Introduction
Because of today's strong competition, most manufacturing organizations continually try to increase their profits and reduce their costs. Accurate sales forecasting is certainly an inexpensive way to meet these goals because it leads to improved customer service, reduced lost sales and product returns, and more efficient production planning (Doganis et al., 2006). Forecasting future demand is central to the planning and operation of retail business at the macro and micro levels. At the organizational level, forecasts of sales are essential inputs to many decision activities in various functional areas such as marketing, sales, production/ purchasing, as well as finance and accounting (Mentzer & Bienstock, 1998). Sales forecasts also provide a basis for regional and national
distribution and replenishment plans. The importance of accurate sales forecasts for efficient inventory management has long been recognized. In addition, accurate forecasts of retail sales can help improve retail supply chain operations, especially for larger retailers who have a significant market share. For profitable retail operations, accurate demand forecasting is crucial in organizing and planning purchasing, production, transportation, and labor force, as well as after-sales services (Zhang, 2009).
In a traditional supply chain, each player has different objectives that conflict with each other. Many times inventory-related decisions are taken without considering the impact of the decisions on other parties in the supply chain, ultimately resulting in chaos and
Multi-criteria decision-making tools assist the decision maker in evaluating the available alternative resources. This article presents the results of a study in which forecasts were made using non-traditional forecasting methods. Various supply chain cost elements were considered for analysis. A comparison was made using multi-criteria decision-making tools. Three tools, namely TOPSIS, MAPPAC, and ELECTRE, were used for evaluation. It was found that the decision taken on the basis of
evaluation assists the organization in saving money and improving profitability significantly.
Keywords: forecasting, nontraditional forecasts, supply chain costs
Comparison of Neural
Network-Based
Forecasting Methods
Using Multi-Criteria
Decision-Making Tools
Atul B. Borade
Jawaharlal Darda Institute of Engineering and Technology, Yavatmal, India
Satish V. Bansod
Professor Ram Meghe Institute of Research and Technology, Bandera, India
© Copyright BEM ISSN print 1625-8312 ISSN online1624-6039
An International Journal
uncertainty (Kiesmuller & Broekmeulen, 2010). Every supply chain manager has to make multiple decisions. Making a forecast of demand is one of those crucial decisions. An error in the forecast can cost an organization too much. For larger firms, the forecast is predicted on the basis of shared data. An ERP (Enterprise Resource Planning) or any other EDI (Electronic Data Interchange) system is adopted for the purpose. However, for small organizations it is not economical to use these systems (Borade & Bansod, 2009a, 2009b). In small enterprises, supply chain managers have to rely on various traditional or nontraditional methods for demand prediction. From the literature, it is found that researchers have used neural network capacities fully to predict future sales. In many studies neural networks along with fuzzy logic, genetic algorithm, and traditional models are used for forecasting. This research extends the work of Borade and Bansod (2011), in which forecasts were made using various neural network models and performance was measured on accuracy parameters. In this article, forecasts are compared on the basis of costs and profits derived from various neural networks. TOPSIS along with MAPPAC and ELECTRE were applied to compare and select the best forecast.The acronym TOPSIS stands for Technique for Order Preference by Similarity to the IdealSituation. MAPPAC stands for Multi-criterion analysis of preferences by means of pairwise actions and criterion comparisons. ELECTRE methods (ELimination and Choice Expressing the Reality ) can be used in choosing efficient strategies that account for human behavioral resistance and technical elements.
Literature Review
A great deal of literature is available on the application of neural networks in sales forecasting. In this section we present recent studies that use artificial neural networks in sales forecasting. Yu et al. (2011) show that Artificial Neural Network (ANN) models are
more efficient and effective than many traditional statistical forecasting models. Despite the reported advantages, it is relatively more time-consuming for ANN to perform forecasting. In this article, a new model that employs the extreme learning machine (ELM) and traditional statistical methods was proposed. Experiments with real data sets were conducted. A comparison with other traditional methods has shown that this ELM fast forecasting (ELM-FF) model is quick and effective. Efendigil et al. (2009) proposed a new forecasting mechanism that is modeled by artificial intelligence approaches including the comparison of artificial neural networks and adaptive network-based fuzzy inference system techniques to manage the fuzzy demand with incomplete information. The effectiveness of the proposed
approach to the demand
forecasting issue was demonst-rated using real-world data from a company that is active in the durable consumer goods industry in Istanbul, Turkey.
