Optimization models and algorithms for complex production planning problems

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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.