Exploiting Virtual Elasticity of Manufacturing Systems to Respect OTD—Part 2: Post-Optimality Conditions for the Cases of Ergodic and Non-Ergodic Order Rate with Deterministic Product-Mix

Respecting the on-time delivery (OTD) for manufacturing orders is mandatory. However, for non-JIT Batch & Queue Push-manufacturing systems, the compliance of OTD is not intrinsically guaranteed. As an OTD related manufacturing theory is largely missing it is crucial to understand and formalize the necessary conditions of OTD compliance for complex production environments for maximum exploitation of the production capacity. This paper evaluates the conditions of post-optimality while being OTD compliant for production systems, which are characterized by stochastic order rate and a deterministic product-mix. Instead of applying discrete event simulation to explore the real case-by-case order scheduling optimization for OTD compliance, a Cartesian approach is followed. This enables to define theoretically the solution space of order backlog for OTD, which contributes to developing further manufacturing theory. At the base stands the recently defined new concept of virtual manufacturing elasticity by reducing lead-time to increase virtually production capacity. The result has led to defining additional two corollaries to the OTD theorem, which sets up basic OTD theory. Apart from defining the post-optimal requirements to guarantee for orders at least a weak solution for OTD compliance, this paper reveals that for a deterministic product-mix a non-ergodic order arrival rate can be rescheduled into an ergodic order input rate to the shopfloor if the virtual elasticity T is large enough, hence the importance of having fast and flexible production lines.