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The retrofit of a closed-loop distribution network: the case of lead batteries
20th European Symposium on Computer Aided Process Engineering ± ESCAPE20 S. Pierucci and G. Buzzi Ferraris (Editors) © 2010 Elsevier B.V. All rights reserved.
The retrofit of a closed-loop distribution network: the case of lead batteries Ana Serra Fernandesa, Maria Isabel Gomes-Salema*b, Ana Paula BarbosaPovoaa, a
Centre for Management Studies, CEG-IST, UTL, Av. Rovisco Pais, 1049-101 Lisboa,
Portugal, [email protected] b
Centro de Matematica e Aplicacoes, FCT, Universidade Nova de Lisboa, Monte de
Caparica, 2825-114 Caparica, Portugal, [email protected]
Abstract Recent advances in global competition with the exhaustion of natural resources, and the increased society awareness towards environment created a new way of thinking when managing supply chains. Companies are now facing the need of seriously considering within their supply chain the presence of their end-of-life products. The concept of closed-loop supply chains has emerged where optimized structures are required. In this paper the design and planning of a real closed-loop supply chain is studied considering the production of lead batteries its distribution to the final clients and its collection at the end-of-life period. The company with a wide distribution network, at Portugal level, and a fleet of owned vehicles reached effectiveness in the delivery service to the final costumer. It is now vital to reach efficiency at costs level. To help reaching this goal the present work looks into the retrofit of the existing structure so as to achieve the optimized design of the closed-loop supply chain. A Mixed Integer Linear Programming (MILP) model is developed which simultaneously designs the forward and reverse chains. Various scenarios are built from which decisions regarding the retrofit of the existing network (namely, elimination, addition and replacement of warehouses) are obtained with a significant reduction of costs. The contemplated costs are: the cost of opening warehouses, the cost of the raw materials acquire to suppliers and of used products acquire to customers, as well as the cost of the different transportation resources. Besides strategic design, plans of supply, production, storage and transportation are also given by the model. The results obtained are compared with the existing network and important conclusions are drawn. Keywords: Closed-loop Supply chain, Retrofit, Network design, Network Planning.
1. Introduction Today companies, to remain competitive, have to provide a good service with very short delivery times and, simultaneously, at the lowest possible cost. To respond to the challenge of cost reduction and service enhancement, companies need to take a close look into the design and planning of their supply chain. Such logistics systems are however quite complex, especially when the recovery of end-of-life products is also at stake. So, it is difficult to take good decisions without the use of efficient tools to help **
Corresponding author
A.Fernandes et al.
the decision support process. The traditional supply chains, which start at raw materials and end at the final customers (forward flows), have been extensively discussed in the literature and reviews on the models studied can be found in Beamon (1998), Min and Zhou (2002), Goetschalckx et al. (2002), Shah (2005), Klose and Drexl (2005). It should be noted that these models are focused on strategic structural aspects of the supply chain, being the work developed by Sabri and Beamon (2000) an exception, as it allows simultaneously the strategic and operational (incorporates the production and the distribution) planning using a multi-objective analysis for of the supply chain. The reverse supply chains start at the collection of the products from the costumers and end when products are adequately recovered or eliminated (reverse flows). These networks also need strategic planning concerning the location of the facilities, such as collection and/or recycling centres. A large number of published models for design or retrofit of reverse networks is reviewed in Barbosa-Povoa et al. (2007). Most of the reviewed models were developed to solve specific problems and not of general application. When the supply chain integrated the forward and reverse networks, the closed-loop supply chain (CLSC) appears. The first generic model for CLSC was proposed by Fleischmann et al. (2001). In this work, the authors compared the simultaneous design of forward and reverse networks, with the design of the reverse network from an existing and operating forward network. Other published models on CLSC only contemplate strategic decisions regarding facility location, such as the case of Lu and Bostel (2007) where a model for the design of a network of producers, customers, intermediate centres and remanufacturing sites is proposed. However, very few models integrate within a single formulation the design of forward and reverse supply chain and, planning of activities such as production, acquisition, distribution, among others. The generic model presented by Salema et al. (2007) and later on generalised by the same authors (Salema et al., 2010) contributed to overcome such lack. In these models, within a single formulation, decisions concerning facilities site location and production, storage and distribution planning are taken into account simultaneously, within a predefined time horizon. The integration of strategic and tactical decisions is achieved through a multiperiod formulation, where two interconnected time scales are modelled. In this paper, this generic model is adapted and applied to the real case of a Portuguese company that produced and distributes lead batteries.
