- Email: [email protected]
Modelling and Analysing Supply Chain Resilience Flow Complexity
Anton Friedl, Jiří J. Klemeš, Stefan Radl, Petar S. Varbanov, Thomas Wallek (Eds.) Proceedings of the 28th European Symposium on Computer Aided Process Engineering June 10th to 13th, 2018, Graz, Austria. © 2018 Elsevier B.V. All rights reserved. https://doi.org/10.1016/B978-0-444-64235-6.50143-1
Modelling and Analysing Supply Chain Resilience Flow Complexity Jo˜ao Pires Ribeiroa,* and Ana Barbosa-P´ovoaa a CEG-IST,
Instituto Superior T´ecnico, University of Lisbon, Av. Rovisco Pais, 1049-001 Lisboa, Portugal [email protected]
Abstract Globalization has increased the exposure of Supply Chains (SC) to higher uncertainties that call for adequate strategies, thus supporting the creation of SC Resilience. There is, however, no absolute strategy that decision makers can follow to guarantee such resilience and the knowledge on how to characterise SC resilience (SCR) is still an open issue. This work focuses on a strategic level of decision and analyses the relationship between SCR and SC complexity, aiming to conclude how SC flow complexity reflects SCR. The design and planning of a multi-product, multi-period SC are addressed through a Mixed Integer Linear Programming (MILP) model where demand uncertainty is considered. A set of disruptions is studied for different SC structures and as main conclusions, it can be stated that SC flow complexity leads to an increase in SC resilient performance and appears as a good indicator of SCR. Keywords: Supply Chain Resilience, Quantitative models, Flow Complexity; Design and Planning
1. Introduction The concept of Supply Chain Management was for the first time introduced in the XX century by Oliver et al. (1982) and since then has evolved. The need to guarantee competitiveness in a global market has lead SC to expand geographically and consequently, SC structures have been facing an increased exposure to risks due to a larger set of uncertainties that they have to deal with. This has created the necessity of deeply analysing the concept of SC resilience as a way to deal with such uncertain context. This is critical in the case of process supply chain as this type of systems are frequently global chains, whose business spreads around the globe, and whose products with great importance to society have to be continuously available, as is the case of pharmaceuticals, food, chemicals, energy, amongst others (Barbosa-P´ovoa, 2014). SCR is one of the newer concepts in SC and it comes as a need to better prepare SC for challenges brought by global SC operations. As stated by Ribeiro and Barbosa-Povoa (2018) in a recent review on the topic, “A resilient supply chain should be able to prepare, respond and recover from disturbances and afterwards maintain a positive steady state operation in an acceptable cost and time”. In such setting, the interest in a sound understanding of SCR has led academics and companies to pursuit efforts regarding such objective (Tang, 2006; Kamalahmadi and Parast, 2016). It is on the best interest of real SC the increase in knowledge in SCR as it is fundamental to better understand not only the resilience concept but also how this can help SC to deal with disruptive events that can endanger their steady-state operation (Cardoso et al., 2015). Several authors have been recently
J. Pires Ribeiro and A. Barbosa Póvoa
816
studying SCR but there is still a lack of understanding on how to quantify SCR (Ribeiro and Barbosa-Povoa, 2018). Cardoso et al. (2015) studied SCR and proposed a set of SC indicators that could be used to analyse SCR. SC flow complexity was identified as one of the most promising indicators and further studies on this should be performed to confirm such result. Based on these results, the present work focus on the design and planning of SC where decisions taken on the SC network structure are analysed. A design and planning multi-product, multiperiod MILP model is developed where demand uncertainty is considered. Five different supply chain structures are analysed and the associated complexity optimized. The resulted SC structures are subject to a set of disruptive events and their resilience is analysed.