According to Doganis et al. (2006), for the food industry, successful sales forecasting systems can be very beneficial because of the short shelf life of many food products and the importance of the product quality being closely related to human health. The study presented a complete framework that could be used for developing nonlinear time series sales forecasting models. The method was a combination of two artificial
intelligence technologies, namely, the radial basis function (RBF) neural network architecture and a specially designed genetic algorithm (GA). The methodology was applied successfully to sales data of fresh milk provided by a major manufacturing company of dairy products. Chen and Ou (2009) argued that managing convenience stores, making the right decision in placing a balanced order, is a critical job that can enhance the competition of the corporation, especially for perishable foods. In this study, the GMFLN forecasting model (Gray-relation-analysis-multilayer-functional-link-network) integrates a Gray relation analysis (GRA), which sieves out the more influential factors from raw data then transforms them as the input data in the multilayer functional link network model to provide the more accurate forecasting results to support decisions. The proposed system evaluated the real data, which are provided by a famous franchise company, and the experimental results indicated the GMFLN model outperforms other time series forecasting models, for example, the moving average model, the Auto Regressive Integrated Moving Average
(ARIMA) model, and the
Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model in the Mean Absolute Deviation (MAD) and THEIL indexes (TI) (Used for measuring disproportionality). Few researchers applied ANNS for printed circuit board (PCB) sales forecasting. For example, Chang et al. (2009) developed a hybrid model by integrating K-mean cluster and fuzzy neural network (KFNN) to forecast the future sales of a printed circuit board factory. Based on the K-mean clustering technique, the historical data were classified into different clusters. The accuracy of the forecasted model was further improved by referring the new data to be forecasted from a more focused region. Numerical data of various affecting factors and actual demand of the past five years of the PCB factory was collected as input to the hybrid model for future
Making a forecast
of demand is one
of those crucial
decisions. An error
in the forecast can
cost an organization
monthly sales forecasted. The experimental results derived from the proposed model showed the effectiveness of the hybrid model when compared with other approaches. In their previous research Chang et al. (2005) developed an evolving neural network (ENN) forecasting model by integrating genetic algorithms and a neural network. Along with trend and seasonal factors considered by Winter's model, effective economical factors were chosen by the grey relation analysis. The numerical data of these factors and actual demand of the past five years were taken as an input into the training stage of ENN, whereas the comparison with other models was evaluated on a testing stage. The experimental result showed that the performance of ENN is superior to traditional statistical models and the back propagation network. The ENN provided a promising solution to the forecasting problem for relevant industries. Chang and Wang (2006) integrated fuzzy logic and an artificial neural network into the fuzzy back propagation network (FBPN) for sales forecasting in the PCB industry. The fuzzy back propagation network was constructed to incorporate production control expert judgments in enhancing the model's performance The proposed system was evaluated through the real-world data provided by a printed circuit board company, and experimental results indicated that the fuzzy back propagation approach outperforms other forecasting models in MAPE
measures (Mean Absolute
Percentage Error).