2. Case-study As referred above the case-study in analysis is of a Portuguese company, A. A. Silva, that produces and distributes lead batteries. This company wants to redesign and plan its current closed-loop supply chain, in order to minimize the total supply chain cost. The company has one factory operating in Oeiras that is responsible for supplying the entire distribution network. This network has in total 12 warehouses located at: Porto, Beja, Coimbra, Santarém, Tondela, Lisboa, Almada, Setúbal, Sines, Loulé, Viseu and Mirandela. All warehouses have maximum capacities of storage and a monthly fixed cost. These facilities work simultaneously as warehouses for the distribution to the customers and as a direct sales point to the public. Besides fulfilling the customers demand (forward flows), the company also collects the end-of-life batteries from the customers and takes them up to the factory (reverse flows), through the warehouses. Even though the demand of their 2300 clients has to be totally satisfied, the same is not imposed for collected. Nowadays, the company collects
The retrofit of a closed-loop distribution network: the case of lead batteries
15% of the total batteries sold. These reverse flows represent raw materials to produce new batteries. In terms of return freights, they are completely dependent on the existence of direct delivery freights. This is to mean, EOL batteries are collected only if new batteries were delivered. The transports used for the forward and reverse flows between the factory and the warehouses are subcontracted. Concerning the forward and reverse flows between the warehouses and the customers, the company uses its owned fleet. Each type of vehicle has its own capacity limit.
3. Model and Data Characterization A graph representation is used in this work to characterize the CLSC structure that goes from the factory to the customers and back to factories. This generic representation was presented by Salema et al. (2010). Nodes represent any supply chain entity, such as factories, warehouses, customers, distribution centres, while arcs between two nodes define an existing flow. The mathematical model integrates the forward chain, which links the factory to the customers through the warehouses, and the reverse chain, which deals with the return of the products from the customers up to the factory, again through the warehouses. Thus, the supply chain comprises three types of entities: factory, warehouses and customers. Each one of these entities is defined by its geographical location, Due to computational difficulties customers have to be clustered. Thus, the 2300 customers (in year 2008) are grouped into 237 customer-clusters with respect to the municipality they belong to (from now on, customer-cluster will be referred as customers). The same locations are assumed as possible candidates to locate warehouses. The model considers a distribution network formed by a single factory. As mentioned above, this factory is already operating and its location is not to be redefined. At the planning level, the macro-time unit is assumed to be equal to one year, and is divided into smaller units representative of one month each (micro-time unit). Customers are characterized by a known demand, for each month (micro-time unit), that needs to be totally satisfied within that month. The amount of products that can be collected at each customer, per year (macro unit), is modelled as fraction of the total product supplied. At the factory, returned products are used, together with new components, to produce new batteries. These returned products are disassembled and the resulting components represent the metals that are needed to produce of a new battery. Four collected batteries are needed to fulfil the necessary amount for the production of a new one. Inventories are modelled in all facilities and are limited to maximum level. The initial stock level at warehouses is assumed as zero. At the factory, the stock level is also limited to minimum value, equal to 10% of storage capacity. Two types of vehicles are considered according to the connection in question: one for the flows between the factory and the warehouses and another one for the flows between warehouses and costumers. Each type of vehicle is characterized by a cost and a transport capacity, by trip. No more collect trips exist than the delivery ones. When owned vehicles are used, the return trip always exists, since the vehicles must return to the warehouses where they belong. The different costs considered in the model are known or estimated. These are: warehouses fixed costs, supplying costs, transportation costs and the amount paid to customers for collecting end-of-life products. The transportation costs are calculated by different approaches, if primary or secondary distribution is considered. The model
A.Fernandes et al.
objective is to design the distribution network structure that minimizes the total supply chain cost.
