Supply chain network design using an integrated neuro-fuzzy and MILP approach: A comparative design study

Expert Systems with Applications 36 (2009) 12570–12577

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Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa

Supply chain network design using an integrated neuro-fuzzy and MILP approach: A comparative design study Alev Taskin Gumus *, Ali Fuat Guneri, Selcan Keles Department of Industrial Engineering, Yildiz Technical University, 34349 Besiktas-Istanbul, Turkey

a r t i c l e

i n f o

Keywords: Supply chain network design Neuro-fuzzy Mixed integer linear programming Artificial neural networks

a b s t r a c t In this study, an integrated supply chain (SC) design model is developed and a SC network design case is examined for a reputable multinational company in alcohol free beverage sector. Here, a three echelon SC network is considered under demand uncertainty and the proposed integrated neuro-fuzzy and mixed integer linear programming (MILP) approach is applied to this network to realize the design effectively. Matlab 7.0 is used for neuro-fuzzy demand forecasting and, the MILP model is solved using Lingo 10.0. Then Matlab 7.0 is used for artificial neural network (ANN) simulation to supply a comparative study and to show the applicability and efficiency of ANN simulation for this type of problem. By evaluating the output data, the SC network for this case is designed, and the optimal product flow between the factories, warehouses and distributors are calculated. Also it is proved that the ANN simulation can be used instead of analytical computations because of ensuring a simplified representation for this method and time saving. Ó 2009 Elsevier Ltd. All rights reserved.

1. Introduction In today’s world, enterprises have to cope with the growing markets and with the increasing customer expectations. Because of the customer expectations about obtaining the products at the right time and quantity, and besides this the improvements against the risks created by the sudden fluctuations in local and global economies, companies need to analyse their working styles. Today, the success measures for the companies are thought as lower costs, shorter production time, shorter lead time, less stock, larger product range, more reliable delivery time, better customer services, higher quality, and providing the efficient coordination between demand, supply and production. For this reason, supply chain management (SCM) concept is occurred and, SCM has become an important necessity. Huang, Sheoran, and Keskar (2005) describe a supply chain (SC) as a network of facilities that procure raw materials, transform them into intermediate goods and then final products, and deliver the products to customers through a distribution system. SCM is strategically and systematically coordination of all functions of the companies in SC in order to increase long term performance of both supply chain and the other companies in the chain (Cakravastia, Toha, & Nakamura, 2002; Gunasekaran, 1999). SCM is the integration of key processes that is started by the first supplier and continues until the end consumer to provide * Corresponding author. Tel.: +90 2122597070/2242; fax: +90 2122585928. E-mail address: [email protected] (A.T. Gumus). 0957-4174/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2009.05.034

product, service and information. Initially an appropriate network design is needed to control efficiently all the elements in all stages, to be flexible against the changing situations, to provide coordination along the supply chain, and so be successful in SCM which is very complicated (Cakravastia et al., 2002; Graves & Willems, 2005). Therefore, SC network design is very important and attempts to create the most efficient and effective SC for the company’s operating environment (Samadhi & Hoang, 1998). A SC network is commonly defined as the integrated system encompassing raw material vendors, manufacturing and assembly plants, and distribution centres, to ensure solutions for effectively meeting customer requirements such as low costs, high product variety, quality and shorter lead times (Chauhan, Nagi, & Proth, 2004; Santoso, Ahmed, Goetschalckx, & Shapiro, 2005). The network is characterised by procurement, production, and distribution functions (Santoso et al., 2005). Leaving aside the procurement function (purchasing of raw materials), the SC network becomes a multi-echelon production/distribution system (Altiparmak, Gen, Lin, & Karaoglan, 2009; Beamon, 1998; Bhaskaran & Leung, 1997; Shapiro, 2001; Taskin Gumus & Guneri, 2007; Tsiakis, Shah, & Pantelides, 2001). The design of SC networks is a difficult task because of the intrinsic complexity of the major subsystems of these networks and the many interactions among these subsystems, as well as external factors such as the considerable uncertainty in product demands (Santoso et al., 2005). In the past, this complexity has forced much of the research in this area to focus on individual components of supply chain networks. Recently, however, attention

