Production to Order with Random Yields: Single-Stage Multiple Lotsizing

Abstract

When production yields are random and orders need to be satisfied in full, several successive production runs may need to be initiated until an order is met. Variants of this multiple lot-sizing production to order problem have long been explored, but some natural fundamental general questions have not been addressed. Also, the consequences of several industrially relevant yield concepts, recently deployed in single lot-sizing models with random yields, have not yet been explored in the multiple lot-sizing setting. Owing to the growing importance of production to order of custom-made products, the multiple lot-sizing problem is perhaps more important today than ever before. This paper highlights new fundamental problems in this area. The fundamental issues include monotonicity of run size in setup cost and demand quantity. We also provide a method for computing the costs’ variance, so that risk/cost tradeoffs can be performed.