© J.C. Baltzer AG, Science Publishers
An efficient heuristic for robot acquisition
and cell formation
Bernard T. Han
a
and Jack S. Cook
b
a
Department of Accounting, Information Systems and Business Laws,
College of Business and Economics, Washington State University,
Pullman, WA 99164-4726, USA
E-mail: hanb@wsu.edu
b
Jones School of Business, 1 College Circle, SUNY – Geneseo,
Geneseo, NY 14454-1401, USA
E-mail: cook@geneseo.edu
In this paper, a mathematical model and a solution algorithm are developed for solving
a robot acquisition and cell formation problem (RACFP). Our model considers purchasing
a proper mix of robots and assigning all given workstations to purchased robots such that
each robot cell satisfies its workstations’ resource demands while minimizing the total system
(acquisition) cost. Specifically, each robot has two capacity constraints – available work
envelope and effective machine time. RACFP is formulated as a multi-type two-dimensional
bin packing problem, a pure 0 – 1 integer program which is known to be NP-hard. In this
paper, a very efficient (polynomial time bound) heuristic algorithm is developed and
implemented. The algorithm consists of two major stages. The first stage employs an LP-
based bounding procedure to produce a tight solution bound, whereas the second stage
repetitively invokes a random search heuristic using a greedy evaluation function. The
algorithm is tested by solving 450 randomly generated problems based on realistic parameter
values. Computational results show that the heuristic algorithm has outperformed algorithms
using general optimization techniques such as Simulated Annealing and Column Generation.
All test problems are solved within an order of magnitude of 10 seconds, with a gap of less
than 1% from the optimum. More importantly, over 70% of all solutions are optimal (334
out of 450). The algorithm can be easily modified for other applications such as file
placement for a multi-device storage system and job scheduling for a multi-processing
system.
1. Introduction
Domestic markets, once secure, are being assailed by a growing number of foreign
competitors producing high-quality products at low prices. Substantial evidence exists
that U.S. industries, world leaders through the 1960s, have over-emphasized product
Annals of Operations Research 77(1998)229 – 252 229