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has increasingly been placed on the performance, design, and analysis of the supply chain as a whole (Tsiakis et al., 2001). Design of the chain should be able to integrate the various elements of the chain and should strive for the optimization of the chain rather than the entities or group of entities. Information sharing and its control play a vital role in integration of the different elements of the chain and require highly coordinated efforts of both engineers and managers (Fisher & Raman, 1996; Lee, Padmanabhan, & Whang, 1997; Wang, Huang, & Dismukes, 2004). In the following section, SC network design concept is detailed. Then, in the third and fourth sections, an integrated SC design model is developed and a SC network design case is examined for a reputable multinational company in alcohol free beverage sector. Here, a three echelon SC network is considered and the proposed integrated neuro-fuzzy and MILP approach is applied to this network to realize the design effectively. Matlab 7.0 is used for neuro-fuzzy demand forecasting and, the deterministic, static, multi-echelon MILP model is solved using Lingo 10.0. Then Matlab 7.0 is used for ANN simulation to supply a comparative study and, to show the applicability and efficiency of ANN simulation for this type of problem. By evaluating the output data, the SC network for this case is designed, and also the optimal product flow between the factories, warehouses and distributors are calculated. Also it is proved that the ANN simulation can be used instead of analytical computations because of ensuring a simplified representation for this method and time saving. 2. Supply chain network design Network design problem that is about determining the elements, numbers, locations and physical flow quantities has a strategic importance for SCM. In this section of the paper, SC network design concept is detailed. The term of supply chain implies that there is only one player for each stage. However in practice, it is possible for a manufacturer to supply material from different companies and working with different distributors. For this reason, actually most of the supply chains are networks (Chopra & Meindl, 2004). A SC network is a complicated whole that contains suppliers, manufacturers, distribution centers, retailers and the systems, sub systems, operations, activities that develop the supply chain and the relations among them (Shapiro, 2001). SC network is a series of processes and stages, which starts with the material/information suppliers and ends with the customer as shown in Fig. 1 (Tsiakis et al., 2001). Every mid-stage is the customer of the next stage and supplier of the previous stage. This means that the participants have different roles in the network; however the basic relationship is seen between suppliers and customers (Wang, 2009). The SC seems different from the various perspectives of the companies, because every company supposes itself at the center and thinks the structure and the participants of the network

from the view of its own vision. Nonetheless it is highly important for the company managers to understand the roles and the perspectives of the other companies along the supply chain, because every company is the participant of the next supply chain. The reason behind is that the integration and management of the work processes in a firm will be successful when they are all important from every firm’s perspective (Lambert & Cooper, 2000). The SC network design is one of the biggest strategic decision problems which are used for efficient long term operations in the whole SC, and for this reason it needs optimization. The design figures out the numbers, capacity, layout and type of the factories, warehouses and distribution centres. In addition it sets up the distribution channels and calculates the quantity of materials which will be consumed in the production process, the quantity of materials which will be transported from suppliers to customers, and the quantity of materials which will be produced. The SC is divided into several stages to bear with the complexity of the designing and calculation problems. The number of the stages can be found due to the balance between the complexity and the integration of the problem (Ballou, 2001; Tsiakis & Papageorgiou, in press). Basically, the SC network design is realized by three stages. These stages are shown in Fig. 2. First stage contains the studies which provide the supply chain processes efficiently managed. There are three important factors in the first stage: (1) emphasizing the suppliers which provide direct input to this chain, (2) converting this integrated design to a modern business application, and (3) taking action by reason of operational decisions are being effected by the suppliers directly. Second

Decision maker

Defining the business processes, inputs, outputs and the data First stage Developing the performance of suppliers, manufacturers and distributors

Second stage

Third stage

Defining capacity, efficiency and the constraints of facility layout

Establishing optimal assignment plan and facility layout plan for supply chain

Fig. 2. The stages of supply chain network design.

Fig. 1. The stages of a supply network.

