Uncapacitated lot-sizing with buying, sales and backlogging

Extended formulations are given for the single item uncapacitated lot-sizing problem with backlogging, piecewise linear concave production costs, sales with piecewise linear selling prices and start-up costs. Without start-up costs, the formulation is shown to be tight. With start-up costs, it is conjectured that the formulations given are tight. Computational results are presented suggesting that certain multi-item instances with joint small or big bucket capacity constraints can be solved using these reformulations. OMPartners, Belgium This paper presents research results of the Belgian Program on Interuniversity Poles of Attraction initiated by the Belgian State, Prime Minister's Office, Science Policy Programming. The scientific responsibility is assumed by the authors.