Cell formation using modular-reconfigurable machines.
Pattanaik, L.N. ; Jain, P.K. ; Mehta, N.K. 等
Abstract: In this research, an approach is made to design machine
cells using modular-reconfigurable machines to achieve certain
characteristics of reconfigurable manufacturing. Each machine considered
in the model consists of some basic and auxiliary machine modules. By
changing the auxiliary modules, different operations can be performed on
the machines. A similarity measure among machines based on production
flow information and auxiliary module requirement is developed. Machine
cells are identified using a multi-objective evolutionary genetic
algorithm for a set of parts with parameters like volumes of production,
alternative operation-based process plans etc. The two objectives
considered are minimization of inter-cell movement and total changes in
auxiliary modules for the given production horizon. An illustrative
problem and experimental results are given.
Key words: Cell Formation, Modular-Reconfigurable machines,
Multi-objective Genetic Algorithm
1. INTRODUCTION
In a Cellular Manufacturing System (CMS) machines are grouped into
several cells, where each cell is dedicated to a particular part family
and objective is to maximize the cell independence. CMS helps in
reducing the material handling, work-in-process, set up time, and
manufacturing lead-time and improve productivity, operation control etc.
However, CMS lacks in flexibility and thus cannot respond appropriately
to the variations in part design and quantity. Once machine cells are
formed for part families, it is difficult to physically relocate the
facilities of the cell as per the new production requirements. This
rigidness prevents CMS to cope with present challenges like dynamic part
mix and demand variation, need of agility in manufacturing, reduction in
manufacturing system lead-time etc. The focus of this work is also to
enable cellular manufacturing attain some degrees of adaptability or
reconfigurability during cell design by using modular machines. The need
to find some ways to reconfigure cellular systems to reduce or even to
eliminate performance deterioration under dynamic environments was
opined in Saad (2003). Further, in order to have a CMS with features of
a Reconfigurable Manufacturing System (RMS); machine-clustering
algorithm used during cell formation can be a suitable stage for
incorporating reconfigurability into the system (Abdi and Labib, 2003).
No model of CMS was found taking reconfiguration issue during the cell
design stage. The model proposed here considers reconfigurable machines,
which consists of basic and auxiliary modules. The basic modules are
structural in nature like base, columns, slide ways, tables and
auxiliary modules are kinematical or motion-giving like spindles, tool
changers etc. A particular combination of different basic and auxiliary
modules gives a particular operational capability to the machine.
The objective of the present model is to improve the performance of
a CMS under dynamic conditions by attaining reconfiguration
capabilities. To achieve this, an objective function is defined to
minimize the total changes in auxiliary modules, in the multi-objective
optimization problem solved using a Non-dominated Sorting Genetic
Algorithm (NSGA) (Srinivas and Deb, 1994). Other objective function
minimizes inter-cell material movements. In the following sections,
definitions of the machine-operation compatibility, similarity measures
and mathematical formulations, evolutionary nondominated sorting genetic
algorithm as applied to the present problem, an illustrative problem
with optimization and simulation results are given.
2. MACHINE-OPERATION COMPATIBILITY
A Machine-Operation Compatibility Matrix (MOCM) is formed from the
data related to the module requirements as shown in Fig. 1. The non-zero
elements of MOCM are the normalized rating factor [[alpha].sub.im]
(rating factor of performing operation 'i' on machine
'm') and are calculated using equation (1).
[FIGURE 1 OMITTED]
[[alpha].sub.im] = ([t.sup.m.sub.a] -
[ti.sup.m.sub.a]/[t.sup.m.sub.a]([o.sub.m] - 1) (1)
Where, [t.sup.m.sub.a]: Total number of auxiliary modules that are
used by machine m, [ti.sup.m.sub.a]: Number of auxiliary modules
required by machine m for operation i, [o.sub.m]: Number of operation
types machine m can perform.
The lesser the number of auxiliary modules required on a machine
for an operation, the higher the rating factor for that operation and
vice-a-versa.
3. OBJECTIVE FUNCTIONS
The operation rating factors on machines discussed in the previous
section along with some more measures are used to define two objective
functions for the cell design problem. The first objective is to
minimize the total changes in the auxiliary modules by maximizing the
similarity measure among machines of each cell and the second objective
is to minimize the inter-cellular movements by maximizing the operation
diversities of the cells. As these two objectives are in conflict with
each other, the cell design problem has been formulated as a
multi-objective problem to get the best results. The first objective
function defined as in equation (2), maximizes the similarity among the
total M machines of the C numbers of the cells. The similarity measure
between machines m and n ([A.sub.mn]) is based on manufacturing
parameters like operation sequence, production volume of parts and
rating factor of performing an operation on a machine. When machine
cells are formed based on maximization of the sum of similarity measures
of machines in each cell, the total changes in the auxiliary modules for
the planned production horizon becomes minimum, because machines with
better rating factor to perform an operation can be selected for parts
having higher production volume.
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
This objective function is in conflict with second objective as
given in equation (3), which minimizes the inter-cellular movements by
maximizing the operation diversity among the machines of each cell.