2. Problem and Model Description In order to be able to discuss how different SC networks behave towards resilience, a five echelons supply chain was considered, where reverse flows are also possible to occur. Such SC involves: Raw Material Suppliers; Plants that can also function as Disassembling Centres with end of life products; Warehouses with added value activities as reconditioning non-conforming products; Outsourcing contractors as an alternative to plants production and finally Markets. In the plants and warehouses, technologies can be installed, which influence production, assembly and disassembly processes. These technologies can be fitted to the entities, or upgraded, to provide better performance. Based on this generic SC structure five different SC cases are studied where different SC structures are considered and allow to compare and construe results on SC resilience: Case A - a forward supply chain; Case B - similar to A, but now integrating also reverse flows between consecutive echelons; Case C - similar to B, but plants and markets can directly exchange products, thus bypassing the warehouses; Case D - similar to B, but with the possibility of transhipment at plants, disassembling centres and warehouses; Case E - the most general case, encompassing all the previous ones, forming a closed-loop supply chain where plants send directly products to markets and can also receive directly from markets the end-of-life products. Transhipment is allowed at plants, warehouses and disassembling centres. The MILP model developed by Cardoso et al. (2015) is taken as a base and was adapted to this work goals, providing a new objective function and a set of constraints to study SC flow complexity. Uncertainty was considered in the SC demand and on Disruptions. A scenario tree is constructed combining the two sources of uncertainty. Demand variability is introduced by generating a scenario on each period from a set of three possibilities (Pessimistic, Realistic or Optimistic). The result probabilistic nodes are then combined with the variability from the disruption that can only assume two options, or it occurs or it does not occur on a specific time period to consider. With this, each scenario probability is given by the probabilities of the path, with all stages, between the root node and each final leaf node. 2.1. Objective Function Two objective functions are studied, Equations 1 and 2. A first one considers the maximization of the network flow complexity (Equation 1), as this would return a network configuration with maximum flow complexity (FC) under the feasibility space generated by problem constraints, being FCt the summation of all positive flows present in the SC for each time period.
Max ∑ FCt
(1)
t
This model formulation, although returning a SC with the maximum amount of feasible possible flows does not take into consideration economic concerns, leading to solutions that may have a
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low performance in financial terms. This issue can, however, be tackled by setting additional constraints in the model, as is the case of establishing a minimum profit that must be obeyed. However, this method was not followed due to two reasons. First, restrictions had to apply to all cases and scenarios, which involve setting up conditions that cannot interfere with the feasibility of the model. Second, by setting up new conditions there is the possibility of endangering the established relationship and compatibility with the original model. Therefore, a two-step approach is followed. Primarily the model is run based on Equation 1 to retrieve the SC with maximum flow complexity within the model feasibility. The second step is used to retrieve the obtained network configuration and then study how much such network configuration maximizes the economic return. The economic return is based on the Expected Net Present Value, Equation 2 (where CF stands for the Cash flow for each scenario and time period, and ir for a defined interest rate). Trough this method it is ensured a network with maximum flow complexity and with the most advantageous economic performance to the company.
MaxENPV = ∑ pbs × NPVs s
pbs = Probability scenarios
NPVs = ∑ t
CFst (2) (1 + ir)t
By fixing the network configuration there is no capability for the SC network to change, however, it can adapt to the variability introduced in each situation by investing in new technologies, or upgrades to the existing facilities as well as optimize the supply chain flows.
3. Case Study The presented model is tested in a Case Study of an European Chemical Process SC. The values associated are scaled down, due to confidentiality reasons. The initial SC configuration comprises a set of European locations, with one plant in Hamburg, one warehouse in Munich, four raw materials suppliers, 3 suppliers of final products and 18 Europeans cities as markets. In broad terms, the company is studying the existent SC in order to access the investment necessary in technologies for current entities, or the implementation of new facilities, to improve the SC’s resilient capability. Four operational conditions are studied; one reference case with perfect operational conditions and three examples of disruptions. The disruptions were chosen following failure modes defined by Rice and Caniato (2003). Disruption 1 (Production Facilities)- ” 100% decrease in the production capacity of the most important plant (plant Pl3), in time period 2, caused, for example, by a major natural catastrophe”. Disruption 2 (Supply)- ”The most important raw materials suppliers (s3, s5, s8, s9 and s10) have their supply suspended in time period 2, due to an assumed industrial action”. Disruption 3 (Transportation)- ”The 3PL hired to operate those transportation links, between plants and warehouses, that carry the highest quantity of products (links between Pl3 and warehouses W1, W2 and W4), goes out of business in time period 2”. The scenario tree responsible for the uncertainty in the demand is built based on the assumption that the demand in the beginning is known and that there are three possible branches for time period 2 and 3, with the same probability in both periods; Optimistic 0.25, Realistic 0.5 and Pessimistic 0.25. (Time period 2: Optimistic with an increase of 10%; Realistic with an increase of 3%; Pessimistic with a decrease of 2%. Time period 3: Optimistic with an increase of 5%; Realistic with an increase of 2%; Pessimistic with a decrease of 2%) For each SC case, two configurations are established based on the SC network provided by the two objective functions: maximization of ENPV and maximization of flow complexity, when there is no disruption. These network designs are then subject to the disruptions and the results are analysed and discussed. The MILP model is developed using the GAMS software. The results when applying a network configuration for ENPV maximization can be seen in Table 1, whereas the results for a SC with its flow complexity maximized are presented in Table 2.
