An Approach Using Lagrangian/surrogate Relaxation for Lot-sizing with Transportation Costs

The aim of this work was to study a distribution and lot-sizing problem that considers costs with transportation to a company warehouse as well as, inventory, production and setup costs. The logistic costs are associated with necessary containers to pack produced items. The company negotiates a long-term contract in which a fixed cost per period is associated with the transportation of the items. On the other hand, a limited number of containers are available with a lower cost than the average cost. If an occasional demand increase occurs, other containers can be utilized; however, their costs are higher. A mathematical model was proposed in the literature and solved using the Lagrangian heuristic. Here, the use of the Lagrangian/ surrogate heuristic to solve the problem is evaluated. Moreover, an extension of the literature model is considered adding capacity constraints and allowing backlogging. Computational tests show that Lagrangian/ surrogate heuristics are competitive, especially when the capacity constraints are tight.