4. Results The generic model formulation presented by Salema et al. (2010) is applied to the casestudy previously presented. Both the network structure and planning are analyzed. 4.1. Network Structure When comparing the results for the optimal network with the existent structure it can be seen that the former one is composed by one more warehouse than the latter one (14 and 13 warehouses, respectively). Six out of the thirteen current warehouses are kept unchanged (Viseu, Coimbra, Lisboa, Oeiras, Setúbal and Sines), two are closed (Almada and Tondela), three new locations are added (Braga, Guarda and Bombarral) and five of the current warehouses are replaced by new locations which are relatively close to the old one: Porto is replaced by Vila Nova de Gaia, Mirandela by Vila Real, Santarém by Torres Novas, Beja by Évora, and Loulé by São Brás de Alportel. The obtained RSWLPDO QHWZRUN SUHVHQWV D FRVW RI ¼ 3, which translates into a UHGXFWLRQRI¼RQWRWDOFRVWV when compared to the cost of the current network. 4.2. Network Planning In terms of the planning a large number of results are obtained. Due to the lack of space only an illustrative case (Barreiro customer) will be shown. This customer is supplied by two warehouses (Setúbal and Oeiras), and sends its returns to both warehouses. When analyzing with more detail the flow between the factory and Oeiras and Setúbal warehouses (figure 1) it can be seen that the flow to Setúbal occurs in every micro time unit, which is not the case for the Oeiras warehouse. The supplying and return plans of Barreiro customer are also presented (figures 2 and 3), followed by the reverse flows from Setúbal and Oeiras warehouses to the factory (figure 4). Here it can be seen that the Barreiro customers is essentially supplied by the Setúbal warehouse (figure 2), while the amount collected at Barreiro goes mainly to Oeiras warehouse (figure 3). It should be noted that the collection only occurs when the customer is supplied by the warehouses, since the return freights can only occur when associated with freights of demand satisfaction.
Fig.1: Flows from factory to Setúbal and Oeiras.
Fig. 2: Barreiro customer supplying plan.
The outbound flows from the Oeiras and Setúbal warehouses to the factory are shown in figure 4. The forward and reverse flows between the factory and the Setúbal and Oeiras warehouses (figures 1 and 4, respectively) are much larger when compared to the flows that occur between these warehouses and Barreiro (figure 2 and 3, respectively). This is explained by the fact that the warehouses of Oeiras and Setúbal are responsible for the supplying/collection of other 11 and 8 municipalities, respectively, besides Barreiro.
The retrofit of a closed-loop distribution network: the case of lead batteries
Fig. 3: Barreiro customer collection plan.
Fig. 4: Oeiras and Setúbal warehouses collection plans.
Figure 5 shows the number of freights for the referred flows that go through the Setúbal warehouse. These include the freights from the factory to Setúbal warehouse (z1) and from this warehouse to Barreiro (z2), from Barreiro back to Setúbal (z3) and from this warehouse to the factory (z4). The return freights (z3 and z4) do not occur every month, although the supplying freights (z1 and z2) do.
Fig. 5: Number of freights between the factory Fig. 6: Supplying and stock plans for the and Barreiro customer, through Setúbal warehouse. factory.
Finally, supplying and storage plans of the factory are shown in figure 6. These results differentiate the amounts that come from the collection of the end-of-life products at the customers from the ones acquired to the suppliers. It also shows the levels of stock created at the factory, in each month which varies according to the minimum and the maximum limits allowed. The recycled raw materials assume a greater importance in the second half of the year VHH µFROOHFWLRQ¶ , which is when return freights, from the warehouses to the factory, bring sufficient amounts that make the subcontracting of transport cost-effective. 4.3. Other Studies Additional analyses to the ones presented above were also conducted through the use of the developed mathematical model. An important one was the study on the maximum amount that could be paid for the EOL batteries using the current network. Taken as basis the current YDOXHSDLGIRUHDFKFROOHFWHGEDWWHU\ ¼ DQGHVWLPDWLQJDSRVVLEOH increase on the number of batteries collected (if an higher price would be paid) it was concluded that the optimal amount that could be supported by the actual network is of ¼VRDVWRJXDUDQWHHDPLQLPXPYDOXHIRUWKHtotal network cost. 4.4. Computational results The resulting MILP model was solved by GAMS/CPLEX (built 22.8), in a Intel (R) &RUH 'XR &38 *% *+] 7KH PRGHO LV FKDUDFWHUL]HG E\ variables (631394 binary) and 1432609 constraints, and took about 20835 CPU seconds to reach a 1% gap solution.
