Cost estimation is a fundamental activity of many engineering and business
decisions and normally involves estimating the quantity of labor, materials,
utilities, floor space, sales, overhead, time and other costs for a set series
of time periods. Smith and Mason (1996) and Drury
(1992) used this estimate as inputs to deterministic analysis methods, such
as net present value or internal rate of return calculations, or as inputs to
stochastic analysis methods, such as Monte Carlo simulation or decision tree
analysis. There has also been some interest in applying newer computational
techniques, such as fuzzy logic and artificial neural networks, to the field
of cost estimation. Applying fuzzy techniques to cash flow analysis has been
used successfully. Musilek et al. (2000) discussed
using fuzzy composition to estimate NPV after specifying the membership functions
for future cash flows and Choobineh and Behrens (1992)
compared interval mathematics and fuzzy approaches in cost estimation. A drawback
of the fuzzy approach is that the relationships are developed from qualitative
information of the cost estimating problem, usually elicited from a knowledgeable
person. Fuzzy relationships are not primarily empirical models like regression
and neural networks.
Artificial neural networks are purely data driven models which through training
iteratively transition from a random state to a final model. Sexton
et al. (1999) and Camargo et al. (2003)
showed that they do not depend on assumptions about functional form, probability
distribution or smoothness and have been proven to be universal approximations.
While theoretically universal approximations, there are practical problems in
neural network model construction and validation when dealing with stochastic
relationships, or noisy, sparse or biased data. Camargo
et al. (2003) showed that ANN had some limitations in learning the
patterns because cost data has tremendous noise and complex dimensionality.
Liu and Setiono (1996) discussed that ANN has preeminent
learning ability while it is often confronted with inconsistent and unpredictable
performance for noisy data. In addition, sometimes the amount of data is so
large that the learning of patterns may not work well.
Gupta and Sexton (1999) and Holland
(1992) used the genetic algorithms such as search techniques based on an
analogy with biology in which a group of solutions evolves through natural selection.
Vafari and Jong (1998) showed that a population of randomly
generated candidate solutions evolves to an optimum solution through the operations
of genetic operators consisting of reproduction, crossover and mutation.
This study proposes a new hybrid model of ANN and Genetic Algorithm (GA) for model optimization. Properly data reduction can simplify the process of learning and may improve the performance of the learned results. This study uses GA to search the optimal or near-optimal the connection weights between layers and thresholds in ANN. The simulation results show that the performance of optimized model is higher than conventional ANN. In addition, model creation will be easier and faster.
ARTIFICIAL NEURAL NETWORK
An artificial neural network is modeled as a massively parallel-interconnected
network of elementary processors or neurons. It has been shown that a three-layer
feed forward network can generate arbitrary complex decision regions.
The multi-layered neural networks operate in two modes: Training and testing.
In the training mode, a set of training data is used to adjust the weights of
the network interconnections so that the network responds in a specified manner.
In the testing mode, the trained network is evaluated by the test data. Rumelhart
et al. (1986) used the backpropagation learning algorithm which is
the most frequently used method in training neural. This study uses a three-layer
neural network which is trained by using the error backpropagation (BP) algorithm
which is shown in Fig. 1. The number of neurons in the layers,
termed as input layer, hidden layer and output layer, are determined by experimentation
with an object that the ANN learns and generalizes the situation. Each neuron
of the ANN uses a mapping function. For the studies reported in this paper,
a sigmoid transfer function for neurons between the input and middle layers
and a linear transfer function for neurons between middle and output layers
are used. The sigmoid transfer function maps the neuron input from the interval
(-∞, +∞) into the interval (0, l), i.e.,
The linear transfer function is f (x) = x, which maps the neuron input from the (-∞, +∞) in to the same interval.
GENETIC ALGORITHM APPROACH
Gupta and Sexton (1999) and Holland
(1992) introduced the GAs such as search techniques based on an analogy
with biology in which a group of solutions evolves through natural selection.
In their implementation, a population of randomly generated candidate solutions
evolves to an optimum solution through the operations of genetic operators consisting
of reproduction, crossover and mutation.
Here, a standard GA approach for searching the optimal or near optimal connection weight in ANN model for cost estimation problem is described.
The principal components of the optimization based on standard GA are given below:
Chromosomes: A chromosome can be taken as an array holding a candidate optimization. The connection weights and thresholds are set as elements in the chromosomes.
Fitness function: This is the evaluation function used to calculate the degree of fitness or appropriateness of the candidate solutions. The following fitness function can be used:
where, M is a constant for amplifying the fitness value. The value of H approaches zero towards convergence. To avoid any numerical difficulty that may occur in calculating F and H is augmented by 10-5.
Crossover operation: This is a genetic operation which is responsible
for producing two new candidate solutions from two selected parent chromosomes.
Vafari and Jong (1998) proves that in the present working,
the two-point crossover method is adopted so that more diversity in the population
of chromosomes can be achieved. In this method, two numbers within the length
of the chromosome are randomly generated. The elements between the two numbers
in the two parent chromosomes are swapped to form two new chromosomes.
Mutation operation: An element of a chromosome is randomly selected.
The voltage value of the element is replaced by a value arbitrarily chosen within
a range of voltage values. Using the above components, a standard GA procedure
for solving the load flow problem is summarized below:
Initialize S chromosomes in the population. The elements of a chromosome
are the candidate modal
||Generate the next generation of S chromosomes in the following way
||The next generation formed in step 2 is now taken to be the current generation.