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stage implements the design by comparing supply and demand at every demand points. In the second stage, the input from suppliers is transformed into final product or service. The third stage of the SC network design includes operational functions which consists of optimal source and plans for all the network points in a minimum cost assignment problem (Talluri & Baker, 2002). 3. The integrated neuro-fuzzy and MILP approach In this section, firstly our integrated neuro-fuzzy and MILP methodology is introduced. Next, neuro-fuzzy approximation concept and ANFIS (adaptive-network-based fuzzy inference system) architecture is detailed, because of using it in demand forecasting. Subsequently, the integrated neuro-fuzzy and MILP model and its analytical equations are presented, and then the alternative ANN simulation model is proposed. 3.1. The integrated neuro-fuzzy and MILP methodology In this paper, an integrated methodology is proposed containing neuro-fuzzy and MILP calculations. This methodology has two steps: (1) Demand forecasting using neuro-fuzzy approximation, (2) network design using MILP. MILP uses the outputs of neurofuzzy approximation (demand forecasts) as demand inputs. Also, there are cost and capacity inputs that are obtained from the SC network under consideration. The flow of the methodology proposed here is shown in Fig. 3.

SONFIN, FINEST, EfuNN (evolving fuzzy neural network), dmEFuNN, NEFCLASS (neuro-fuzzy classification), evolutionary design of neuro-fuzzy systems and the others (Abraham & Nath, 2000). In this paper, ANFIS is used to eliminate demand uncertainty. For this reason, a stochastic-neuro-fuzzy model is proposed with demand forecasting using neuro-fuzzy calculations. The ANFIS is a multilayer feed forward network which uses neural network learning algorithms and fuzzy reasoning to map an input space to an output space (Chang & Chang, 2006). For simplicity, we assume the fuzzy inference system under consideration has two inputs, x and y, and one output, z. For a first-order Sugeno fuzzy model (Takagi & Sugeno, 1985), a typical rule set with two fuzzy if–then rules can be expressed as:

Rule-1 : If xA1 and yB1 Then f 1 ¼ p1  x þ q1  y þ r 1 Rule-2 : If xA2 and yB2 Then f 2 ¼ p2  x þ q2  y þ r 2

where pi, qi and ri (i = 1 or 2) are linear parameters in the then-part (consequent part) of the first-order Sugeno fuzzy model. The architecture of ANFIS consists of five layers, and a brief introduction of the model is as follows (Chang & Chang, 2006; Escoda, Ortega, Sanz, & Herms, 1997; Esen, Inalli, Sengur, & Esen, 2008; Jang, 1993; Taskin Gumus & Guneri, 2009). Layer 1: Input nodes. Each node of this layer generates membership grades to which they belong to each of the appropriate fuzzy sets using membership functions.

O1;i ¼ lAi ðxÞ for i ¼ 1; 2

ð2Þ

O1;i ¼ lBi2 ðyÞ for i ¼ 3; 4

3.2. Neuro-fuzzy approximation Both neural networks and fuzzy systems are dynamic, parallel processing systems that estimate input–output functions (Taskin Gumus & Guneri, 2009). They estimate a function without any mathematical model and learn from experience with sample data. A fuzzy system adaptively infers and modifies its fuzzy associations from representative numerical samples. Neural networks, on the other hand, can blindly generate and refine fuzzy rules from training data (Kosko, 1991). Fuzzy sets are considered to be advantageous in the logical field, and in handling higher order processing easily. The higher flexibility is a characteristic feature of neural nets produced by learning and, hence, this suits data-driven processing better (Takagi, 1990). Hayashi and Buckley (1994) proved that (1) any rule-based fuzzy system may be approximated by a neural net and (2) any neural net (feed forward, multilayered) may be approximated by a rule-based fuzzy system (Mitra & Hayashi, 2000). Basic studies about neuro-fuzzy integration are GARIC, FALCON, ANFIS (adaptive-network-based fuzzy inference system), FUN,