A.Fernandes et al.
5. Conclusions In this work, it was developed a mathematical formulation to model the real problem for the design and planning of a Portuguese supply chain with forward and reverse flows (CLSC). Within a single formulation, strategic decisions concerning warehouses number and location as well as tactical decisions concerning the planning level (supplying, production, storage and distribution planning) are taken simultaneously. Through the developed model, decisions on the distribution network retrofit were obtained which show the possibility of reducing significantly the current network costs. The carried out study illustrates the great advantage of using optimization models as they allow different test conditions to study and comparative results analysis. It also shows how a mathematical model can be a useful tool to solve complex logistic problems which corroborates the generic model applicability to study different supply chains and its adequacy to real world problems. As future work improvements of the present model are mentioned since computational difficulties led to the need of modelling, not only time but also space, in aggregated ways. When doing so, the model will allow more detailed planning throughout time and greater accuracy concerning the locations chosen for the warehouses.
References Barbosa-Povoa, A.P.F.D., M. I. Salema, M.I.G, and A. Q. Novais, (2007) Design and Planning of Closed-Loop Supply Chains. In Supply Chain Optimization in Supply Chain Optimization, Editores L. Papageorgiou e M.C. Georgiadis, Wiley-VCH, 7, 187-218. Beamon, B., (1998), "Supply Chain Design and Analysis: Models and Methods", International Journal of Production Economics, 55 (3), 281-294. Fleischmann, M., P.Beullens, J.Bloemhof-Ruwaard e L.Van Wassenhove,(2001),"The Impact of product recovery on logistics network design", Production and Operations Management, 10(2), 156-173. Goetschalckx, M., C. J. Vidal, and K. Dogan, (2002). Modeling and design of global logistics systems: A review of integrated strategic and tactical models and design algorithms. European Journal of Operational Research 143:1-18. Klose, A. e A. Drexl, (2005), "Facility Location Models for Distribution System Design", European Journal of Operational Research, 162 (1), 4-29. Lu, Z. e N. Bostel, (2007), "A facility location model for logistics systems including reverse flows: the case of remanufacturing activities", Computers and Operations Research, 34 (2), 299323. 0LQ + H * =KRX ³6XSSO\ FKDLQ PRGHOLQJ SDVW SUHVHQW DQG IXWXUH´ &RPSXWHUV DQG Industrial Engineering, 43, 231-249. 6DEUL(H%0%HDPRQ ³$0XOWL-Objective Approach to Simultaneous Strategic and 2SHUDWLRQDO3ODQQLQJLQ6XSSO\&KDLQ'HVLJQ´Omega, 28, 581-598. Salema, M.I.G., A. P. F. D. Barbosa-Povoa, e A. Q. Novais (2007), An Optimization Model for the Design for a Capacitated Multi-product Reverse Logistics Network with Uncertainty, European Journal of Operations Research (EJOR), 179,1063-1077 Salema, M. I. G., Barbosa-Povoa, A. P., and Novais, A. Q. (2010). "Simultaneous design and planning of supply chains with reverse flows: A generic modelling framework." European Journal of Operational Research, 203(2), 336-349. Shah, N., (2005), "Process Industry Supply Chains: Advances and Challenges", Computers and Chemical Engineering, 29 (6), 1225-1235.
