This paper considers the multi-product dynamic Lot-size model with individual and joint setup costs. An extremely simple extension of the Silver Meal heuristic for single product problems is given. The main contribution, however, of the paper is to describe a methodology for finding lower bounds on the (unknown) optimum, using information from the heuristic. This gives an a posteriori performance guarantee on the heuristic. Both the Bound and heuristic are linear in the number of time periods. Computational experience on realistically sized problems 30 products, 24 periods) show performance usually within 5% of the (unknown) optimum.
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Atkins et al. (1988) studied this question.