Characterization of the existing SC network

where x, y are the crisp inputs to node i, and Ai, Bi (small, large, etc.) are the linguistic labels characterized by appropriate membership functions lAi and lBi , respectively. Layer 2: Rule nodes. In the second layer, the AND operator is applied to obtain one output that represents the result of the antecedent for that rule, i.e., firing strength. Firing strength means the degrees to which the antecedent part of a fuzzy rule is satisfied and it shapes the output function for the rule. Hence the outputs O2;k of this layer are the products of the corresponding degrees from Layer 1:

O2;k ¼ wk ¼ lAi ðxÞ  lBj ðyÞ;

k ¼ 1; . . . ; 4; i ¼ 1; 2; j ¼ 1; 2

Obtaining cost and capacity data from existing SC network

Aggregation and integration of the inputs of the MILP model

Running the MILP model and designing the most cost efficient SC network via analytical calculations and ANN simulation comparatively

w  i ¼ P4 i O3;i ¼ w

k¼1 wk

;

i ¼ 1; . . . ; 4

ð4Þ

Layer 4: Consequent nodes. The node function of the fourth layer computes the contribution of each ith rule’s toward the total output and the function defined as:

i ¼ 1; . . . ; 4

ð5Þ

 i is the ith node’s output from the previous layer. As for where w fpi ; qi ; r i g, they are the coefficients of this linear combination and are also the parameter set in the consequent part of the Sugeno fuzzy model. Layer 5: Output nodes. The single node computes the overall output by summing all the incoming signals. Accordingly, the defuzzification process transforms each rule’s fuzzy results into a crisp output in this layer:

O5;i ¼ Fig. 3. The integrated neuro-fuzzy and MILP methodology.

ð3Þ

Layer 3: Average nodes. In the third layer, the main objective is to calculate the ratio of each ith rule’s firing strength to the sum of all  i is taken as the normalized rules’ firing strength. Consequently, w firing strength:

 i fi ¼ w  i ðpi x þ qi y þ r i Þ; O4;i ¼ w Estimation of distributor demands by neuro-fuzzy approximation

ð1Þ

4 X i¼1

P4 wi fi  i fi ¼ Pi¼1 w 4 i¼1 wi

ð6Þ

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3.3. The integrated MILP model

3.4. The ANN simulation model

This model is based on Yan, Yu, and Cheng’s (2003) model. This is a deterministic, static, multi-echelon MILP model with linear constraints, while Yan et al.’s (2003) contains logical constraints concerning material requirements, in addition to linear ones. Also, differently, the proposed model uses neuro-fuzzy approximation outputs as demand inputs. The objective function to be minimized includes both the transportation costs from factories to warehouses and from warehouses to distributors, fixed costs for factories and warehouses. The objective function is set by the Eq. (7). The nomenclature is given in Appendix A. The objective function:

We simulate the proposed integrated model, including the neuro-fuzzy module computing demand, to design and calculate the approximate minimum total cost of the SC network with an artificial neural network (ANN) here. The analytical computations of the integrated neuro-fuzzy and MILP model are very complex and time-consuming. Also, in analytical solution the neuro-fuzzy forecast values are considered deterministically as the inputs of the MILP model, while neuro-fuzzy forecasting can be realized during the ANN model simulation in an integrated manner. A quick estimate can be obtained by simulation. We use ANNs here, because simulation can serve as a simplified representation of analytical model while neural network can serve as a simplified representation of simulation model. Also, conventional simulation software (ARENA, SLAM II, etc.) could not be used because our model incorporated neuro-fuzzy forecasting. ANNs are heavily used in the engineering and scientific fields to model systems ranging from control systems to artificial intelligence (Guneri & Taskin Gumus, 2008; Taskin & Guneri, 2006). ANNs are networks of simple processing elements capable of processing information in response to external inputs (Badiru, 1992; Freeman & Skapura, 1991; Haykin, 1999; Hecht-Nielsen, 1989). The ANN we used is a multi layer perceptron (MLP) network, the most common neural network model. The network consists of an input layer, one or more hidden layers, and an output layer. Each layer computes a nonlinear activation function of a weighted sum of the layer’s inputs. The learning algorithm is the generalized delta rule, which ‘‘learns” by performing gradient descent on the error surface (Jondarr, 1996; Rumelhart, Hinton, & Williams, 1987; Vysniauskas, Groen, & Kröse, 1993; Zurada, 1995). The solution structure of the proposed ANN simulation model can be seen from Fig. 4.