New generations are produced by repeating the solution process starting
from step 2 until the specified maximum number of generations is reached
ACTIVITY BASED COSTING SYSTEM
Innes and Mitchell (1993) divide the Activity Based
Costing (ABC) system to several steps. In a first step, a company's most significant
activities are identified base on the Brimson (1991).
In a second step, overhead costs associated with each of these activities are
determined. Then factors determining the cost of an activity are ascertained
and are referred to as cost drivers which are used to describe the events or
forces that are the significant determinants of the cost of these activities.
Finally, overhead costs per unit cost driver (cost driver rate) are applied
to cost objects. Kaplan (1990) showed that the ABC system
are associated with the hierarchical structure of activities and cost drivers
and consist usually of five levels:
||Activities and cost drivers
ABC techniques have been applied to support new approaches to pricing decisions, profitability analysis and internal performance measurement and cost management.
The design processes in textile printing follows a chronological sequence of steps, starting with the concept design to product process plan definition.
Thus, this dynamic process starts with a set of ideas proposed by the designer
that are classified by a complex evaluation system before the product arrives
to the market as well explained by Moxey and Studd (2000).
The first designer inspiration sources are for example, the intent to create
new forms or the use of elements, coming from the social or natural environment.
At this stage the designer decisions depending mainly on the below factors:
||Aesthetical factors: Color, texture, brightness, touch and pattern
||Functional factors: Isolation, chemical resistance, heat transfer
and dissipation etc.
||Commercial factors: Delay, quality and price
The classical idea is that the designers make choices based only on aesthetical
parameters. But in practice the product definition process takes into account
the economical and functional constraints. For a designer the paradigm of aesthetic
conventions that determine creative solutions within printed fabric design are
constrained by technological and market factors. The creative design must be
new related to the previous collections and must be validated by the members
of the system. For the specific case of the textile printing industry, we have
carried a research study about the process of selecting design. The results
show it is highly speculative and could take and the financial investment is
extremely high in comparison to the potential product commercial success.
Unfortunately, all the esthetical paradigms and customer requirements are explicit only in part until the product freeze point, when a lot of time has passed it could take between three and four months. Thus, makes very important to have reliable economical evaluation of the product changes in the phase when the product is being defined. For the manufacturers in that kind of highly dynamic environment the product development implies to react as soon as possible to customer requirements and at the same time to optimize the capital investment. In fact, the product total cost depends on several components related to the direct and indirect cost. The time and resources spent in the product development process, the technological capabilities (production infrastructure, human knowledge and skills) and of course the product features. The combination of those factors results in a specific product cost.
Following an experimental research and the considerations in for the textile
printing industry, we have treated a database in order to obtain an accurate
cost model but more easily interpretable than models obtained from others modeling
techniques. Moxey and Studd (2000) introduced the methods
of creativity in the Development of Fashion Textiles. In the textile industry
unfortunately, all the esthetical paradigms and customer requirements are explicit
only in part until the product freeze point, when a lot of time has passed it
could take between three and four months. Thus, make very important to have
reliable economical evaluation of the product changes in the phase when the
product is been defined. For the manufacturers in that kind of highly dynamic
environment the product development implies to react as soon as possible to
customer requirements and at the same time optimize the capital investment.
The results show that the accuracy of the simplified model (BPLT) remains acceptable compared with the optimized neural network model. In this case, we define 4 input parameters to estimate the cost of product.
of the auxiliary parameters
average predictive accuracy for BPLT and optimized ANN models
||No. of pattern
||No. of fabric color
||No. of pattern color (complexity)
Linear transformation with the back propagation neural network (BPLT) and the
linear transformation with ANN trained by GA is simulated using Matlab software.
We defined four auxiliary parameters to calculate the performance of each model.
Daniel-Ramirez et al. (2004) introduced auxiliary
parameters which are shown in Table 1.
To compare the performance of the models, we calculate the below parameters:
||Recall rate or sensitivity
Two models are compared according to the methods of determining the connection weights and feature transformation. Figure 2 describes the average prediction accuracy of each model for 10 different types of products.
In Fig. 2, the optimized model has higher prediction accuracy than BPLT by 8≈11% for the training data. It is a mistake to compare the prediction accuracy between the training data and holdout data. There is a wide difference between the training data and the holdout data for the two models. This result may be caused by the fact that the globally searched discretization simplifies the learning process and eliminates the irrelevant patterns. This prevents the network from falling into the problem of over fitting. We also find that the average prediction performances of BPLT and Optimized model are similar. The reasons for this result may be summarized in two points. First is that there is a generic limitation of global search algorithms. Although, a global search is more desirable than a local search for learning ANN, sometimes a local search is also needed. The other factor may be a problem is dimensionality in data. The GA is a global search algorithm; however, financial data including the stock market data is too complex to be searched easily. It is necessary to reduce the dimensionality of data and irrelevant factors before searching.
In this research, a novel ANN model is proposed and simulated. The connection weights and thresholds are optimized with genetic algorithm. The GA searches for the optimal or near-optimal solutions of connection weights in the learning algorithm. Experimental data for the textile printing industry have provided a database in order to obtain an accurate cost model. Four auxiliary parameters were defined to calculate the performance of models. The performance of the optimized model is higher than BPLT and conventional models. The optimized model has higher prediction accuracy than BPLT by 8≈11% for the training data.
The authors would like to acknowledge the active participation and financial support of the Management Faculty of Tehran University.