Optimization Models and Algorithms for Complex Production Planning Problems

为了按时、以最低的成本满足客户的需求，制造企业必须事先对生产活动进行周密的计划。必须根据生产数量和时间做出决定。这是一项复杂的任务，因为必须考虑到许多内在的权衡和限制，因此有效的生产计划工具对于创造竞争优势很重要。我的研究将集中在数学优化模型和算法上，这些模型和算法有助于在考虑生产环境中的许多约束的同时捕捉到这些权衡，以便在合理的时间内获得高质量的生产计划。许多挑战依然存在。首先，生产环境变得越来越复杂，这需要在数学模型中详细捕捉。如果这一点做得不好，生产成本可能会比预期的更高。其次，大多数生产过程由几个步骤组成，其中一个步骤的输出成为下一个步骤的输入。因此，规划必须同时进行多个层面的规划。第三，在供应链中，零部件的采购、生产和分销是连续的活动。通过协调这些活动，可以实现全球效率。然而，这些相互关联的生产和运输活动的计划也变得更加复杂。最后，在大多数环境中，不确定性是需要考虑的一个重要因素。不确定性通常与需求的不确定性有关，但供应的不确定性也是生产计划中的一个重要问题。我的研究项目的主要目标是开发基于混合整数规划的模型和精确的启发式优化方法来解决生产计划问题，其中的核心问题是满足多种产品的需求。具体目标与四项挑战直接相关。研究计划中的个别项目将专注于所描述的四个广泛挑战中的每一个特定问题。首先，我们将考虑一个生产环境，为库存产品设立单独的产能限制区域。除了传统的生产决策外，还必须将库存分配到特定的库存区。其次，我们将考虑一种生产系统，在该系统中，必须生产标准项目(例如钢梁)，然后将其切割成定制的部件，最后组装成最终产品。这导致了三个层次的组合批量和削减库存问题。第三，我们考虑了一个装配生产系统，在这个系统中，零部件必须在工厂之间运输。最后，我们考虑了一个生产问题，在需求和供应都存在不确定性的情况下，必须确定零部件的采购水平以及最终产品的生产水平。

In order to satisfy their customers' demand on time and at the lowest cost, manufacturing companies must carefully plan their production activities in advance. Decisions have to be taken related to the production quantities and the timing. This is a complex task because of the many inherent trade-offs and constraints that must be taken into account and efficient production planning tools are therefore important in order to create a competitive advantage. My research will focus on mathematical optimization models and algorithms which help to capture these trade-offs while taking into account the many constraints in the production environment in order to obtain high-quality production plans within a reasonable amount of time. Many challenges remain. First, the production environment is becoming more and more complex and this needs to be captured in detail in the mathematical models. If this is not properly done, production is likely to become more costly than anticipated. Second, most production processes consist of several steps, where the output of one step becomes the input for the next step. The planning hence must be done for several levels simultaneously. Third, in a supply chain, the procurement of components, production and distribution are sequential activities. By coordinating these activities, global efficiencies can be achieved. The planning of these interrelated production and transportation activities, however, also becomes more complex. Finally, in most environments, uncertainty is an important factor that needs to be taken into account. Uncertainty typically relates to the demand uncertainty, but also supply uncertainty is an important issue in production planning. The main objective of my research program is to develop Mixed Integer Programming based models and exact and heuristic optimization approaches for production planning problems in which the core issue is to satisfy demand for several products. The detailed objectives directly relate to the four challenges. The individual projects within the research program will focus on a specific issue within each of the four broad challenges described. First, we will consider a production environment with separate capacity-restricted areas for stocking products. In addition to the traditional production decisions, inventory also has to be assigned to specific stocking areas. Secondly, we will consider a production system in which standard items (e.g. steel beams) have to be produced, which are next cut into customized pieces and finally assembled into final products. This leads to a combined lot sizing and cutting stock problem with three levels. Thirdly, we consider an assembly production system in which components have to be transported between facilities. Finally, we consider a production problem in which the procurement level of components has to be decided as well as the production levels for the final products when there is both demand and supply uncertainty.