Minimum concave cost production system: A further generalization of multi-echelon model
Minimum concave cost production system: A further generalization of multi-echelon model
复制标题
最小凹成本生产系统：多梯队模型的进一步推广
DOI：
10.1007/bf01580763
复制
发表时间：
1988
影响因子：
2.7
通讯作者：
H. Konno
中科院分区：
文献类型：
--
作者：
H. Konno
我们将考虑一个与系列生产系统相关的凹最小化问题，其中原材料是在不连续的设备中加工的。某个工厂的产品要么被送到下一个工厂，要么被储存在仓库里。在i= 1，⋯n期间，最终产品的需求量是事先已知的。我们的问题是最小化加工、保持和积压成本的总和，所有这些成本都假定为凹。该模型的起源是Wagner和whtin的经典经济批量问题，Zangwill对此进行了广泛的研究。该模型具有重要的理论意义和实际应用价值，是为数不多的用多项式时间算法求解凹极小化问题的实例。本文的目的是将模型进一步扩展到与每个设施的处理相关的时滞情况。我们将针对这类问题提出一种高效的O（n4m）算法。
We will consider a concave minimization problem associated with a series production system in which raw material is processed inmconsecutive facilities. The products at some facility are either sent to the next facility or stocked in the warehouse. The amount of demand for the final products during periodi, i= 1,⋯,n, are known in advance. Our problem is to minimize the sum of processing, holding and backlogging cost, all of which are assumed to be concave.The origin of this model is the classical economic lot size problem of Wagner and Whitin and was extensively studied by Zangwill. This model is very important from the theoretical as well as practical point of view and this is one of the very rare instances in which polynomial time algorithm has been constructed for concave minimization problems.The purpose of this paper is to extend the model further to the situation in which time lag is associated with processing at each facility. We will propose an efficient O(n4m) algorithm for this class of problems.