Few hybrid approaches are also seen in research. Wong and Guo (2010) developed a hybrid intelligent (HI) model, comprising a data preprocessing component and an HI forecaster, to tackle the medium-term fashion sales forecasting problem. The HI forecaster first adopted a novel learning, algorithm-based neural network to generate initial sales forecasts and then used a heuristic fine-tuning process to obtain more accurate forecasts based on the
initial ones. The learning algorithm integrated an improved harmony search algorithm and an extreme learning machine to improve the network generalization performance. The experimental results demonstrated a superior performance of the proposed model compared to traditional ARIMA models for fashion sales forecasting. Khashei and Bijari
(2011) proposed a novel
hybridization of artificial neural networks and an ARIMA model in order to overcome limitation of ANNs and yield more general and more accurate forecasting model than traditional hybrid ARIMA-ANNs models. In the proposed model, the unique advantages of ARIMA models in linear modeling were used in order to identify and magnify the existing linear structure in data, and then a neural network was used in order to determine a model to capture the underlying data-generating process and predict using preprocessed data. Au et al. (2008) presented an evolutionary computation for the ideal network structure for a forecasting system. The optimized neural networks structure for the forecasting of apparel sales was developed. The study found that the proposed algorithms were better than the traditional SARIMA model for products with features of low demand uncertainty and weak seasonal trends
A decomposition approach could also be seen in literature. Guo et al. (2012) proposed a modified EMD-FNN model (empirical mode decomposition [EMD] based feed-forward neural network [FNN] ensemble learning paradigm) for wind speed forecasting. The nonlinear and non-stationary original wind speed series was first decomposed into a finite and often small number of intrinsic mode functions (IMFs) and one residual series using EMD technique for a deep insight into the data structure. Then these sub-series, except the high frequency, were forecasted respectively by FNN whose input variables were selected by using partial autocorrelation function (PACF). Finally, the prediction results of the
modeled IMFs and residual series were summed to formulate an ensemble forecast for the original wind speed series. Ni and Fan (2011) proposed a two-stage dynamic forecasting model, which is combined with long-term and short-term predictions. The model
introduced the improved
adjustment methods, the main adjustment model, and an error forecasting model in the adjustment system collaborated by each other. The real-time data were demonstrated by applying the model in a wireless mobile environment. The experiment showed that the model provides good results for fashion retail forecasting.
Problem Context and
Solution Methodology
Supply chain managers are supposed to make a forecast on the basis of past data. There are various neural network models available for forecasting. This research choose five networks that provide best results, namely, the multi-layer perceptron neural network (MLPNN), the Jordan-Elman neural network, the self-organizing feature maps neural network (SOFMNN), the radial basis function neural network (RBFNN), and the focused time-lagged recurrent neural network (FTLRNN) (Borade & Bansod, 2011). Forecasts were compared using MDCM tools. The considered
parameters were supplier
inventory cost, retailer inventory cost, total supply chain cost, retailer profit, and supplier profit. Overview of Artificial Neural Network Models
The general procedure of forecasting and steps for k-fold cross-validation were adopted from Murat and Ceylan (2006). The multi-layer perceptron neural network was adopted from Azadeh et al. (2007) and http://www.stowa-nn.ihe.nl/ANN.htm. The Jordan-Eleman neural network, self-organizing feature maps network, and radial basis function neural network were adopted from h t t p : / / w w w. s t o w a - n n . i h e . n l /
ANN.htm, Min et al. (2006), and Haykin 2006). And the focused time-lagged recurrent neural network was adopted from Dudul (2007). The general procedure that was adopted for forecasting is discussed in the following.
Multi-layer Perceptron Model
Figure 1 shows a three-layer feed forward model that was used for forecasting purposes. The input nodes were the previous year's sales data and the output was the forecast for the future. Hidden nodes with appropriate transfer functions were used to process the information received by the input nodes. In fact, to build an appropriate neural network architecture model, the k-fold cross-validation method was used and available data were divided into three folds: training, validation, and testing (Borade & Bansod 2011).
Jordan-Eleman Model
The Jordan-Eleman network model is realized by adding recurrent links from the network's output to a set of context units of a context layer and from the context units to themselves. Context units copy the activations of the output node from the previous time step through the feedback links with unit weights. Jordan-Eleman networks extend the multilayer perceptron with context
units, which are processing elements (PEs) that remember past activity. Context units provide the network with the ability to extract temporal information from the data (Mankar & Ghatol, 2009).
Self-Organizing Feature Maps Model
Self-organizing feature maps (SOFMs) are competitive neural networks in which neurons are organized in a two-dimensional grid (in the most simple case) representing the feature space. According to the learning rule, vectors that are similar to each other in the multidimensional space will be similar in the two-dimensional space. SOFMs are often used just to visualize an n-dimensional space, but its main application is data classification. The SOFMNN consists of two layers of neurons. The first layer is not actually a neuron layer; it only receives the input data and transfers it to the second layer (Magomedov, 2006).
Radial Basis Function Model
The RBF network has a feed forward structure consisting of a single hidden layer of locally tuned units, which are fully interconnected to an output layer of linear units. All hidden units simultaneously receive the n-dimensional real-valued input vector. The main difference from that of MLP is the absence of
layer weights. The hidden-unit outputs are not calculated using the weighted-sum mechanism/ sigmoid activation; rather, each hidden-unit output is obtained by closeness of the input to an n-dimensional parameter vector associated with the hidden unit (Venkatesan & Anitha, 2006).
