Optimization models and algorithms for complex production planning problems

生产计划是指制定最优生产计划的活动。必须对生产批次的水平和时间做出决定，通常是同时生产几种不同的产品。目标通常是在满足客户需求的同时使总成本最小化。生产计划是优化整个供应链活动的核心步骤。高效的计划通过降低成本和改善客户服务为公司带来竞争优势。在这项研究计划中，我们将着眼于动态需求的生产计划问题。不立即使用的产品可以保留库存。这种模型也被称为批量模型。拟议的研究计划的总体目标是优化复杂的工业扩展的基本生产计划问题，使用混合规划技术。对于每一个扩展，我们计划开发定制的算法来找到好的甚至是最优的解决方案。我们将具体考虑以下四个扩展。 1.如今，大多数公司都关心减少碳足迹，无论是出于立法还是出于社会关注。由于生产是碳排放的主要来源，因此有必要在生产规划中考虑排放限制。考虑到运输也会产生大量的碳排放，如果我们还考虑到分配规划，问题就会变得更加复杂。 2.大多数产品都是由几种成分按固定比例制成的。然而，在某些行业（例如食品工业、钢铁制造业），只要满足某些全球约束条件，每种成分（或成分）的确切用量就有一定的灵活性。这些“混合”模型可以扩展到多周期计划范围，包括最终产品和组件的生产和订购决策。 3.在生产环境中，有些机器专用于制造一种特定的产品，而另一些机器则是灵活的，可以制造多种类型的产品。通过拥有更灵活的机器，公司可以减少总积压，加班和外包成本。所提出的模型将有助于我们评估柔性的价值，并决定最好的方式来实现制造柔性。 4.在一些行业，如钢铁行业，几个较小尺寸的长度是从一个较大的标准梁尺寸切割。为了最小化浪费而规划切割操作是非常复杂的，但是当规划需要在几周内完成时变得更加困难。这需要同时规划标准梁的生产和切割操作。 这项研究是创新的，因为所提出的扩展要么是新的批量生产的文学或扩展，到目前为止很少受到关注。这些新的扩展将需要新的和定制的算法来解决它们。该提案的重要性源于相关性和影响。建议的扩展适用于特定行业（如混合行业的产品灵活性和钢铁行业的切割库存扩展），或一般（如确定最佳灵活性水平或考虑碳排放限制）。此外，模型和算法将帮助决策者获得更具成本效益的解决方案和更好地利用稀缺资源。这些项目将是高素质的硕士培训的一个组成部分。和PhD。学生我们还希望这项研究的结果将通过高质量学术期刊的出版物传播。

Production planning concerns the activity of constructing an optimal production plan. Decisions have to be taken on the level and timing of production lots, usually for several different products at the same time. The objective is typically to minimize the total costs while satisfying the customers’ demand. Production planning is a central step in the optimization of overall supply chain activities. Efficient plans give companies a competitive advantage through lower costs and improved customer service. In this proposed research program, we will look at production planning problems with dynamic demands. Products that are not immediately used can be kept in stock. Such models are also known as lotsizing models. The general objective of the proposed research program is to optimize complex industrial extensions of the basic production planning problem using Mixed Integer Programming techniques. For each of the extensions, we plan to develop customized algorithms to find good or even optimal solutions. We will specifically consider the following four extensions. 1. Most companies are nowadays concerned with decreasing their carbon footprint, either because of legislation or out of social concern. Since production is a major source of carbon emission, it will become necessary to take into account the emission restrictions in the production planning. The problem becomes more complex if we also take into account the distribution planning, given that transportation also generates high levels of carbon emissions. 2. Most products are made using several components in a fixed proportion. In some industries (e.g. food industry, steel manufacturing), however, there is some flexibility with respect to the exact amount used of each component (or ingredient) as long as some global constraints are met. These ‘blending’ models can be extended to a multi-period planning horizon, with production and ordering decisions on both the final products and the components. 3. In a production environment, some machines are dedicated to making one specific product, whereas others are flexible and can make several types of products. By having more flexible machines, companies can decrease their total backlog, overtime and outsourcing costs. The proposed models will help us to evaluate the value of flexibility and to decide on the best way to implement manufacturing flexibility. 4. In some industries like the steel industry, several smaller size lengths are cut from a larger standard beam size. The planning of the cutting operations in order to minimize waste is very complex, but becomes even more difficult when the planning needs to be done over several weeks. This requires simultaneously planning the production of standard beams, and the cutting operations. The research is innovative since the extensions that are proposed are either novel in the lotsizing literature or extensions that have received little attention up to now. These novel extensions will require new and customized algorithms to solve them. The significance of the proposal stems from the relevance and impact. The proposed extensions are relevant for specific industries (like the product flexibility for the blending industry and the cutting stock extension for the steel industry), or in general (like determining the optimal flexibility level or taking into account carbon emission constraints). Furthermore, the models and algorithms will help decision makers to obtain more cost efficient solutions and a better use of scarce resources. These projects will be an integral part of the training of highly qualified MSc. and PhD. students. We also expect that the results of this research will be disseminated through publications in high quality academic journals.