Single- and multi-objective facility layout with workflow interference considerations

Abstract

The effect of workflow interference is a major concern in facility layout design. Yet, despite the extensive amount of research conducted on the facility layout problem, very little has been done to incorporate interference as part of an overall approach to layout design. This paper examines the impact of workflow interference considerations on facility layout analyses. Linear and nonlinear integer programming formulations of the problem are presented. The structural properties of the resulting formulations, as applied to facility design, are investigated. Finally, a multi-objective approach to facility layout design is presented, incorporating the traditional distance-based objective with that of workflow interference.

Introduction

An extensive amount of research has been conducted on the facility layout problem, much of it based on the quadratic assignment problem (QAP) formulation. The QAP objective is to minimize the distance-based transportation cost expressed as the product of the quantity of workflow and the distance traveled. Since Lawler (1963) and Gilmore (1962) developed optimal solution procedures for the QAP, many heuristics have been developed due to the difficulty in finding the optimal solution to this problem, and several alternative approaches have been examined (for recent reviews of the QAP literature, see Rendl, 2002, Hahn, 2004). From a facility-layout perspective, a variety of applications and alternative formulations have also been investigated; however, relatively little has been done to incorporate workflow interference in facility layout design.

Several authors have identified workflow interference as a major concern in traditional facility layout design. Tompkins and White (1984) discussed the importance of minimizing interruptions on flow paths and recognized that the effect of interruptions results in congestion and undesirable intersections. Apple (1972) acknowledged the need to arrange equipment to optimize materials flow and suggested we “be aware of cross traffic and take necessary precautions. Avoid traffic jams”. Luggen (1991) also noted the benefits of eliminating complex material flow patterns, stating “complex material flow patterns create extensive part move and queue time, result in lost or misplaced parts, and contribute to damaged parts due to excessive movement”.

Workflow interference is also a problem with automated manufacturing systems. Concerning automated guided vehicle systems (AGVS), Egbelu and Tanchoco (1986) noted that there is a “problem of traffic control at intersections”, such that a significant amount of cross traffic can result in considerable delays. Krishnamurthy et al. (1993) also recognized the importance of conflict-free routes on the static routing problem for an AGVS. An excessive amount of cross traffic can also impact the initial cost of an automated manufacturing system, either through the need for more complex traffic management systems (Miller, 1987), such as buffering areas or interchange ramps, or through the cost of acquiring control software to manage intersection activities (Egbelu and Tanchoco, 1986). If the number of intersections at which conflict could occur can be minimized as well as minimizing the interference at those intersections that are necessary, the cost of the system can obviously be reduced.

The minimization of interference between pairs of “facilities” is important in other types of layout analyses as well. For example, in the layout design of multilayer IC technology, the overlap of wires between the nets (a set of terminals on the devices to be connected) is not allowed. If the devices are located in such a manner that results in a crossing (interference), the connection would be made by routing it through another layer of the IC. Therefore, we want to place the nets in such a manner to minimize the number of vias (points connecting the different layers) as they increase the fabrication cost and degrade system performance (Cong et al., 1993).

To illustrate the effect of conducting a layout analysis that fails to account for workflow interference, consider an eight-department example with the workflow matrix shown in Fig. 1. The solution to this problem using traditional layout analyses (the quadratic assignment problem is solved using Euclidean distances) is provided in Fig. 1a. While this layout arrangement will minimize the total distance traveled, it is obvious that there are several points at which workflow interference could occur. An alternative layout (Fig. 1b) can provide a workflow in which there are no conflicting workflows. As shown in this figure, the flow pattern is considerably less congested, with more of a uni-directional flow clockwise from facility 6 to facility 2, resembling the U-shaped layout advocated by many researchers and practitioners (e.g., Sekine, 1992, and Miltenburg and Wijngaard, 1994, identify several advantages of using U-lines).

Recently, Chiang et al. (2002) modeled workflow interference in facility layout design as a quartic assignment problem, and developed a branch-and-bound procedure and a tabu search heuristic to solve the problem. The term “quartic assignment problem” was used since the objective function is a fourth-degree polynomial function of the variables and the constraints are those of the assignment problem. Assignment problems with fourth-degree polynomial objectives were discussed by Lawler (1963); however, they were not presented in the context of the minimization of workflow interference. It has also been noted that this type of problem arises in the area of VLSI synthesis (Burkard et al., 1994, Burkard and Çela, 1995). A related problem models congestion in facility layout design through the use of queueing networks (Benjaafar, 2002), measuring congestion by the amount of work-in-process in the system in lieu of workflow interference.

The paper is organized as follows. In Section 2, we analyze the structural properties of the quartic assignment problem (QrAP) as applied to facility design. In Section 3, the problem is also modeled as a modified quadratic assignment problem (MQAP) as an alternative to the quartic formulation. A multi-objective approach to facility design is presented in Section 4 by integrating the quadratic and quartic assignment problems; in particular, we focus on identifying an efficient frontier for the two objectives. We conclude with a summary of the research in Section 5.