Focused Time-Lag Recurrent Model
Time-lagged recurrent networks (TLRNs) are MLPs extended with short-term memory structures. Here, a static NN (e.g., MLP) is
augmented with dynamic
properties. This, in turn, makes the network reactive to the temporal structure of information bearing signals. For an NN to be dynamic, it must be given memory. This memory may be classified into short-term and long-term memories. Long-term memory is built into an NN through supervised learning, whereby the information content of the training data set is stored (in part or in full) in the synaptic weights of the network. However, if the task at hand has a temporal dimension, some form of short-term memory is needed to make the network dynamic (Badjate & Dudul, 2009). Supply Chain Costs
The total supply cost was taken as the sum of the various cost components. It included manu-facturing costs, order processing costs, transportation costs, overstock or salvage costs, inventory handling costs, ordering costs, and understock or penalty costs. Many authors have used supply chain cost as a performance measure but did not take into account the overstock or understock cost. Management decided to take care of the inventory of the retailer. Hence, understock or overstock costs were also taken into consideration. The notations and the costs taken into account were as follows: Notations
M- Manufacturing cost per unit
O- Ordering cost per order
P- Order processing cost per unit
T- Transportation cost per unit
Figure 1
H- Inventory handling cost per unit per day
S- Salvage cost for overstock per unit
U- Penalty for stock outs per unit
Q- Ordering quantity
N- Number of orders
F- Forecasted quantity supplied to retailer
D- Actual demand at retailers' end The various costs and profit calculations were calculated as follows:.
1. Supplier Inventory Cost S.I.C = T.M.C+T.O.P.C+T.T.C - T.O.S.C (1)
2. Retailer Inventory Cost R.I.C = T.I.H.C + T.O.C+ T.U.S.C (2)
3. Total Supply Chain Cost, T.S.C.C= R.I.C. +S. I.C. (3)
4. Supplier Profit = Sales Revenue - Suppliers' cost (4)
5. Retailer Profit = Sales Revenue - Retailers' cost (5)
where
Total Manufacturing Cost,
T.M.C = M * F (6)
Total Order Processing Cost,
T.O.P.C = P * F (7)
Total Transportation Cost,
T.T.C = T * F (8)
Total Overstock Cost,
T.O.S.C = (F -D) * S if F > D (9)
Total Inventory Handling Cost,
T.I.H.C = Q * H (10)
Total Ordering Cost,
T.O.C = O * N (11)
Total Understock Cost,
T.U.S.C = (D-F) * U if D > F (12)
The various cost elements were as follows:
M- Manufacturing cost per unit: Rs 6.00
O- Ordering cost per order: Rs 100.00
P- Order processing cost per unit: Rs 0.75
T- Transportation cost per unit: Rs 1.25
H- Inventory handing cost per unit per day: Rs 0.10
S- Salvage cost for overstock per unit: Rs 0.50
U- Penalty for stock outs per unit: Rs 1.10
If forecasts were higher than actual figures, then it was taken as an overstock cost whereas for lower
forecasts it was considered as an understock cost. Suppliers analyzed past years' data and made a forecast. These quantities were supplied to retailers.If the retailer is sure about the product demand, the ordering quantity (forecasted quantity) was modified and the supplier supplied a revised order quantity. The supplier then sent a modified ordering quantity to the retailer. Similarly, for all situations, this methodology was adopted whenever there was a wide deviation between forecasted demand and actual demand. Thus, neural network-based forecasts and information sharing about the demand patterns helped to modify the demand and execute the supply chain decisions (Borade & Bansod, 2011). The methodology is depicted in Figure 2. In this study we considered a forecast for a single product. The forecast was done on weekly basis. The product was perishable in nature, hence, orders were placed twice a week. All the forecast were added to make a year's forecast. For ease of calculation, we have considered all costs for a year. At the end of the
Problem of Forecasting and Inventory Management Collaboration
Manufacturer Retailer
Collect Demand Information from Retailer Provide Information to Manufacturer Determine Parameters of Forecasting Model
Decide Optimal Values Develop Forecast From Neural Model Select Best
Communicate to Retailer Supply to Retailer
M O D I F Y Accepted By Retailer (No) (Yes) Figure 2
Adopted Methodology
year we compared the actual demand and the forecast for calculation of costs.
