bc – prod: A specialized branch-and-cut system for lot-sizing problems

bc – prod is a prototype modelling and optimization system designed and able to tackle a wide variety of the discrete-time lot-sizing problems arising both in practice and in the literature. To use bc – prod, the user needs to formulate his/her problem as a mixed integer program using XPRESS-MP's mp – model, a standard mathematical programming modelling language, taking into account a reserved set of key words for specific lot-sizing objects, such as production variables, storage, and demand data, etc. The problem is then solved by the XPRESS-MP branch-and-bound system including lot-sizing specific preprocessing, cutting planes for different aspects of lot-sizing problems, plus general cutting planes, and a lot-sizing-specific primal heuristic. Results are presented for a wide variety of big bucket and small bucket models with set-up and start-up costs and times.