The retrofit of a closed-loop distribution network: the case of lead batteries Ana Serra Fernandesa, Maria Isabel Gomes-Salema*b, Ana Paula BarbosaPovoaa, a
Centre for Management Studies, CEG-IST, UTL, Av. Rovisco Pais, 1049-101 Lisboa,
Portugal, [email protected] b
Centro de Matematica e Aplicacoes, FCT, Universidade Nova de Lisboa, Monte de
Caparica, 2825-114 Caparica, Portugal, [email protected]
Abstract Recent advances in global competition with the exhaustion of natural resources, and the increased society awareness towards environment created a new way of thinking when managing supply chains. Companies are now facing the need of seriously considering within their supply chain the presence of their end-of-life products. The concept of closed-loop supply chains has emerged where optimized structures are required. In this paper the design and planning of a real closed-loop supply chain is studied considering the production of lead batteries its distribution to the final clients and its collection at the end-of-life period. The company with a wide distribution network, at Portugal level, and a fleet of owned vehicles reached effectiveness in the delivery service to the final costumer. It is now vital to reach efficiency at costs level. To help reaching this goal the present work looks into the retrofit of the existing structure so as to achieve the optimized design of the closed-loop supply chain. A Mixed Integer Linear Programming (MILP) model is developed which simultaneously designs the forward and reverse chains. Various scenarios are built from which decisions regarding the retrofit of the existing network (namely, elimination, addition and replacement of warehouses) are obtained with a significant reduction of costs. The contemplated costs are: the cost of opening warehouses, the cost of the raw materials acquire to suppliers and of used products acquire to customers, as well as the cost of the different transportation resources. Besides strategic design, plans of supply, production, storage and transportation are also given by the model. The results obtained are compared with the existing network and important conclusions are drawn. Keywords: Closed-loop Supply chain, Retrofit, Network design, Network Planning.
1. Introduction Today companies, to remain competitive, have to provide a good service with very short delivery times and, simultaneously, at the lowest possible cost. To respond to the challenge of cost reduction and service enhancement, companies need to take a close look into the design and planning of their supply chain. Such logistics systems are however quite complex, especially when the recovery of end-of-life products is also at stake. So, it is difficult to take good decisions without the use of efficient tools to help **
Corresponding author
A.Fernandes et al.
the decision support process. The traditional supply chains, which start at raw materials and end at the final customers (forward flows), have been extensively discussed in the literature and reviews on the models studied can be found in Beamon (1998), Min and Zhou (2002), Goetschalckx et al. (2002), Shah (2005), Klose and Drexl (2005). It should be noted that these models are focused on strategic structural aspects of the supply chain, being the work developed by Sabri and Beamon (2000) an exception, as it allows simultaneously the strategic and operational (incorporates the production and the distribution) planning using a multi-objective analysis for of the supply chain. The reverse supply chains start at the collection of the products from the costumers and end when products are adequately recovered or eliminated (reverse flows). These networks also need strategic planning concerning the location of the facilities, such as collection and/or recycling centres. A large number of published models for design or retrofit of reverse networks is reviewed in Barbosa-Povoa et al. (2007). Most of the reviewed models were developed to solve specific problems and not of general application. When the supply chain integrated the forward and reverse networks, the closed-loop supply chain (CLSC) appears. The first generic model for CLSC was proposed by Fleischmann et al. (2001). In this work, the authors compared the simultaneous design of forward and reverse networks, with the design of the reverse network from an existing and operating forward network. Other published models on CLSC only contemplate strategic decisions regarding facility location, such as the case of Lu and Bostel (2007) where a model for the design of a network of producers, customers, intermediate centres and remanufacturing sites is proposed. However, very few models integrate within a single formulation the design of forward and reverse supply chain and, planning of activities such as production, acquisition, distribution, among others. The generic model presented by Salema et al. (2007) and later on generalised by the same authors (Salema et al., 2010) contributed to overcome such lack. In these models, within a single formulation, decisions concerning facilities site location and production, storage and distribution planning are taken into account simultaneously, within a predefined time horizon. The integration of strategic and tactical decisions is achieved through a multiperiod formulation, where two interconnected time scales are modelled. In this paper, this generic model is adapted and applied to the real case of a Portuguese company that produced and distributes lead batteries.
2. Case-study As referred above the case-study in analysis is of a Portuguese company, A. A. Silva, that produces and distributes lead batteries. This company wants to redesign and plan its current closed-loop supply chain, in order to minimize the total supply chain cost. The company has one factory operating in Oeiras that is responsible for supplying the entire distribution network. This network has in total 12 warehouses located at: Porto, Beja, Coimbra, Santarém, Tondela, Lisboa, Almada, Setúbal, Sines, Loulé, Viseu and Mirandela. All warehouses have maximum capacities of storage and a monthly fixed cost. These facilities work simultaneously as warehouses for the distribution to the customers and as a direct sales point to the public. Besides fulfilling the customers demand (forward flows), the company also collects the end-of-life batteries from the customers and takes them up to the factory (reverse flows), through the warehouses. Even though the demand of their 2300 clients has to be totally satisfied, the same is not imposed for collected. Nowadays, the company collects
The retrofit of a closed-loop distribution network: the case of lead batteries
15% of the total batteries sold. These reverse flows represent raw materials to produce new batteries. In terms of return freights, they are completely dependent on the existence of direct delivery freights. This is to mean, EOL batteries are collected only if new batteries were delivered. The transports used for the forward and reverse flows between the factory and the warehouses are subcontracted. Concerning the forward and reverse flows between the warehouses and the customers, the company uses its owned fleet. Each type of vehicle has its own capacity limit.