Figures 3 to 7 show that there no single forecast that could be considered as optimum. Supplier
inventory cost is maximum with Jordan-Eleman and minimum with FTLRNN. Retailer inventory cost is minimum with Jordan-Eleman and maximum with FTLRNN. Total supply chain cost is maximum with Jordan-Eleman and minimum with FTLRNN. Supplier profit is maximum with FTLRNN and minimum with MLPNN. Retailer profit is maximum with
Jordan-Eleman and minimum with
FTLRNN. In this research we made the forecasts form five models and chose the best by using MDCM techniques - Multi Criteria Decision Making Methods. There are multiple techniques to aid selection in conditions of multiple criteria. In order to choose the best forecast we adopted TOPSIS, MAPPAC, and ELECTRE. Authors studied the effect of resistance from each subsystem of the organization to ensure the reliability of the chosen strategy (Milani et al., 2006).
MAPPAC adopts the same
procedure as that of TOPSIS, however, paired comparisons are made. In the following section an overview of neural networks and TOPSIS and ELECTRE methods is provided.
TOPSIS Method
The idea of TOPSIS can be expressed in a series of steps: 1. Obtain performance data for n
alternatives over k criteria. Raw measurements are usually standardized, converting raw measures xij into standardized measures sij.
2. Develop a set of importance weights wk, for each of the criteria. The basis for these weights can be anything but usually is ad hoc respective of relative importance. Scale is not an issue if standardizing was accomplished in Step 1.
3. Identify the ideal alternative (extreme performance on each criterion) s+:.
4. Identify the nadir alternative (reverse extreme performance on each criterion) s-:.
5. Develop a distance measure over each criterion to both ideal (D+) and nadir (D-).
6. For each alternative, determine a ratio Requal to the distance to the nadir divided by the sum of
Figure 3
Supplier's inventory cost
Figure 4
Retailer's inventory cost
Figure 5
Total supply chain cost
Figure 6
Supplier's profit
Figure 7
the distance to the nadir and the distance to the ideal, R= D- / (D- + D+).
7. Rank order alternatives by maximizing the ratio in Step 6. Thus, TOPSIS minimizes the distance to the ideal alternative while maximizing the distance to the nadir. There are a number of specific procedures that can be used for Step 2 (developing weights) and for Step 5 (distance measures). Additionally, different conventions can be applied to donning best performance (Step 3) and worst performance (Step 4) (Olson, 2004).
ELECTRE Method
In this method two indexes are found.
Concordance index
The concordance index clk is defined for each pair of alternatives A al; ak as a sum of criteria weight according to which al is not weaker than ak: The values of all the concordance indexes are being written into the concordance matrix C. The concordance index is a measure of intensity of the domination of the alternative al
over the alternative ak.
Discordance index
This index measures the resistance of one alternative against the domination of the other. Because of different measuring scales belonging to different criteria, first it is necessary to transform all criteria values to comparable scales. It can be done in a few ways, but the authors suggest the procedure of vector normalization for the ELECTRE method.
Let c and d be average values of the concordance indexes, that is, of the discordance indexes. According to this, the MI matrix is formed from the concordance matrix and discordance matrix. Its elements are
mij= 1; iff cij> c and dij< d = 0;otherwise.
