As one of the basic inventory cost models, the （Q, τ）inventory cost model of dual suppliers with random procurement lead time is mostly formulated by using the concepts of ＂effective lead time＂ and ＂lead time de...As one of the basic inventory cost models, the （Q, τ）inventory cost model of dual suppliers with random procurement lead time is mostly formulated by using the concepts of ＂effective lead time＂ and ＂lead time demand＂, which may lead to an imprecise inventory cost. Through the real-time statistic of the inventory quantities, this paper considers the precise （Q, τ） inventory cost model of dual supplier procurement by using an infinitesimal dividing method. The traditional modeling method of the inventory cost for dual supplier procurement includes complex procedures. To reduce the complexity effectively, the presented method investigates the statistics properties in real-time of the inventory quantities with the application of the infinitesimal dividing method. It is proved that the optimal holding and shortage costs of dual supplier procurement are less than those of single supplier procurement respectively. With the assumption that both suppliers have the same distribution of lead times, the convexity of the cost function per unit time is proved. So the optimal solution can be easily obtained by applying the classical convex optimization methods. The numerical examples are given to verify the main conclusions.展开更多
This paper deals with the problem of planned lead time calculation in a Material Requirement Planning （MRP） environment under stochastic lead times. The objective is to minimize the sum of holding and backlogging co...This paper deals with the problem of planned lead time calculation in a Material Requirement Planning （MRP） environment under stochastic lead times. The objective is to minimize the sum of holding and backlogging costs. The proposed approach is based on discrete time inventory control where the decision variables are integer. Two types of systems are considered： multi-level serial-production and assembly systems. For the serial production systems （one type of component at each level）, a mathematical model is suggested. Then, it is proven that this model is equivalent to the well known discrete Newsboy Model. This directly provides the optimal values for the planned lead times. For multilevel assembly systems, a dedicated model is proposed and some properties of the decision variables and objective function are proven. These properties are used to calculate lower and upper limits on the decision variables and lower and upper bounds on the objective function. The obtained limits and bounds open the possibility to develop an efficient optimization algorithm using, for example, a Branch and Bound approach. The paper presents the proposed models in detail with corresponding proofs and se＇~eral numerical examples. Some advantages of the suggested models and perspectives of this research are discussed.展开更多
基金supported by the National High Technology Research and Development Program of China(863 Program)(2007AA04Z102)the National Natural Science Foundation of China(6087407160574077).
文摘As one of the basic inventory cost models, the （Q, τ）inventory cost model of dual suppliers with random procurement lead time is mostly formulated by using the concepts of ＂effective lead time＂ and ＂lead time demand＂, which may lead to an imprecise inventory cost. Through the real-time statistic of the inventory quantities, this paper considers the precise （Q, τ） inventory cost model of dual supplier procurement by using an infinitesimal dividing method. The traditional modeling method of the inventory cost for dual supplier procurement includes complex procedures. To reduce the complexity effectively, the presented method investigates the statistics properties in real-time of the inventory quantities with the application of the infinitesimal dividing method. It is proved that the optimal holding and shortage costs of dual supplier procurement are less than those of single supplier procurement respectively. With the assumption that both suppliers have the same distribution of lead times, the convexity of the cost function per unit time is proved. So the optimal solution can be easily obtained by applying the classical convex optimization methods. The numerical examples are given to verify the main conclusions.
文摘This paper deals with the problem of planned lead time calculation in a Material Requirement Planning （MRP） environment under stochastic lead times. The objective is to minimize the sum of holding and backlogging costs. The proposed approach is based on discrete time inventory control where the decision variables are integer. Two types of systems are considered： multi-level serial-production and assembly systems. For the serial production systems （one type of component at each level）, a mathematical model is suggested. Then, it is proven that this model is equivalent to the well known discrete Newsboy Model. This directly provides the optimal values for the planned lead times. For multilevel assembly systems, a dedicated model is proposed and some properties of the decision variables and objective function are proven. These properties are used to calculate lower and upper limits on the decision variables and lower and upper bounds on the objective function. The obtained limits and bounds open the possibility to develop an efficient optimization algorithm using, for example, a Branch and Bound approach. The paper presents the proposed models in detail with corresponding proofs and se＇~eral numerical examples. Some advantages of the suggested models and perspectives of this research are discussed.