3. Model and Data Characterization A graph representation is used in this work to characterize the CLSC structure that goes from the factory to the customers and back to factories. This generic representation was presented by Salema et al. (2010). Nodes represent any supply chain entity, such as factories, warehouses, customers, distribution centres, while arcs between two nodes define an existing flow. The mathematical model integrates the forward chain, which links the factory to the customers through the warehouses, and the reverse chain, which deals with the return of the products from the customers up to the factory, again through the warehouses. Thus, the supply chain comprises three types of entities: factory, warehouses and customers. Each one of these entities is defined by its geographical location, Due to computational difficulties customers have to be clustered. Thus, the 2300 customers (in year 2008) are grouped into 237 customer-clusters with respect to the municipality they belong to (from now on, customer-cluster will be referred as customers). The same locations are assumed as possible candidates to locate warehouses. The model considers a distribution network formed by a single factory. As mentioned above, this factory is already operating and its location is not to be redefined. At the planning level, the macro-time unit is assumed to be equal to one year, and is divided into smaller units representative of one month each (micro-time unit). Customers are characterized by a known demand, for each month (micro-time unit), that needs to be totally satisfied within that month. The amount of products that can be collected at each customer, per year (macro unit), is modelled as fraction of the total product supplied. At the factory, returned products are used, together with new components, to produce new batteries. These returned products are disassembled and the resulting components represent the metals that are needed to produce of a new battery. Four collected batteries are needed to fulfil the necessary amount for the production of a new one. Inventories are modelled in all facilities and are limited to maximum level. The initial stock level at warehouses is assumed as zero. At the factory, the stock level is also limited to minimum value, equal to 10% of storage capacity. Two types of vehicles are considered according to the connection in question: one for the flows between the factory and the warehouses and another one for the flows between warehouses and costumers. Each type of vehicle is characterized by a cost and a transport capacity, by trip. No more collect trips exist than the delivery ones. When owned vehicles are used, the return trip always exists, since the vehicles must return to the warehouses where they belong. The different costs considered in the model are known or estimated. These are: warehouses fixed costs, supplying costs, transportation costs and the amount paid to customers for collecting end-of-life products. The transportation costs are calculated by different approaches, if primary or secondary distribution is considered. The model
A.Fernandes et al.
objective is to design the distribution network structure that minimizes the total supply chain cost.
4. Results The generic model formulation presented by Salema et al. (2010) is applied to the casestudy previously presented. Both the network structure and planning are analyzed. 4.1. Network Structure When comparing the results for the optimal network with the existent structure it can be seen that the former one is composed by one more warehouse than the latter one (14 and 13 warehouses, respectively). Six out of the thirteen current warehouses are kept unchanged (Viseu, Coimbra, Lisboa, Oeiras, Setúbal and Sines), two are closed (Almada and Tondela), three new locations are added (Braga, Guarda and Bombarral) and five of the current warehouses are replaced by new locations which are relatively close to the old one: Porto is replaced by Vila Nova de Gaia, Mirandela by Vila Real, Santarém by Torres Novas, Beja by Évora, and Loulé by São Brás de Alportel. The obtained RSWLPDO QHWZRUN SUHVHQWV D FRVW RI ¼ 3, which translates into a UHGXFWLRQRI¼RQWRWDOFRVWV when compared to the cost of the current network. 4.2. Network Planning In terms of the planning a large number of results are obtained. Due to the lack of space only an illustrative case (Barreiro customer) will be shown. This customer is supplied by two warehouses (Setúbal and Oeiras), and sends its returns to both warehouses. When analyzing with more detail the flow between the factory and Oeiras and Setúbal warehouses (figure 1) it can be seen that the flow to Setúbal occurs in every micro time unit, which is not the case for the Oeiras warehouse. The supplying and return plans of Barreiro customer are also presented (figures 2 and 3), followed by the reverse flows from Setúbal and Oeiras warehouses to the factory (figure 4). Here it can be seen that the Barreiro customers is essentially supplied by the Setúbal warehouse (figure 2), while the amount collected at Barreiro goes mainly to Oeiras warehouse (figure 3). It should be noted that the collection only occurs when the customer is supplied by the warehouses, since the return freights can only occur when associated with freights of demand satisfaction.
