This paper presents an Integer Linear Programming model for a multi-product lot-sizing problem. The problem considers demands, inventory policies, backorder costs and the search of an efficient use of resources (machines and workers). The real-world case used to illustrate the model is from a Colombian company, which produces raw material for the bakery industry. The short term planning for the company under study is critical, because there is a multi-product environment whit shared resources by different products and processes. The computational experiments show the effectiveness of the proposed model.