If mij = 1, it is presumed that the alternative ai dominates over the alternative aj (the intensity of the domination of aj over aj is higher than the average and the resistance
Supplier Inventory Cost Retailer Inventory Cost Total Supply Chain Cost Supplier Profit Retailer Profit MLP 729,952 46,500 776,452 28.22 5.01 Jordan-Eleman 747,526 45,526 793,053 26.49 5.1 SOFM 745,197 45,540 790,737 26.72 5.09 RBF 709,937 48,564 757,961 30.2 4.82 FTLRNN 644,105 53,644 697,749 36.37 4.8 Table 1
Costs and profit obtained from various forecasts
MIN MIN MIN MAX MAX
Supplier Inventory Cost Retailer Inventory Cost Total Supply Chain Cost Supplier Profit Retailer Profit MLP 729,952 46,500 776,452 28.22 5.01 Jordan-Eleman 747,526 45,526 793,053 26.49 5.1 SOFM 745,197 45,540 790,737 26.72 5.09 RBF 709,937 48,564 757,961 30.2 4.82 FTLRNN 644,105 53,644 697,749 36.37 4.8 Weights 0.15000 0.15000 0.20000 0.17500 0.17500 Table 2
Input for TOPSIS
MAX MAX MAX MAX MAX
Supplier Inventory Cost Retailer Inventory Cost Total Supply Chain Cost Supplier Profit Retailer Profit MLP 0.15767 0.49485 0.16128 0.42318 0.45120 Jordan-Eleman 0.00000 0.56231 0.00000 0.39724 0.45931 SOFM 0.02090 0.56135 0.02250 0.40069 0.45841 RBF 0.33725 0.35188 0.34092 0.45288 0.43409 FTLRNN 0.92788 0.00000 0.92588 0.54540 0.43229 Weights 0.17647 0.17647 0.23529 0.20588 0.20588 Table 3
Modified input data for TOPSIS
MAX MAX MAX MAX MAX
Supplier Inventory Cost Retailer Inventory Cost Total Supply Chain Cost Supplier Profit Retailer Profit MLP 0.15767 0.49485 0.16128 0.42318 0.45120 Jordan-Eleman 0.00000 0.56231 0.00000 0.39724 0.45931 SOFM 0.02090 0.56135 0.02250 0.40069 0.45841 RBF 0.33725 0.35188 0.34092 0.45288 0.43409 FTLRNN 0.92788 0.00000 0.92588 0.54540 0.43229 Weights 0.17647 0.17647 0.23529 0.20588 0.20588 Table 4
Normalized Matrix for TOPSIS
MAX MAX MAX MAX MAX
Supplier Inventory Cost Retailer Inventory Cost Total Supply Chain Cost Supplier Profit Retailer Profit MLP 0.02782 0.08733 0.03795 0.08713 0.09289 Jordan-Eleman 0.00000 0.09923 0.00000 0.08179 0.09456 SOFM 0.00369 0.09906 0.00529 0.08250 0.09438 RBF 0.05951 0.06210 0.08022 0.09324 0.08937 FTLRNN 0.16374 0.00000 0.21785 0.11229 0.08900 Weights 0.17647 0.17647 0.23529 0.20588 0.20588 Ideal 0.16374 0.09923 0.21785 0.11229 0.09456 Basal 0.00000 0.00000 0.00000 0.08179 0.08900 Table 5
of the alternative aj to that domination is weaker than the average). The matrix can be considered to be a matrix of graph indexes where the alternatives are knots and only those with dominance are connected by arches. The exit knot of the arch belongs to the alternative that dominates over the one with the corresponding entrance knot (Hunjak, 1997).
Results and Discussions
Supply chain managers used past data and made forecasts retailers. Five neural networks were used as mentioned previously. The different costs associated as a result of different forecasts are provided in Table 1. It is observed that from the supplier cost point of view that the FTLRN forecast is best, however, from the retailer cost point of view Jordan-Eleman was the best. The total cost was low for FTLRNN. As profit is concerned the supplier profit was best from FTLRNN and the retailer profit was best for Jordan-Eleman. We wanted to minimize supplier, retailer, and total cost simultaneously by increasing retailer and supplier profit. Supplier and retailer cost was weighted as 0.15 each and total cost was weighted as 0.20. The profits were weighted as 0.175 each. These data were taken as a reference for applying TOPSIS as shown in Table 2. The weights were taken by consulting the experts and using Satty's procedure for weight calculation. The result could be different for different weights. However, the weights in the study would provide the optimum results, hence we relied on these weights.MIN MIN MIN MAX
