A dynamic uncapacitated lot-sizing problem with co-production

We consider an extension of the dynamic uncapacitated lot-sizing problem to account for co-production, where multiple products are produced simultaneously in a single production run. We formulate the problem as a mixed-integer linear programming problem. We then show that a variant of the well-known zero-inventory property holds for this problem, and use this property to extend a dynamic program given for the single-item lot-sizing to solve the problem with co-production. Finally, we provide an illustrative example for our approach.