A general lotsizing problem with uncertain product returns

We consider a single-stage system that produces a range of final products. The demands of the final products are supposed deterministic over a finite planning horizon. Each unit of demand has to be fulfilled at the period that it appears using either the production of that
period or the inventory carried over from the earlier periods. The final products can either be manufactured using purchased materials or remanufactured using remanufacturable returned products. For each final product, the manufactured and remanufactured items are perfectly
substitutable. The returned products are collected at the start of each period but the quantities obtained are unknown until the collection. The return inventories accumulate as remanufacturable returned items are received. The manufacturing and remanufacturing processes of all the final products are executed on a same machine. In each time period,
multiple products can be processed but the total production quantity is limited by the time availability of the machine during this period. Whenever production is switched from one final product to another, a sequence dependent setup cost is incurred and a sequence depen-
dent setup time is consumed from the available time capacity. Different stochastic combinatorial optimization methods as well as dynamic programming methods are proposed, tested and compared.