Supplier Inventory Total Supply Chain R
Ranking Alternative R.U.V
1 MLP 0.30439 2 FTLRNN 0.73399 3 RBF 0.39940 4 SOFM 0.27077 5 Jordan-Eleman 0.26601 Table 6
Rankings by TOPSIS
MIN MIN MIN MAX MAX
Supplier Inventory Cost Retailer Inventory Cost Total Supply Chain Cost Supplier Profit Retailer Profit MLP 729,952 46,500 776,452 28.22 5.01 Jordan-Eleman 747,526 45,526 793,053 26.49 5.1 SOFM 745,197 45,540 790,737 26.72 5.09 RBF 709,937 48,564 757,961 30.2 4.82 FTLRNN 644,105 53,644 697,749 36.37 4.8 Weights 0.15000 0.15000 0.20000 0.17500 0.17500 Table 7
Input for MAPPAC
MAX MAX MAX MAX MAX
Supplier Inventory Cost Retailer Inventory Cost Total Supply Chain Cost Supplier Profit Retailer Profit
MLP 17,574 7,144 16,601 28.22 5.01 Jordan-Eleman 0 8,118 0 26.49 5.1 SOFM 2,329 8,104 2,316 26.72 5.09 RBF 37,589 5,080 35,092 30.2 4.82 FTLRNN 103,421 0 95,304 36.37 4.8 Weights 0.17647 0.17647 0.23529 0.20588 0.20588 Ideal 103421 8118 95304 36.37 5.1 Basal 0 0 0 26.49 4.8 Table 8
Modified input data for MAPPAC
Supplier Inventory Cost Retailer Inventory Cost Total Supply Chain Cost Supplier Profit Retailer profit MLP 0.16993 0.88002 0.17419 0.17510 0.70000 Jordan-Eleman 0.00000 1.00000 0.00000 0.00000 1.00000 SOFM 0.02252 0.99828 0.02430 0.02328 0.96667 RBF 0.36346 0.62577 0.36821 0.37551 0.06667 FTLRNN 1.00000 0.00000 1.00000 1.00000 0.00000 Weights 0.17647 0.17647 0.23529 0.20588 0.20588 Table 9
Matrix C for MAPPAC
Weights 0.17647 0.17647 0.23529 0.20588 0.20588
MLP Jordon SOFM RBF FTLRNN From Above
MLP 0.00000 0.60181 0.59099 0.48215 0.37401 2 Jordan-Eleman 0.39819 0.00000 0.29409 0.45001 0.38235 5 SOFM 0.40901 0.70591 0.00000 0.45616 0.38313 3 RBF 0.51785 0.54999 0.54384 0.00000 0.25703 4 FTLRNN 0.62599 0.61765 0.61687 0.74297 0.00000 1 FROM BELOW 2 5 4 3 1 Table 10
All criteria are considered for maximization. The modified input is shown in Table 3. Tables 4 and 5 show the normalized and weighted
matrix. Table 6 shows the final ranking. Based on the TOPSIS analysis, MLP neural networks got first priority. These are closely
followed by FTLRNN, RBF, and SOFM. From the results it can be inferred that a forecast based on MLP neural networks would give optimum results, whereas forecasts from Jordan-Eleman would be less preferred. In order to verify the results the MAPPAC method was applied. Table 7 shows an input to MAPPAC. On the condition of minimization and maximization the data are modified in Table 8. The data are normalized in Table 9. These paired comparisons are made in Table 10. The MAPPAC analysis, as seen from Table 11, shows that the best forecast is obtained by FTLRNN followed by MLP, RBF, SOFM, and Jordan-Eleman.
Finally, the ELECTRE method was applied. The input was as shown in Table 12. The data are modified as shown in Table 13. The matrix as discussed in the methodology is prepared as shown in Table 14. Finally, the ranking is obtained as shown in Table 15 and shows that the best forecast is obtained by FTLRNN followed by RBF, MLP, Jordan-Eleman, and SOFM. From the study we find that the FTLRNN networks provided the best results in MAPPAC and ELECTRE whereas MLP provided the best results in TOPSIS. Because FTLRNN emerged as the winner in two instances we must choose FTLRNN forecasts to optimize costs and profits.
