Product grouping for batch processes

This paper considers a production environment in which multiple products produced in a batch process share several facilities, and the products must be grouped (or, equivalently, assigned to facilities) so as to minimize associated inventory carrying costs (an NP-hard problem). The main contributions of the paper are (1) to derive a polynomial-time procedure that computes optimal solutions to an important special case of the problem, (2) to extend the procedure as an heuristic to the more general case, and (3) to demonstrate computationally that the heuristic is remarkably effective in the general case.