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Table 1: Combined results for ENPV Maximization Case A Reference Disruption 1 Disruption 2 Disruption 3 Case B Reference Disruption 1 Disruption 2 Disruption 3 Case C Reference Disruption 1 Disruption 2 Disruption 3 Case D Reference Disruption 1 Disruption 2 Disruption 3 Case E Reference Disruption 1 Disruption 2 Disruption 3
Complexity 46 46 44 44 Complexity 89 84 87 87 Complexity 110 109 108 108 Complexity 90 83 89 88 Complexity 106 102 104 104
ENPV 1.96E+07 1.65E+07 1.78E+07 1.83E+07 ENPV 1.91E+07 1.64E+07 1.77E+07 1.79E+07 ENPV 2.05E+07 1.66E+07 1.45E+07 1.84E+07 ENPV 1.91E+07 1.55E+07 1.77E+07 1.79E+07 ENPV 2,05E+07 1,64E+07 1,65E+07 1,84E+07
FCI 7.61E+05 8.10E+05 1.06E+06 7.80E+05 FCI 7.65E+05 7.99E+05 1.04E+06 7.89E+05 FCI 8.45E+05 9.58E+05 9.84E+05 9.31E+05 FCI 7.65E+05 8.28E+05 1.04E+06 7.88E+05 FCI 8,46E+05 9,68E+05 1,00E+06 9,31E+05
Investment 7.32E+05 7.81E+05 1.03E+06 7.52E+05 Investment 7.20E+05 7.56E+05 9.92E+05 7.45E+05 Investment 7.90E+05 9.03E+05 9.30E+05 8.77E+05 Investment 7.20E+05 7.86E+05 9.95E+05 7.44E+05 Investment 7,91E+05 9,14E+05 9,47E+05 8,77E+05
Inventory 1450.707 1084.072 1231.576 1278.613 Inventory 1449.68 1091.136 1229.269 1301.026 Inventory 913.478 791.844 720.256 885.054 Inventory 1452.711 1123.564 1227.958 1301.334 Inventory 913,478 796,152 805,425 885,033
Purchases 342670 356550 373537.712 313616.662 Purchases 334490 346070 302462.827 304995.435 Purchases 380870 377550 374369 457070 Purchases 334880 266442.058 302704.653 304860.924 Purchases 380670 379080 348862,167 4,55E+05
Sales 50563000 43821000 47473000 48435000 Sales 50548000 44301000 47672000 48744000 Sales 52937000 45538000 40396400 51674000 Sales 50586000 42559300 47651000 48747000 Sales 52940000 45463000 44065000 51674000
ECSL 85.7% 63.3% 72.1% 75.7% ECSL 85.6% 63.8% 72.0% 77.0% ECSL 99.4% 83.4% 71.8% 98.4% ECSL 85.8% 65.5% 72.0% 77.0% ECSL 96,4% 83,7% 77,8% 98,4%
3.1. Case A Case A represents a simple SC structure allowing only forward flows. One relevant analysis can be made regarding the delta of ENPV value between the two options, maximizing ENPV versus maximizing complexity. Comparing the results from both configurations, respectively in Tables 1 and 2 it can be seen an increase in service quality (ECSL) and that the loss in ENPV by incrementing complexity (-0.01E7e) is easily compensated by the gains in disruption 1 and 2 (0.15E7e and 0.1E7e), representing gains of 9% and 5% respectively. During Disruption 3 the leaner SC network is able to provide the same economic return than the network with increased complexity, however, it does so with a decreased service quality. 3.2. Case B Case B represents a SC structure where reverse flows are allowed between consecutive echelons adding complexity to the operation. It is expected an increase in flow complexity in order to cope with such requirement. The SC configuration with ENPV maximization has an increased impact from disruptions causing a decrease in ENPV of 14%, 7% and 6% for disruptions 1, 2 and 3 respectively. When no disruption is present a variation of -0.03E7e in ENPV is expected, when the SC shifts to a more complex network the ENPV variation are positive, with a gain more than the double of the cost if no disruption is present. The service quality is also impacted by a more complex configuration with improvements of 21%, 15% and 7% for disruptions 1, 2 and 3 respectively. 3.3. Case C Case C introduces a different kind of flexibility to the network, it allows the same flows as Case B and also allows for plants and markets to exchange products without any warehouse intervention. There is an increased susceptibility to Disruption 2 in Case C and this is much related with the non-existence of transhipment between entities in the same echelon. The leaner SC has a decrease in ENPV of 19%, 30% and 10% for disruptions 1, 2 and 3 respectively, while the more complex
