The integrated uncapacitated lot sizing and bin packing problem

In the integrated uncapacitated lot sizing and bin packing problem, we have to couple decisions of replenishment from single product suppliers with in delivery client orders. A order is composed quantities each product, such an must be delivered all together no later than a given period. The packed same bin, may advance if it advantageous terms costs. We assume large enough set homogeneous bins available at costs involved are setup inventory holding cost use as well. All variable planning horizon, objective minimize total incurred. propose mixed integer linear programming formulations combinatorial relaxation where longer necessary keep track specific packed. An aggregate delivering capacity computed instead. also heuristics using different strategies subproblems. Computational experiments on instances configurations showed that proposed methods efficient ways obtain small optimality gaps reduced computational times.