables. Therefore, it is necessary to evaluate the influence of the planned lead times on the total cost. An exact performance evaluation technique is developed to calculate the total cost as a function of the planned lead times when the actual lead times are random discrete variables. The sum of the average component holding and tardiness costs at each level, plus the average finished product backlogging cost is considered. Several properties of this function are proven. A numerical example is reported.
A multilevel linear supply chain is considered in this paper. The lead times at each level are random discrete variables, and the finished product demand is fixed and known. The objective is to minimize the sum of holding and backlogging costs for the finished product. We propose a novel mathematical model which gives the optimal order release dates for the components. From a theoretical point of view, this formulation is equivalent to the discrete Newsboy model. Numerical tests are reported.
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