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Modelling and Analysing Supply Chain Resilience Flow Complexity
Table 2: Combined results for Complexity Maximization Case A Reference Disruption 1 Disruption 2 Disruption 3 Case B Reference Disruption 1 Disruption 2 Disruption 3 Case C Reference Disruption 1 Disruption 2 Disruption 3 Case D Reference Disruption 1 Disruption 2 Disruption 3 Case E Reference Disruption 1 Disruption 2 Disruption 3
Complexity 156 156 151 154 Complexity 346 343 341 344 Complexity 495 495 491 493 Complexity 376 373 372 374 Complexity 525 516 520 523
ENPV 1.95E+07 1.80E+07 1.88E+07 1.83E+07 ENPV 1.89E+07 1.75E+07 1.83E+07 1.78E+07 ENPV 2.03E+07 1.89E+07 1.83E+07 1.94E+07 ENPV 1.89E+07 1.75E+07 1.82E+07 1.78E+07 ENPV 2,03E+07 1,89E+07 1,92E+07 1,94E+07
FCI 8.30E+05 9.54E+05 9.56E+05 8.78E+05 FCI 9.01E+05 1.01E+06 1.03E+06 9.41E+05 FCI 1.05E+06 1.22E+06 1.29E+06 1.09E+06 FCI 9.21E+05 1.03E+06 1.07E+06 9.59E+05 FCI 1,07E+06 1,23E+06 1,25E+06 1,10E+06
Investment 7.32E+05 8.56E+05 8.61E+05 7.81E+05 Investment 7.19E+05 8.30E+05 8.47E+05 7.61E+05 Investment 7.90E+05 9.59E+05 1.03E+06 8.29E+05 Investment 7.20E+05 8.28E+05 8.75E+05 7.59E+05 Investment 7,89E+05 9,51E+05 9,80E+05 8,26E+05
Inventory 1451.691 1305.564 1409.266 1392.458 Inventory 1451.139 1320.152 1409.159 1390.301 Inventory 914.547 915.528 918.789 914.66 Inventory 1456.127 1355.382 1381.246 1391.087 Inventory 915,493 916,495 975,706 915,648
Purchases 342800 316095.608 333077.386 328540 Purchases 334770 310323.917 324379.133 320275.72 Purchases 381050 364530 345240 378400 Purchases 335370 314110.778 316696.483 319616.258 Purchases 380820 365270 354997,874 377860
Sales 50572000 48831000 50058000 49883000 Sales 50564000 49012000 50053000 49855000 Sales 52933000 52193000 51382000 52886000 Sales 50607000 49432000 49723000 49853000 Sales 52933000 52210000 51803000 52886000
ECSL 85.8% 76.9% 83.1% 82.2% ECSL 85.7% 76.9% 83.1% 82.1% ECSL 99.4% 95.1% 90.1% 98.9% ECSL 85.9% 79.9% 81.5% 82.1% ECSL 99,4% 95,2% 92,8% 99,0%
SC shows improvements of 14%, 27% and 5% for disruptions 1, 2 and 3 respectively. In terms of service quality it is perceptible an increase in ECSL for the more complex structure, maintaining levels of above 90% even during disruptions. 3.4. Case D Case D allows forward and reverse flows between consecutive echelons and adds a new set of possibilities by allowing transhipment at plants, disassembling centres and warehouses. Applying the leaner configuration, disruptions cause an ENPV decrease of 19%, 7% and 6% for disruptions 1, 2 and 3 respectively. These results can be improved by 13% and 3% for disruptions 1 and 2 respectively, if a more complex network is deployed. In terms of ECSL the leaner configuration leads to a decrease of 24%, 16% and 10% for disruptions 1, 2 and 3 respectively, the more complex network allows for a steady service level of around 80%, improving the alternative configuration by 22%, 13% and 7% for disruptions 1, 2 and 3 respectively. 3.5. Case E Case E represents a network that includes all the possibilities from previous cases. This closed loop SC can perform transhipment at all levels, except for markets, and flows bypassing intermediate entities are also allowed. ENPV variations between steady-state operation and disruptive scenarios are visible, resulting in a decrease of 20%, 20% and 10% for disruptions 1, 2 and 3 respectively on the network provided by the ENPV maximization. On the other hand, applying the more complex network the results of ENPV during the disruptive events are improved by 15%, 16% and 5% for disruptions 1, 2 and 3 respectively. With the maximization of complexity, the SC can return ECSL higher than 90% in all scenarios, even when a disruption does occur. When a leaner network is implemented disruptive scenarios cause a decrease in service level of 13% and 19% for disruptions 1 and 2 respectively. Applying the network with a higher amount of permitted flows leads to an improvement of 14%, 19% and 1% for disruptions 1, 2 and 3 respectively.
