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The sequential production of identical jobs and the flow-shop machine setting are extremely common in real-life applications. We study a scheduling problem that combines these two elements: jobs of identical processing time, with job-dependent weights, and a given common due date processed on an m-machine flow-shop. The (just-in-time) objective is to minimize the maximum earliness/tardiness cost. We introduce a polynomial time solution in both cases of (i) a non-restrictive (ie, sufficiently large) due date, and (ii) a restrictive due date (which restricts the number of early jobs). Keywords: scheduling; flow-shop; just-in-time

The basic production model of economic order quantity states that set-up costs create inventory and make batch production efficient. Zero inventory (ZI) is another production efficiency model, also known as just-in-time inventory control. ZI proposes reducing inventory to a minimum. The prevailing belief is that by reducing set-up, inventory and costs are reduced, but results of this study suggest the opposite. Reducing set-up costs does not necessarily entail reducing inventory, or total production and inventory costs. Set-up cost reduction in fact does the opposite, producing marginally increasing, not decreasing, returns. By analyzing certain ZI concepts with mathematical models, it is shown that the ZI concept is sometimes valid and sometimes not.