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-inTime 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-inprocess (WIP). In contrast to some recent research, we show that layouts obtained using a WIPbased 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.