" # " # X XX XX X Min C ij X ij þ C jk Y jk þ /i Ui þ d j Dj i

j

j

k

i

ð7Þ

j

The constraints of the model and their definitions are as below: The constraints:

1:

X

X ij 6 ai Ui ; 8i

ð8Þ

Y jk 6 bj Dj ; 8j

ð9Þ

j

2:

X k

3:

X

Ui 6 F

ð10Þ

Dj 6 D

ð11Þ

i

4:

X j

5:

X i

6:

X

X ij 

X

Y jk ¼ 0; 8j

ð12Þ

k

Y jk P ck ; 8k

ð13Þ

j

7: Ui ; Dj ¼ f0; 1g; 8i;j

ð14Þ

8: X ij ; Y jk P 0; 8i;j;k

ð15Þ

1. The first constraint is given by Eq. (8) and about factory capacity. It implies that the product quantity which is distributed from a factory to the warehouses cannot be more than the current capacity of the factory. 2. This is warehouse capacity constraint (Eq. (9)). Here, the product quantity which is distributed from a warehouse to the distributors can’t be more than the current capacity of the warehouse. 3. According to number of factories constraint the number of the opened factories can’t be more than 2, and it is shown by the Eq. (10). 4. This constraint, presented by Eq. (11), is about the number of warehouses. Likewise, the number of the opened warehouses cannot be more than 3. 5. Balance constraint for the first echelon mean that the total product quantity from factories to warehouses must be equal to the total product quantity from warehouses to distributors (see Eq. (12)). 6. According to the balance constraint for the second echelon (demand constraint) given by the Eq. (13), the capacity of the warehouses should be equal to or more than the demand of the distributor calculated by neuro-fuzzy approximation. 7. Constraint of 0–1 integers. If the factories/warehouses are open, the value should be 1, otherwise it should be 0 (Eq. (14)). 8. Constraint of cardinal numbers is given by the Eq. (15) and implies that the quantity of the products that will be sent from the factories to the warehouse and from the warehouses to the distributors should be cardinal numbers and also they should be integers.

4. A practical design case in alcohol free beverage sector Here, a SC network design case is presented for a reputable multinational company in alcohol free beverage sector using the proposed integrated neuro-fuzzy and MILP approach. First of all, the existing supply network is described. Then, the multi stage MILP model is run by using the inputs calculated via neuro-fuzzy calculations and obtained from the existing network for this case. 4.1. Characterization of the existing supply network The core business of the company observed is production, sales and distribution of the carbonated and non carbonated soft drinks. The sales network in Turkey is divided into 14 parts (e.g. Istanbul Asia, Istanbul Europe). Sales centres are established in these 14 sales areas. There are 44 area sales managers (ASM) who manage sales centres. Planning is realized for 16 different brands and with their 223 stock keeping units (SKU). Here, the SCM department is in coordination with all other departments. The demand of distributors, key accounts and cold drink points are informed to the SC managers by ASMs. Then they gather the information and evaluate them. This information is turned into production plans. After production, these plans become sales plans. Predictions are revised in 24 h to meet the goals of the company. The structure of SC network is suitable for sales trends. Also SC specialists make suggestions to sales department in order to work with suitable profit margins. When the company’s SC network is designed, SCM department concentrates on the transportation costs, the demands of the distributors, the quotas of the areas and the decision of selection

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Design ANN simulation network structure

Define the inputs and outputs of the ANN

Ask the current values of variables

Call ANFIS forecast values for demand

Define the proposed integrated model

Change the ANN parameters (eg. acitivation and transfer functions, Iearning rate, etc.) and validate the results Design optimal SC network and, calculate product quantities flowing through the network and min. SC cost

Fig. 4. The structural steps of the proposed ANN simulation model.

