Formulations and algorithms for integrated maintenance and production planning problems

An important challenge in Lot Sizing faces to decision makers when there are capacity constraints. Decisions related to these problems have a direct impact at the operational level of the company, and consequently, they have an effect over the global performance of the company. One of the capacity constraints in Lot Sizing Problems arises when the machines produce with variable productivity. It means that their production capacity changes over time. Moreover, when the production capacity decreases over time, it is vital to stop the production line and fix the machines to bring them back to full productivity. Thus, another problem is about the maintenance scheduling. Given that the machines do not work during the maintenance period, it is important to synchronize maintenance and Lot Sizing decisions. Taking into consideration the company’s freight, transportation decisions should be incorporated into the model as well in order to exploit the freight efficiently. The latter aspect adds to the complexity of the problem significantly. Throughout this thesis, we aim to propose an improved formulation to deal with Dynamic Productivity Lot Sizing Problem (DPLSP) by extending traditional approaches provided for the Capacitated Lot Sizing Problems (CLSPs). Many of these problems are hard and hence are unlikely to admit polynomial time solutions. Therefore, we approach DPLSP based on the already existing common sense or specialized heuristics for CLSPs. Because of the nonincreasing capacity assumption we apply in our model, it is vital to integrated the aforementioned problem with the maintenance scheduling in order to bring the machines back to their full productivity. Specifically, in this research we plan to cope with a single (multi)-product(s), single (multi)-machine(s) CLSP, as a basic production/inventory problem with decreasing capacity. Then, we plan to synchronize maintenance and transport aspects to best satisfy the demand, while minimizing the total cost of the process. We propose two types of algorithms to solve such an integrated problem. The first algorithm (off-line algorithm) is suggested when the demand is deterministic. We exploit MIP-based Fix-and-Optimize heuristic which results is compared to the results obtained using the MIP solver. The second algorithm which called online algorithm is propounded when the demand is not known in advance. The effectiveness of the proposed online algorithms is measured by their competitive ratio, defined as the ratio between the maximum number of the demands can be satisfied and that of a hypothetical offline algorithm (Dynamic Programming) which knows the entire sequence of requests in advance and chooses its actions optimally.(ECGE - Sciences économiques et de gestion) -- UCL, 201