Conclusion
In this article a study of a small company was presented. In order to assist the supply chain manager in making inventory related decisions, decision support tools were used. In all, five neural networks were adopted. These were tested on cost parameters. The three MDCM tools were applied to compare and to choose the best one. It was found that when both criteria, that is, maximization of profit and minimization of cost, was considered, FTLRNN networks provide the best results. The proper choice of neural network can help managers improve the profitability in the supply chain and reduce supply chain cost. This Class Alternative Upper Lower
2 MLP 2 2 1 FTLRNN 1 1 3 RBF 4 3 SOFM 3 4 4 Jordan-Eleman 5 5 Table 11
FINAL RANKING by MAPPAC
MIN MIN MIN MAX MAX
Supplier Inventory Cost Retailer Inventory Cost Total Supply Chain Cost Supplier Profit Retailer Profit MLP 729,952 46,500 776,452 28.22 5.01 Jordan-Eleman 747,526 45,526 793,053 26.49 5.1 SOFM 745,197 45,540 790,737 26.72 5.09 RBF 709,937 48,564 757,961 30.2 4.82 FTLRNN 644,105 53,644 697,749 36.37 4.8 Weights 0.15000 0.15000 0.20000 0.17500 0.17500 Table 12
Input data for ELECTRE
MAX MAX MAX MAX MAX
Supplier Inventory Cost Retailer Inventory Cost Total Supply Chain Cost Supplier Profit Retailer Profit
MLP 17,574 7,144 16,601 28.22 5.01 Jordan-Eleman 0 8,118 0 26.49 5.1 SOFM 2,329 8,104 2,316 26.72 5.09 RBF 37,589 5,080 35,092 30.2 4.82 FTLRNN 103,421 0 95,304 36.37 4.8 Weights 0.17647 0.17647 0.23529 0.20588 0.20588 Table 13
Modified input data for ELECTRE
MLP Jordon SOFM RBF FTLRNN MLP 0.00000 0.61765 0.61765 0.38235 0.38235 Jordan-Eleman 0.38235 0.00000 0.38235 0.38235 0.38235 SOFM 0.38235 0.61765 0.00000 0.38235 0.38235 RBF 0.61765 0.61765 0.61765 0.00000 0.38235 FTLRNN 0.61765 0.61765 0.61765 0.61765 0.00000 Table 14
Matrix S for ELECTRE
Indiferent Class Alternative
1. FTLRNN 2. RBF 3. MLP 4 Jordan-Eleman 5 SOFM Table 15
study considered a single echelon supply chain with a single product. In the future multiple echelons with multiple products could be considered. The results could be applied and tested with other models and industries.
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About the authors
Atul B. BORADEis working as a Professor at
Jawaharlal Darda Institute of Engineering and Technology, Yavatmal, India. He has completed his PhD at Sant Gadge Baba Amravati University. India. He has published 15 papers in journals and conferences. His papers have been published in journals such
as Journal of Technology Management and
Innovation, International Journal of Knowledge Management, ICFAI Journal of Supply Chain Management, International Journal of
Occupational Safety and Ergonomics,
International Journal of Management Science and Engineering Management, International Journal of Service Sciences, Journal of Industrial Engineering and Management and
Journal of Manufacturing Technology
Management. He is a reviewer with Omega, Journal of Manufacturing Engineers, Journal of Information, Information Technology and Organisations, Journal of Information System and Technology Management, Journal of Industrial Engineering and Management and International Journal of Industrial Engineering -Theory, Applications and Practice. He has worked as Editorial Board Member with
International Journal of Information
Technology and Knowledge Management, International Journal of Manufacturing Science and Manufacturing Management. Currently he is working as Editorial Board Member with
Contemporary Management Research,
International Journal of Manufacturing Systems, Asian Journal of Industrial Engineering, and International Journal of Business Research. His areas of interest are, supply chain management, manufacturing management and ergonomics.
Satish V. BANSODis working as a Professor at
Professor Ram Meghe Institute of Technology and Research, Bandera, India. He received his PhD in Production Engineering. He has guided many under and post graduates students. Currently, he is supervising 10 PhD students. He has published 50 papers in journals and conferences. His papers have been published in journal such as Journal of Technology Management and Innovation, International Journal of Knowledge Management, ICFAI Journal of Supply Chain Management, International Journal of Occupational Safety and Ergonomics, Journal of Productivity, Journal of Modeling and Simulation, Journal of Transportation Research, International Journal of Management Science and Engineering Management, International Journal of Service Sciences, Journal of Industrial Engineering and Management, Journal of Manufacturing Technology Management, Journal of Industrial Engineering and Asian Journal of Industrial Engineering, He is a Distinguished Professor of Mechanical Engineering. He is Reviewer and Editorial Board Member of numerous journals. He is a member of prestigious academic and professional bodies. His areas of interest are, supply chain management, manufacturing management and ergonomics.