the factory and the product which will be produced. Except the unusual circumstances, the factory or the warehouse that feeds an area is obviously known. However, when it is difficult to supply the demand of the areas or when a problem occurs in the production, products are sent from another factory or from another warehouse. The quotas of the areas are constant. When these quotas are multiplied by estimated demand, the quantity that will be sent to the warehouses is found. Products are tried to be sent to the distributors directly, instead of sending them firstly from factories to city warehouses and then to the distributors in order to minimize the costs. Due to the estimated demand values are not exact; the best way is working with a safety stock after defining the risk levels and then the quantity for each warehouse. The relationship between the production plan and demand and safety stock is calculated as:

Demand from ASMs þ Safety Stock  Current Stock ¼ Production Plan There are dispatchers who work for the company, and their job is determining the sales route, so they are helpful to enhance the SC’s impact. Also distribution routes are determined according to the incoming orders. In addition to this, dispatchers visit the key account points periodically and take the orders with their barcode readers in their hands. Then, these orders are downloaded to the

main computer in the same day at evening, invoices for the next day’s products which will be distributed are prepared and the production and distribution plans are evaluated. Moreover, dispatchers are responsible for informing the distributors about price amendments, handling the procedures against broken or defective products and delivering the new ones to the customers. 4.2. Running the model To run the model, firstly the transportation cost and capacity data of existing SC network members are presented. Then distributor demand is forecasted using neuro-fuzzy approximation. And finally, analytical and ANN simulation model results are compared and discussed via sensitivity analysis. 4.2.1. Obtaining cost and capacity data from existing SC network Here, a deterministic, static, multi-echelon MILP model is used as mentioned before. 2 factories (F1, F2), 3 warehouses (W1, W2, W3) and 6 distributors (D1, D2, D3, D4, D5, D6) are selected from the company’s system in order to explain the existing design of the network. During this model application the product flow is followed by considering only one product of the company. It can be seen from Fig. 5 that the product flows through 2 factories, 3 warehouses and 6 distributors in our model.

Fig. 5. The SC network that consists of factories, warehouses and distributors.

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IF Price is low AND Quality is high AND NtwFlex is high THEN Demand is very high, IF Price is normal AND Quality is normal AND NtwFlex is high THEN Demand is normal, ............

Table 1 The transportation costs from the factories to the warehouses (cent/case). Factories

Warehouses W1

W2

W3

F1 F2

0.01 1.15

1.15 0.01

0.41 0.74

The forecast values of ANFIS and ARIMA for each distributor demand, and their MSE (mean square error) values are compared in Table 5. The MSEs of ANFIS forecast values are found to be lower than ARIMA’s for all distributors in this case, and this can be seen from Fig. 6.

Table 2 The transportation costs from the warehouses to the distributors (cent/case). Warehouses

W1 W2 W3

Distributors B1

B2

B3

B4

B5

B6

0.48 0.60 0.13

0.65 0.36 0.25

0.63 0.55 0.17

0.71 0.52 0.39

0.45 0.72 0.06

0.42 0.76 0.05

Table 3 The capacities and fixed costs of the factories and warehouses. Factories/Warehouses

Capacity

Fixed Costs (Cent/Case)

F1 F2 W1 W2 W3

3,011,970 1,298,716 3,785,630 1,564,479 346,094

4.0 3.9 2.6 2.4 2.3

The following tables (Tables 1–3) indicate us the costs, capacities and demands of the different elements in our model. We can see the transportation costs from the factories to the warehouses in Table 1, and from the warehouses to the distributors in Table 2. Capacities and fixed costs are given in Table 3 for the factories and warehouses. 4.2.2. Estimation of distributor demands via neuro-fuzzy approximation The network is trained with 84 demand data and then the demand forecasts for each of the distributors are realized. According to the test results, the outputs are close to real values with rather low error. Also ARIMA is used to forecast demand with the same data to make a comparison and test the success of neuro-fuzzy method. For neuro-fuzzy computations Matlab 7.0 Fuzzy Logic Toolbox and ANFIS module, and for statistical analysis Eviews 3.0 are used. Demand data membership functions for neuro-fuzzy computations can be seen from Table 4. There are 12 rules set as below:

4.2.3. Analytical and simulation model results During the implementation process 2 factories, 3 warehouses and 6 distributors of the reference company’s SC network are considered in the model. An integrated neuro-fuzzy and MILP approach is proposed to this network to realize the design effectively. The neuro-fuzzy outputs are used in MILP model as inputs together with other input data. The model is solved in two ways; analytically and via ANN simulation, to show the applicability and efficiency of ANNs in this type of design problem. The purpose of this approach is making open/close decisions of the factories and warehouses, and calculating the quantity of production that flows from factories to warehouses and from warehouses to distributors with minimum cost. The model is run using Lingo 10.0 for analytical computations and Matlab 7.0 for ANN simulation. The model outputs and results can be seen from Tables 6 and 7. The results of the two methods are observed in a comparative way, and it is decided that ANN simulation can be used to come out with reliable conclusion, although it is seen that Lingo has better performance in this kind of model. Table 6 implies that the quantity of product that flows from F1 to W1 should be 255.162. As it is seen in Tables 6 and 7, U1 equals to 1, and this means that the first factory should be in progress in the process. According to the result of ANN simulation, the first and second factories, and the first and second warehouses are open, but the

Table 5 The forecasted demand values of the distributors and their MSEs. Distributors

ANFIS

MSEANFIS

ARIMA

MSEARIMA

D1 D2 D3 D4 D5 D6

116,803 55,425 74,668 9,660 81,539 56,820

0.00298 0.00387 0.00305 0.00450 0.00359 0.00380

120,573 54,380 73,965 10,250 82,832 56,305

0.00689 0.00450 0.00392 0.00597 0.00443 0.00389

0.008 Table 4 Demand data membership functions.

0.007 Membership functions

Demand

Product unit price (Price)

Product quality (Quality)

Network flexibility (NtwFlex)

Very low - [5000] (unit) Low - [10,000] Normal - [50,000] High - [85,000] Very High - [120,000] Low - [0 0.5 1.1] ($) Normal - [0.95 1.25 1.3] High - [1.25 1.35 1.4] Low - [0 2 4] Normal - [3 6 7] High - [6 8 10] Low - [0 2 4] High - [3 7 10]

0.006 0.005 0.004 0.003 0.002 0.001 0 D1

D2

D3 MSEANFIS

D4

D5 MSEARIMA

Fig. 6. The MSEs of ANFIS and ARIMA forecast values.

D6

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Table 6 Analytical solution outputs (using Lingo 10.0). Variable Flow of products X 11 X 12 X 13 X 21 X 22 X 23 Y 11 Y 12 Y 13 Y 14 Y 15 Y 16

U1 U2

0.04000

Value

Variable

Value

255,162 0 55,425 0 28,903 0 116,803 0 0 0 81,539 56,820 1 1

Y 21 Y 22 Y 23 Y 24 Y 25 Y 26 Y 31 Y 32 Y 33 Y 34 Y 35 Y 36 D1 D2 D3

0 0 19,243 9660 0 0 0 0 55,425 0 0 0 1 1 1 167,231

Value

Variable

Value

255,162 0 0 0 129,753 0 116,803 0 0 0 81,513 56,820 1 1

Y 21 Y 22 Y 23 Y 24 Y 25 Y 26 Y 31 Y 32 Y 33 Y 34 Y 35 Y 36 D1 D2 D3

0 75,450 44,568 9660 0 0 0 0 0 0 0 0 1 1 0 182,021

Objective value

Table 7 ANN simulation outputs (using Matlab 7.0). Variable Flow of products X 11 X 12 X 13 X 21 X 22 X 23 Y 11 Y 12 Y 13 Y 14 Y 15 Y 16

