We consider an integrated planning problem that combines production, inventory and inbound transportation decisions in a context where several suppliers each provide a subset of the components necessary for the production of a final product at a central plant. We provide a mixed integer programming formulation of the problem and propose several families of valid inequalities to strengthen the linear programming relaxation. We propose two new algorithms to separate the subtour elimination constraints with fractional node visits. The inequalities and separation procedures are used in a branch-and-cut algorithm. Computational experiments on a large set of generated test instances show that both the valid inequalities and the new separation procedures significantly improve the performance of the branch-and-cut algorithm.