Fig.1: Flows from factory to Setúbal and Oeiras.
Fig. 2: Barreiro customer supplying plan.
The outbound flows from the Oeiras and Setúbal warehouses to the factory are shown in figure 4. The forward and reverse flows between the factory and the Setúbal and Oeiras warehouses (figures 1 and 4, respectively) are much larger when compared to the flows that occur between these warehouses and Barreiro (figure 2 and 3, respectively). This is explained by the fact that the warehouses of Oeiras and Setúbal are responsible for the supplying/collection of other 11 and 8 municipalities, respectively, besides Barreiro.
The retrofit of a closed-loop distribution network: the case of lead batteries
Fig. 3: Barreiro customer collection plan.
Fig. 4: Oeiras and Setúbal warehouses collection plans.
Figure 5 shows the number of freights for the referred flows that go through the Setúbal warehouse. These include the freights from the factory to Setúbal warehouse (z1) and from this warehouse to Barreiro (z2), from Barreiro back to Setúbal (z3) and from this warehouse to the factory (z4). The return freights (z3 and z4) do not occur every month, although the supplying freights (z1 and z2) do.
Fig. 5: Number of freights between the factory Fig. 6: Supplying and stock plans for the and Barreiro customer, through Setúbal warehouse. factory.
Finally, supplying and storage plans of the factory are shown in figure 6. These results differentiate the amounts that come from the collection of the end-of-life products at the customers from the ones acquired to the suppliers. It also shows the levels of stock created at the factory, in each month which varies according to the minimum and the maximum limits allowed. The recycled raw materials assume a greater importance in the second half of the year VHH µFROOHFWLRQ¶ , which is when return freights, from the warehouses to the factory, bring sufficient amounts that make the subcontracting of transport cost-effective. 4.3. Other Studies Additional analyses to the ones presented above were also conducted through the use of the developed mathematical model. An important one was the study on the maximum amount that could be paid for the EOL batteries using the current network. Taken as basis the current YDOXHSDLGIRUHDFKFROOHFWHGEDWWHU\ ¼ DQGHVWLPDWLQJDSRVVLEOH increase on the number of batteries collected (if an higher price would be paid) it was concluded that the optimal amount that could be supported by the actual network is of ¼VRDVWRJXDUDQWHHDPLQLPXPYDOXHIRUWKHtotal network cost. 4.4. Computational results The resulting MILP model was solved by GAMS/CPLEX (built 22.8), in a Intel (R) &RUH 'XR &38 *% *+] 7KH PRGHO LV FKDUDFWHUL]HG E\ variables (631394 binary) and 1432609 constraints, and took about 20835 CPU seconds to reach a 1% gap solution.
A.Fernandes et al.
5. Conclusions In this work, it was developed a mathematical formulation to model the real problem for the design and planning of a Portuguese supply chain with forward and reverse flows (CLSC). Within a single formulation, strategic decisions concerning warehouses number and location as well as tactical decisions concerning the planning level (supplying, production, storage and distribution planning) are taken simultaneously. Through the developed model, decisions on the distribution network retrofit were obtained which show the possibility of reducing significantly the current network costs. The carried out study illustrates the great advantage of using optimization models as they allow different test conditions to study and comparative results analysis. It also shows how a mathematical model can be a useful tool to solve complex logistic problems which corroborates the generic model applicability to study different supply chains and its adequacy to real world problems. As future work improvements of the present model are mentioned since computational difficulties led to the need of modelling, not only time but also space, in aggregated ways. When doing so, the model will allow more detailed planning throughout time and greater accuracy concerning the locations chosen for the warehouses.
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