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4. Conclusions and Discussion From the above study, it can be concluded that the obtained results vary not only with the SC complexity but also with the SC structure (e.g. forward or closed-loop) as well with the different types of disruptions. Different disruptions cause different results and so decision makers should have enough information to make the most acceptable decision considering model results and available information. It is in this line that, studying SC Resilience factors gain importance, as it allows the development of better models to aid decision making. Considering the behaviour on ENPV caused by the increased complexity, when no disruption occurs, is observed an increment on costs, due to the obligations that come from opening and maintaining more facilities and flows. However, if disruptions occur, there is an evident benefit of operating a more complex SC. The difference in ENPV in disruptive scenarios between the more complex and a leaner SC is always positive, in comparison with not investing in preventive strategies. There is a more evident benefit from deploying a more complex SC in terms of ECSL. The notable shift is made possible by the increased flexibility and redundancy allowed by the higher amount of entities and flows involved resulting in an increased SC responsiveness. The investment made in increasing complexity is completely overcome by the resilience created in the supply chain structures as they are able to better react to disruptions guaranteeing higher service levels and higher profit values. However, this characteristic should be always met by a specific analysis of each SC and to its, perceptible, vulnerabilities. As a final analysis, it is relevant to compare the results of this paper with those from the original publication of Cardoso et al. (2015), aimed at maximizing ENPV for each SC structure and scenario. As expected, our results produce a network with lower ENPV but with a trade-off for better ECSL. As main conclusions, it can be said that investing in proactive resilient Supply Chain Design can reduce losses, generate value to companies and reduce the need for reactive strategies, in case of facing a disruptive event. With this work, we are also capable of attesting the positive correlation between the increased SC complexity with a positive outcome in case of some disruptions, as suggested by Cardoso et al. (2015) in their study. Acknowledgements The authors acknowledge the project DPI2015-67740-P (MINECO/FEDER)
References A. P. Barbosa-P´ovoa, 2014. Process supply chains management - where are we? where to go next? Frontiers in Energy Research 2, 23. URL https://www.frontiersin.org/article/10.3389/fenrg.2014.00023 S. R. Cardoso, A. P. Barbosa-P´ovoa, S. Relvas, A. Q. Novais, 2015. Resilience metrics in the assessment of complex supply-chains performance operating under demand uncertainty. Omega 56, 53–73. M. Kamalahmadi, M. M. Parast, 2016. A review of the literature on the principles of enterprise and supply chain resilience: Major findings and directions for future research. International Journal of Production Economics 171, 116–133. R. K. Oliver, M. D. Webber, et al., 1982. Supply-chain