U1 U2 Objective value

third warehouse is closed. On the other hand analytical method gives us a solution in which all the factories and the warehouses are open. The cost of Warehouse 3 seems less than the others. However the cost of transportation from the factories to the warehouse is higher and it has a lower capacity. Because of being located near to the factories for Warehouse 1 and Warehouse 2, the transportation cost from factories to the warehouses costs lower. For this reason, it is considered to close the Warehouse 3. While ANN simulation finds 182,021 $ for the minimum cost, analytical method’s result is 167,231 $. It should be remembered that the alterations in the fixed costs or in capacities change the model results. If it is needed to make a sensitivity analysis to detail the MILP model structure, a variable must be changed while the others are constant. Demand is considered and emphasized as to be uncertain in this paper. For this reason, the right-hand side of the constraints under ‘‘balance constraint for the second echelon (demand constraint)” title is changed alternately, and then the changes in the objective value are observed. There are six demand constraints because of six distributors. So there are six sensitivity analysis results that are gained by changing the demand values on right-hand side of the constraints, consecutively. The objective value changes are shown in Fig. 7 by demand constraint changes, in a comparative manner. The demand values at the right-hand sides of the constraints are increased by the rate of 10%. Then the objective values that are

0.03000 0.02000 0.01000 0.00000 D1

D2

D3 AnalyticalCalc .

D4

D5

D6

ANN Sim.

Fig. 7. The sensitivity analysis results for analytical and ANN simulation methods.

needed to be minimized are increased, too. All experiments have global optimum after running the revised model. As seen from Fig. 6, maximum increase in the objective value is realized by the increase of the demand value for the first distributor demand constraint, for two of the methods. It means, the first constraint is the most sensitive one over against changes and affects the objective value intensively. The least increase is seen by the second distributor demand value increase in analytical method, while it is by the fourth distributor demand increase in ANN simulation. There are differences between objective value change amounts for two methods, but they are not far out from each other. Our model analyses the production flow among the members of supply chain and aims network cost minimization. It should be emphasized that our model contains limited echelons, data titles and decision criteria to realize the implementation process. But it is possible to expand the concept of SC and also to obtain more beneficial information by increasing the amount of data and diversifying the decision criteria. 5. Conclusion It is known that now the competition is not between the companies, competition is between the SCs that consist of several companies. As we think that the supply network efficiency is related to the weakest participant’s efficiency, the system should be improved by handling the problems with an integrated point of view for flexibility and efficiency. The basic priority for managing the SC in the right way is designing the SC network properly. In this study, an integrated SC design model is developed and a SC network design case is examined for a reputable multinational company in alcohol free beverage sector. Here, a three echelon SC network is considered and the proposed integrated neuro-fuzzy and MILP approach is applied to this network to realize the design effectively. Matlab 7.0 is used for neuro-fuzzy demand forecasting and, the deterministic, static, multi-echelon MILP model is solved using Lingo 10.0. Then Matlab 7.0 is used for ANN simulation to supply a comparative study and, to show the applicability and efficiency of ANN simulation for this type of problem. By evaluating the output data, the SC network for this case is designed, and also the optimal product flow between the factories, warehouses and distributors are calculated. Also it is proved that the ANN simulation can be used instead of analytical computations because of ensuring a simplified representation for this method and time saving. Our implementation considers only a part of the reference company’s supply chain system; however it can enlighten us about the whole system. To conclude, it can be said that, it is possible to expand the supply chain concept and having more accurate results about the whole system by increasing the amount of data and diversifying the decision criteria. Also, there is uncertainty for the cost and capacity variables in addition to demand. So, these variables can be calculated by benefiting from statistics, neuro-fuz-

A.T. Gumus et al. / Expert Systems with Applications 36 (2009) 12570–12577

zy approximation or another high-performance heuristic to ensure more realistic results. Appendix A. List of notation ai bj ck C ij C jk D F X ij Y jk

ui dj

the capacity of factory i the capacity of warehouse j the demand of distributor k the cost of transportation from factory i to warehouse j the cost of transportation from warehouse j to distributor k maximum total number of warehouses maximum total number of factories the quantity of the product from factory i to warehouse j the quantity of the product from warehouse j to distributor k fixed cost of factory i fixed cost of warehouse j



Ui ¼



Dj ¼

1; if factory is in use 0;

other

1; if warehouse is in use 0; other

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