[F.sub.2] = [C.summation over (c=1)] [D.sub.m(c)][for all]m(c)[not
equal to][phi] (3)
Where [D.sub.m(c)] is the operation diversity measure of a cell c
found by dividing the cardinality (number of elements) of the union of
sets of operation types that can be performed by machines in the cell
with the total number of operation types.
4. AN EXPERIMENT
A data set of 10 parts using 13 operation types with a minimum of 3
and maximum of 6 operations per part and 10 machines is taken as a
hypothetical test problem (Refer Table 1).
Corresponding to each possible cell configuration that satisfies
the size constraints of maximum four and minimum two machines per cell a
set of Pareto-optimal solutions are obtained implementing NSGA. A set of
the non-dominated solutions on the Pareto-optimal front is presented in
Table 2 for a 4-4-2 configuration of the 10 machines. The strings with
10 genes representing the ten machines to be grouped are implemented
with an initial population size of 100. Selections are based on the
shared fitness values of the chromosomes and during reproduction the
probabilities of crossover and mutation are taken as 0.8 and 0.1
respectively as found suitable from the several experiments conducted on
converging the search to the Pareto front. The number of generations
used during the search is 500. Each solution represents a potential
solution to the cell design problem with the associated fitness values
as shown in the same table.
From these solutions, the decision-maker is required to select a
solution on the basis of fitness values indicated for the two criteria.
Consider a solution (3112312221) representing machine groups (2, 3, 6,
10), (4, 7, 8, 9), and (1, 5) from the sample of non-dominated solutions
as given in Table 2. A static and discrete simulation model is developed
using ProModel[R] software package to find exactly the numbers of
inter-cell movements and the total numbers of changes in auxiliary
modules to produce the given set of part types. In the simulation model,
replicas of machines are used to represent their multi-operation
capabilities.
During the simulation of part's production, a selection logic
is applied to the alternative process plans to minimize inter-cell
movement. Hence alternative process plans for parts are compared in
terms of cell dependence and the best one is selected. Once a process
plan is selected on this basis then the corresponding part uses this and
the total inter-cell movements and changes in auxiliary modules required
are obtained. For the taken solution of (3112312221), the Total
Inter-Cell Movements (TICM) and Total Module Changes (TMC) are found to
be 2475 and 156 respectively.
5. CONCLUSION
The research issue discussed here is a new approach to form machine
cells in cellular manufacturing systems. For grouping
modular-reconfigurable machines capable of performing multiple
operations, a multi-objective evolutionary algorithm with two
conflicting objectives are formulated based on some defined measures
from several production parameters, machine-operation compatibility and
alternative process plans is proposed. As a non-dominated sorting
genetic algorithm is adopted, more than one optimal solutions result,
that gives opportunity to observe the relative performance of resulting
cell configurations and it can be extremely favorable to the
decision-maker in selecting cell sizes as well as configurations.
6. REFERENCES
Abdi, M. R. and Labib, A. W. (2003). A design strategy for
reconfigurable manufacturing systems (RMSs) using analytical
hierarchical process (AHP): a case study, International Journal of
Production Research, 41, 2273-2299.
Saad, S. M. (2003). The reconfiguration issues in manufacturing
systems, Journal of Materials Processing Technology, 138, 277-283.
Srinivas, N. and Deb, K. (1994). Multi-objective function
optimisation using non-dominated sorting genetic algorithm, Evolutionary
Computation, 2 (3), 221-48.
Table 1. Alternative process plans and demands for the parts
Parts Process Operation-based Demand
Plans process plans
1 1 3-6-8-11-12 60
2 3-11-12-8-11
2 1 7-1-10-12 350
2 10-11-1-7-10
3 1 2-4-6-2-8 550
2 4-6-8-2-13-4
4 1 3-5-9-12 120
2 3-9-12-9
5 1 5-7-10-13-1 320
2 7-5-1-10-5
6 1 2-7-12 75
2 2-12-10
3 2-10-2
7 1 4-9-11-13-8 400
2 11-13-8-11-4
8 1 3-7-11-5 205
2 7-5-11-5
9 1 1-3-8 45
10 1 7-8-12-2-12 175
2 8-2-9-12
Table 2. Set of Pareto-optimal solutions for 4-4-2 configuration
Pareto-optimal
Solution solution [F.sub.1] [F.sub.2]
1 1 2 1 3 2 2 2 1 1 3 5.065 1.769
2 1 1 1 2 2 2 3 1 2 3 5.123 1.692
3 2 2 1 2 3 1 3 1 1 2 5.702 1.538
4 3 2 1 3 1 2 2 1 1 2 4.983 1.923
5 1 1 3 2 2 2 2 1 1 3 4.485 2.000
6 2 2 1 2 1 3 3 1 1 2 5.234 1.692
7 2 1 1 2 3 1 3 1 2 2 5.532 1.538
8 3 1 1 2 3 1 2 2 2 1 6.139 1.461
9 1 1 1 2 3 2 3 1 2 2 4.992 1.846
