Romain Guillaume

Romain Guillaume, Adam Kasperski, Szymon Wrobel et al.

In this paper, a single-item lot sizing problem with backordering is discussed. The time horizon is divided into planning periods, characterized by fixed and variable production costs, and future delivery periods with specified demands, where inventory holding and backordering costs may occur. For each planning period, a common nominal lead time is given. The true lead times can deviate to some extent from the nominal one, and their exact values are unknown at the planning step. We assume that lead times take only integer values and splitting production orders is not allowed. Furthermore, order crossovers are prohibited; thus, an order placed earlier cannot arrive after one placed later. A budgeted uncertainty set of possible lead-time scenarios is defined, where a budget allows us to control the amount of uncertainty of lead times. It is shown how to construct a family of production plans varying from the most optimistic (a best lead-time scenario occurs) to the most pessimistic (a worst lead-time scenario occurs). In order to compute these plans the R* criterion is applied which generalizes the conservative robust min-max criterion, commonly used in robust optimization. The computational complexity of the problem is investigated. Polynomial, pseudopolynomial time algorithms, and mixed integer programming formulations are proposed to solve the general problem and its special cases. The results of computational tests are provided that demonstrate that using the R* criterion can significantly enlarge the set of candidate production plans.

Zied Bouraoui, Antoine Cornuéjols, Thierry Denœux et al.

This paper proposes a tentative and original survey of meeting points between Knowledge Representation and Reasoning (KRR) and Machine Learning (ML), two areas which have been developing quite separately in the last three decades. Some common concerns are identified and discussed such as the types of used representation, the roles of knowledge and data, the lack or the excess of information, or the need for explanations and causal understanding. Then some methodologies combining reasoning and learning are reviewed (such as inductive logic programming, neuro-symbolic reasoning, formal concept analysis, rule-based representations and ML, uncertainty in ML, or case-based reasoning and analogical reasoning), before discussing examples of synergies between KRR and ML (including topics such as belief functions on regression, EM algorithm versus revision, the semantic description of vector representations, the combination of deep learning with high level inference, knowledge graph completion, declarative frameworks for data mining, or preferences and recommendation). This paper is the first step of a work in progress aiming at a better mutual understanding of research in KRR and ML, and how they could cooperate.