Embedding optimisation algorithms with Mosel

Algebraic modelling language allow models to be implemented in such a way that they can easily be understood and modified. They are therefore a working environment commonly used by practitioners in Operations Research. Having once developed models, they need to be integrated inside the company information system. This step often involves embedding a model into a programming language environment: many existing algebraic modelling languages make possible to run parameterised models and subsequently retrieve their results, but without any facility for interacting with the model during the model generation or solution process. In this paper we show how to use the Mosel environment to implement complex algorithms directly in the modelling language. The “Office cleaning” problem is solved by a branch-and-cut algorithm, implemented entirely in the modelling language (including the definition of the callback function for the solver). Secondly, a “cutting stock” problem is solved by column generation, also implemented in the modelling language.