一种最小化交货费用的供应链优化模型

An Optimal Supply-chain Model for Minimizing the Delivery Cost

当销售合同规定的物资量相当大时 ,一个储备中心通常不能提供合同的全部物资 ,因此需要多个储备中心共同参与 ,企业于是就会面临选择参与供货的储备中心的决策问题 .综合考虑合同的交货期、运输费用以及设置费用 ,通过引入延迟交货的惩罚函数 ,提出了最小化交货费用的优化模型 .由于交货时间只可能为有限个数值之一 ,因此经过适当变换 ,可以将最小化交货费用模型转化为有限个子优化问题 ,容易证明这些子问题的最优解中至少存在一个为交货费用优化模型的最优解 .最后通过仿真算例说明了模型最优解的求取过程 .

Material dispatch problems, especially multi depot problems in a supply chain system (SCS), are a major concern of inventory planners. When the quantity of a sales contract is too large, a sole depot usually can not provide all the requirements of the contract, and it is much practical for multiple depots to meet them. Planners will thus be in the face of deciding which depots should be selected and how much material should be provided by each selected depot. In order to obtain a multi depot dispatch scheme with the lowest delivery cost, three important factors should be considered: (1) date of delivery; (2) transportation costs; (3) setup costs or ordering costs. As the setup cost is often decided by the number of selected depots, in order to decrease this cost, planners always want a scheme with few depots involved. However, a scheme with too few depots sometimes means a delay for the delivery, which will finally result in a punishment, so the lowest delivery cost problem can not be intuitively solved. Given a scheme , if T(φ) denotes the date of delivery by the scheme φ, and f(t) denotes a fine function to measure the cost of exceeding the date of delivery stipulated by the contract, then the cost of exceeding the deadline will be f(T(φ)) . Let N(φ) denote the number of depots involved in φ , and s be the cost of placing an order to a depot. The total setup cost will be N(φ) s. If the transportation cost per unit is a constant denoted by u, then the transportation cost will be ux (Let x be the quantity of the contract). Therefore, Considering the date of delivery, transportation cost and setup cost, the total delivery cost c(φ) can be depicted as c(φ)=f(T(φ))+N(φ)s+ux (we assume that all the delivery cost consists of transportation costs, setup costs and punishment costs). As described in this paper, T(φ) affirmatively equals one of the n possible values or lead times corresponding to all depots (n is the number of all available depots). Thereby, this optimal model can be divided into n sub-problems, and the optimal scheme will surely be one of the optimal solutions of these sub problems. Aimed at obtaining an optimal scheme φ * for minimizing the total cost of delivery c(φ) , this paper first presents an algorithm to solve these sub problems. When all the solutes for these sub problems have been obtained, the optimal solution of the model for minimizing c(φ) will certainly be the 'best' among them. In the end of this paper, a simulative example is proposed, and it clearly shows readers the process to obtain the optimal scheme φ * .