Here, an attempt is made to present a state-of-the-art review of papers on facility layout problems. This paper aims to deal with the current and future trends of research on facility layout problems based on previous research including formulations, solution methodologies and development of various software packages. New developments of various techniques provide a perspective of the future research in facility layout problems. A trend toward multi-objective approaches, developing facility layout software using meta-heuristics such as simulated annealing (SA), genetic algorithm (GA) and concurrent engineering to facility layout is observed.

A review of different approaches to the facility layout problems

An example of the quadratic assignment problem QAP is the facility location problem, in which n facilities are assigned, at minimum cost, to n sites Between each pair of facilities, there is a given amount of flow, contributing a cost equal to the product of the flow and the distance between sites to which the facilities are assigned Proving optimality of QAPs has been limited to instances having fewer than 20 facilities, largely because known lower bounds are weak We compute lower bounds for a wide range of QAPs using a linear programming-based lower bound studied by Z Drezner 1995 On the majority of QAPs tested, a new best known lower bound is computed On 87% of the instances, we produced the best known lower bound On several instances, including some having more the 20 facilities, the lower bound is tight The linear programs, which can be large even for small QAPs, are solved with an interior point code that uses a preconditioned conjugate gradient algorithm to compute the interior point directions Attempts to solve these instances using the CPLEX primal simplex algorithm as well as the CPLEX barrier primal-dual interior point method were successful only for the smallest instances

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Computing Lower Bounds for the Quadratic Assignment Problem with an Interior Point Algorithm for Linear Programming

A multi-phase examination scheduling process applicable to large university settings in general and SUNY at Buffalo (SUNYAB) in particular is proposed. Each scheduling phase is considered an integral part of the overall scheduling process and solved independently. Phase one of scheduling process is wth the assignment of examinations to exam blocks (each containing one or more exams). The objective of this phase is to minimize the number of students taking more than one exam in the same exam block. The problem is solved using a variation of the quadratic assignment problem. Phase two of the scheduling process uses the results from phase one as input. The exam blocks are assigned to exam days in such a way that some measure of students' comfort is maintained. Phase two of the scheduling process is formulated as a set covering problem with an extra constraint. Phase three of the scheduling process which is involved wt h the assignment of exam blocks to exam periods in each day and optimal ordering o...

A Three Phased Approach To Final Exam Scheduling

This paper presents the implementation of a multi-phase final-exam-scheduling package at a large university. The problem as it had evolved over time is discussed and a solution is presented. The implementation was undertaken over a three-year period and involved a multi-phase approach. The multi-phase final-exam-scheduling process consists of first grouping the final exams into sets called `blocks' in such a way as to minimize the number of students with simultaneous exams. Second, the blocks are assigned to exam days while minimizing the number of students with two or more exams per day. Third, the exam days and exam blocks within days are arranged so as to minimize the number of students with consecutive exams. Fourth, exams are assigned to classrooms so as to maximize the space utilization. New formulations and solution methods for the stated four phases are presented. The approach is well suited for a practical application and has been implemented at a large university.

A Final-Exam-Scheduling Package

This paper describes recent experience in tackling large nonlinear integer programming problems using the MINOS large-scale optimization software. A technique is presented for extending the constrained search approach used in MINOS to exploring integer-feasible solutions once a continuous optimal solution is obtained. Computational experience with this approach is described for two classes of problems: quadratic assignment problems and pipeline network design problems.

T.R Jefferson

Papers

A heuristic procedure for solving the quadratic assignment problem