Extensions of the lot sizing problem: new approaches of flexibility

Abstract

The lot sizing problem consists of determining the quantity of products to be produced in each period of a finite time horizon, in order to meet the demand and optimize an objective function, for example, to minimize costs. With the natural evolution of the industrial decisions-making process due, among others factors, the strong competition imposed by the globalized market, different strategies have been used to improve the decisions, making them more complex. Among these strategies, recently it has appeared studies which consider that some data, although deterministic, have certain flexibility, making the problem similar to what happens in practice. This project is in line with this trend of the evolution of the decision process. Despite the relevance, there are few works that make a detailed study about adding flexibility in lot sizing problems. Note that in the supply chain literature, for example, it has been shown that adding flexibility on the production process can provide good results. In this research project we intend to help fill this gap in the lot sizing literature with the study of flexibility from two different sources.The first source of flexibility is machine flexibility. In the standard lot sizing problem on parallel machines, each item can be produced on any of the machines and incurs a setup cost and time before production. In this case we have complete machine flexibility. However, in practice, it can be very costly to install machines that have complete flexibility, especially if the products are very different. Therefore, it might be interesting to only implement a limited amount of flexibility (each machine can produce only certain types of items). A second source of flexibility is Bill-Of-Material (BOM) flexibility. In this case, we consider a lot sizing problem of a final product that can be produced by blending different ingredients. The Bill-Of-Material indicates which ingredients are used and in which proportion. In some productive process there is some flexibility with respect to the proportion imposed for each of the ingredients, where it can vary between a minimum and maximum, this provides flexibility in the production planning process. Finally, there is still the setup flexibility. We consider a extension of the standard problem in which any period of the planning horizon starts with the setup to produce the first item to be produced in the period. In several practical applications it is possible to start a period with production (setup carryover) or to finish a setup that was started in the previous period (setup crossover). This provides more flexibility in planning and increases the possibility of finding more feasible and better solutions compared to the standard assumption. (AU)