Modeling and analysis of congestion in the design of facility layouts

Reducing manufacturing lead times and minimizing work-in-process (WIP) inventories are the cornerstones of popular manufacturing strategies such as Lean, Quick Response, and Just-in-Time Manufacturing. In this paper, we present a model that captures the relationship between facility layout and congestion-related measures of performance. We use the model to introduce a formulation of the facility layout design problem where the objective is to minimize work-in-process (WIP). In contrast to some recent research, we show that layouts obtained using a WIP-based formulation can be very different from those obtained using the conventional quadratic assignment problem (QAP) formulation. For example, we show that a QAP-optimal layout can be WIP-infeasible. Similarly, we show that two QAP-optimal layouts can have vastly different WIP values. In general, we show that WIP is not monotonic in material-handling travel distances. This leads to a number of surprising results. For instance, we show that it is possible to reduce overall distances between departments but increase WIP. Furthermore, we find that the relative desirability of a layout can be affected by changes in material-handling capacity even when travel distances remain the same. We examine the effect of various system parameters on the difference in WIP between QAP- and WIP-optimal layouts. We find that although there are conditions under which the difference in WIP is significant, there are those under which both layouts are WIP-equivalent.