Performance evaluation of small-batch container delivery systems used in lean manufacturing - Part 1: system stability and distribution of container starts

In lean manufacturing, milk run (MR) systems represent route-based, cyclic material-handling systems that are used widely to enable frequent and consistent deliveries of containerised parts on an as-needed basis from a central storage area (the 'supermarket') to multiple line-side deposit points on the factory floor. MR systems generally result in short lead times, low variability, and low line-side inventory levels. In the first part of this two-part paper, a basic, single-tugger MR system is described. Stability conditions are derived with respect to the 'physical capacity' of the tugger, and the 'time utilisation' of the driver/material handler, both of which are key criteria since the number of containers that can be delivered during each MR is limited, and each MR targets a prescribed cycle time to ensure timely and consistent deliveries. We also derive the distribution of the number of containers requested per MR, which allows the model to estimate the probability of exceeding the physical capacity of the tugger or the prescribed cycle time, under the assumption that sufficient kanban are available for each part type delivered by the MR system. The results of the study facilitate the design and analysis of MR systems used in industry.