A probabilistic bi-level linear multi-objective programming problem to supply chain planning
A probabilistic bi-level linear multi-objective programming problem to supply chain planning
复制标题
DOI：
10.1016/j.amc.2006.10.032
复制
发表时间：
2007-05
期刊：
影响因子：
--
通讯作者：
E. Roghanian;S. Sadjadi;M. Aryanezhad
中科院分区：
文献类型：
--
作者：
E. Roghanian;S. Sadjadi;M. Aryanezhad
双层规划是一种去中心化决策的建模工具，它由第一层领导者的目标和第二层跟随者的目标组成。当第二级本身是二级编程时，产生三级编程。通过扩展这个想法，可以定义具有任意数量级别的多层程序。在大多数真实的数学规划问题中，参数都被看作是随机变量。数学规划的分支研究随机参数不完全信息下条件极值问题的求解理论和方法，称为随机规划。供应链计划问题涉及同步和优化企业中涉及的多个活动，从过程的开始，如原材料的采购，通过一系列过程操作，到结束，如最终产品分配给客户。工厂范围的供应链规划问题自然地呈现出多级决策网络结构，其中例如，一个级别可以对应于本地工厂控制/调度/规划问题，而另一个级别对应于对应的工厂范围的规划/网络问题。这种多级决策网络结构可以通过使用“多级编程”原理来数学地表示。本文研究了一个概率双层线性多目标规划问题及其在企业级供应链计划问题中的应用，其中（1）市场需求、（2）各工厂的生产能力和（3）各工厂对每种产品的可用资源都是随机变量，约束条件可以是联合概率分布，也可以不是联合概率分布。该概率模型首先在每一层转化为一个等价的确定性模型，然后应用模糊规划技术求解多目标非线性规划问题，得到一个折衷解。
Bi-level programming, a tool for modeling decentralized decisions, consists of the objective(s) of the leader at its first level and that is of the follower at the second level. Three level programming results when second level is itself a bi-level programming. By extending this idea it is possible to define multi-level programs with any number of levels. In most of the real life problems in mathematical programming, the parameters are considered as random variables. The branch of mathematical programming which deals with the theory and methods for the solution of conditional extremum problems under incomplete information about the random parameters is called “stochastic programming”. Supply chain planning problems are concerned with synchronizing and optimizing multiple activities involved in the enterprise, from the start of the process, such as procurement of the raw materials, through a series of process operations, to the end, such as distribution of the final product to customers. Enterprise-wide supply chain planning problems naturally exhibit a multi-level decision network structure, where for example, one level may correspond to a local plant control/scheduling/planning problem and another level to a corresponding plant-wide planning/network problem. Such a multi-level decision network structure can be mathematically represented by using “multi-level programming” principles. In this paper, we consider a “probabilistic bi-level linear multi-objective programming problem” and its application in enterprise-wide supply chain planning problem where (1) market demand, (2) production capacity of each plant and (3) resource available to all plants for each product are random variables and the constraints may consist of joint probability distributions or not. This probabilistic model is first converted into an equivalent deterministic model in each level, to which fuzzy programming technique is applied to solve the multi-objective nonlinear programming problem to obtain a compromise solution.