Russell D. Meller

The facility layout problem: Recent and emerging trends and perspectives

Abstract Recent and emerging trends in the facility layout problem, covering the last 10 years of research, are presented, including new methodologies, objectives, algorithms, and extensions to this well-studied combinatorial optimization problem. The state of the art in facility layout software is compared to the state of the art in facility layout research. New developments in emerging layout research provide a perspective on what the future of the field will be like. A trend toward concurrent engineering approaches to layout and production system design is observed.

The interaction of location and inventory in designing distribution systems

Many companies face the strategic decision of deciding on the number of Distribution Centers (DCs), their location, and which customers they serve. One objective for a company facing this decision is to maintain acceptable service while minimizing the fixed costs of operating the DCs, inventory holding costs at the DCs, and transportation costs between plants and DCs, and DCs and customers. For insight into this problem, we develop an analytical model for a stylized version of it. However, since the general version of the problem is NP-Hard, we also develop heuristic procedures. We solve a variety of example problems to test the performance of these heuristics relative to optimal solutions and a lower bound based on a relaxation of the original problem. Managerial insight based on our computational studies is provided. We also present a small case-study example motivated by our interaction with Frito-Lay, Inc.

Optimal facility layout design11This study was supported in part by an Auburn College of Engineering infrastructure award made to Drs. Meller and Vance, and NSF CAREER Grants DMII 9623605 and DMII 9502502.

The facility layout problem (FLP) is a fundamental optimization problem encountered in many manufacturing and service organizations. Montreuil introduced a mixed integer programming (MIP) model for FLP that has been used as the basis for several rounding heuristics. However, no further attempt has been made to solve this MIP optimally. In fact, though this MIP only has 2n(n-1) 0-1 variables, it is very difficult to solve even for instances with n~5 departments. In this paper we reformulate Montreuils model by redefining his binary variables and tightening the department area constraints. Based on the acyclic subgraph structure underlying our model, we propose some general classes of valid inequalities. Using these inequalities in a branch-and-bound algorithm, we have been able to moderately increase the range of solvable problems. We are, however, still unable to solve problems large enough to be of practical interest. The disjunctive constraint structure underlying our FLP model is common to several other ordering/arrangement problems; e.g., circuit layout design, multi-dimensional orthogonal packing and multiple resource constrained scheduling problems. Thus, a better understanding of the polyhedral structure of this difficult class of MIPs would be valuable for a number of applications.

Enhanced Model Formulations for Optimal Facility Layout

This paper presents an improved mixed-integer programming (MIP) model and effective solution strategies for the facility layout problem and is motivated by the work of Meller et al. (1999). This class of problems seeks to determine a least-cost layout of departments having various size and area requirements within a rectangular building, and it is challenging even for small instances. The difficulty arises from the disjunctive constraints that prevent departmental overlaps and the nonlinear area constraints for each department, which existing models have failed to approximate with adequate accuracy. We develop several modeling and algorithmic enhancements that are demonstrated to produce more accurate solutions while also decreasing the solution effort required. We begin by deriving a novel polyhedral outer approximation scheme that can provide as accurate a representation of the area requirements as desired. We also design alternative methods for reducing problem symmetry, evaluate the performance of several classes of valid inequalities, explore the construction of partial convex hull representations for the disjunctive constraints, and investigate judicious branching variable selection priority schemes. The results indicate asubstantial increase in the accuracy of the layout produced, while at the same time providing adramatic reduction in computational effort. In particular, three previously unsolved test problems from the literature for which Meller et al.s algorithm terminated prematurely after 24 cpu hours of computation (on a SUN Ultra 2 workstation with 390 MB RAM) with respective optimality gaps of 10.14%, 26.45%, and 40%, have been solved to exact optimality with reasonable effort using our proposed approach.

A new simulated annealing algorithm for the facility layout problem

In this paper we present an application of simulated annealing to facility layout problems with single and multiple floors. The facility layout problem is highly combinatorial in nature and generally exhibits many local minima. These properties make it a suitable candidate for simulated annealing. Using a new candidate layout generation routine and spacefilling curves, we develop an improvement-type layout algorithm based on simulated annealing that considers an expanded set of department exchanges. The resulting algorithm achieves low-cost solutions that are much less dependent on the initial layout than other approaches. We compare the performance of the simulated-annealing based algorithm with both steepest-descent and randomized approaches from the literature. Unlike other simulated annealing papers which typically present a statistical experiment to evaluate the effect of numerous control settings, all the experiments presented in this paper were conducted with control settings that are constant or e...

The impact of preventive maintenance on system cost and buffer size

Abstract In this paper we consider a system with two production operations (typically machines) and a buffer between them. Our objective is to determine the optimal buffer inventory level, b ∗ , that triggers preventive maintenance on the first production operation. We assume that periodic preventive maintenance will, in the long run, decrease the first production operations failure rate. A cost model for the system is specified that includes the costs of preventive maintenance and unscheduled repairs, starving the second production operation, and inventory. The cost model is dependent on the values of performance measures that are a function of b ∗ , which defines the preventive maintenance policy. We model the stochastic buffer content process of this system and obtain the performance measures with an embedded absorbing Markov chain analysis. Under certain scenarios, the implementation of the preventive maintenance program is shown to decrease the system cost and the output process variation. Furthermore, our model can be used to indicate oversized buffers in such an environment.

Aisle configurations for unit-load warehouses

Unit-load warehouses are used to store items—typically pallets—that can be stowed or retrieved in a single trip. In the traditional, ubiquitous design, storage racks are arranged to create parallel picking aisles, which force workers to travel rectilinear distances to picking locations. We consider the problem of arranging aisles in new ways to reduce the cost of travel for a single-command cycle within these warehouses. The proposed models produce alternative designs with piecewise diagonal cross aisles, and with picking aisles that are not parallel. One of the designs promises to reduce the expected distance that workers travel by more than 20% for warehouses of reasonable size. We also develop a theoretical bound that shows that this design is close to optimal.

Multi-shuttle automated storage/retrieval systems

Multi-shuttle automated storage/retrieval systems have been developed for use in factories and distribution centers because they are more efficient than single-shuttle systems (owing to less empty travel). This improved efficiency results in more agile support (flexible response, less waiting time, etc.) for the production system the storage/retrieval system serves. In this paper we develop analytical models to estimate the throughput in multi-shuttle systems. Throughput improvements greater than 100% are illustrated when triple-shuttle systems are compared with single-shuttle systems.

The effects of pick density on order picking areas with narrow aisles

The cost and service performance of an order fulfillment center are determined partly by how workers are organized into an order picking system. One common approach is batch picking, in which workers circumnavigate a picking area with other workers, gathering items on a pick list. In some systems with high space utilization, narrow aisles prohibit workers from passing one another when in the same aisle, and this leads to congestion. We build analytical and simulation models of these systems to investigate their behavior under different levels of activity. Among other things, our results suggest that when the system is busier and pick density is high (that is, when workers stop often to make picks) congestion is less of a problem and workers are more productive.

Applying the sequence-pair representation to optimal facility layout designs

We present a new formulation for the facility layout problem based on the sequence-pair representation, which is used successfully in VLSI design. By tightening the structure of the problem with this formulation, we have extended the solvable solution space from problems with nine departments to problems with eleven departments.