When production yields are random and orders need to be satisfied in f
ull, several successive production runs may need to be initiated until
an order is met. Variants of this multiple lot-sizing production to o
rder problem have long been explored, but some natural fundamental gen
eral questions have not been addressed. Also, the consequences of seve
ral industrially relevant yield concepts, recently deployed in single
lot-sizing models with random yields, have not yet been explored in th
e multiple lot-sizing setting. Owing to the growing importance of prod
uction to order of custom-made products, the multiple lot-sizing probl
em is perhaps more important today than ever before. This paper highli
ghts new fundamental problems in this area. The fundamental issues inc
lude monotonicity of run size in setup cost and demand quantity. We al
so provide a method for computing the costs' variance, so that risk/co
st tradeoffs can be performed.