management: logistics catches up with strategy. Outlook 5 (1), 42–47. J. P. Ribeiro, A. Barbosa-Povoa, 2018. Supply Chain Resilience: Definitions and quantitative modelling approaches - A literature review. Computers & Industrial Engineering 115, 109 – 122. URL https://www.sciencedirect.com/science/article/pii/S0360835217305272 J. B. Rice, F. Caniato, 2003. Building a secure and resilient supply network. Supply Chain Management Review, V. 7, No. 5 (Sept./Oct. 2003), P. 22-30: Ill. C. S. Tang, 2006. Perspectives in supply chain risk management. International Journal of Production Economics 103 (2), 451–488.
Modelling and Analysing Supply Chain Resilience Flow Complexity Jo˜ao Pires Ribeiroa,* and Ana Barbosa-P´ovoaa a CEG-IST,
Instituto Superior T´ecnico, University of Lisbon, Av. Rovisco Pais, 1049-001 Lisboa, Portugal [email protected]
Abstract Globalization has increased the exposure of Supply Chains (SC) to higher uncertainties that call for adequate strategies, thus supporting the creation of SC Resilience. There is, however, no absolute strategy that decision makers can follow to guarantee such resilience and the knowledge on how to characterise SC resilience (SCR) is still an open issue. This work focuses on a strategic level of decision and analyses the relationship between SCR and SC complexity, aiming to conclude how SC flow complexity reflects SCR. The design and planning of a multi-product, multi-period SC are addressed through a Mixed Integer Linear Programming (MILP) model where demand uncertainty is considered. A set of disruptions is studied for different SC structures and as main conclusions, it can be stated that SC flow complexity leads to an increase in SC resilient performance and appears as a good indicator of SCR. Keywords: Supply Chain Resilience, Quantitative models, Flow Complexity; Design and Planning
1. Introduction The concept of Supply Chain Management was for the first time introduced in the XX century by Oliver et al. (1982) and since then has evolved. The need to guarantee competitiveness in a global market has lead SC to expand geographically and consequently, SC structures have been facing an increased exposure to risks due to a larger set of uncertainties that they have to deal with. This has created the necessity of deeply analysing the concept of SC resilience as a way to deal with such uncertain context. This is critical in the case of process supply chain as this type of systems are frequently global chains, whose business spreads around the globe, and whose products with great importance to society have to be continuously available, as is the case of pharmaceuticals, food, chemicals, energy, amongst others (Barbosa-P´ovoa, 2014). SCR is one of the newer concepts in SC and it comes as a need to better prepare SC for challenges brought by global SC operations. As stated by Ribeiro and Barbosa-Povoa (2018) in a recent review on the topic, “A resilient supply chain should be able to prepare, respond and recover from disturbances and afterwards maintain a positive steady state operation in an acceptable cost and time”. In such setting, the interest in a sound understanding of SCR has led academics and companies to pursuit efforts regarding such objective (Tang, 2006; Kamalahmadi and Parast, 2016). It is on the best interest of real SC the increase in knowledge in SCR as it is fundamental to better understand not only the resilience concept but also how this can help SC to deal with disruptive events that can endanger their steady-state operation (Cardoso et al., 2015). Several authors have been recently
J. Pires Ribeiro and A. Barbosa Póvoa
816
studying SCR but there is still a lack of understanding on how to quantify SCR (Ribeiro and Barbosa-Povoa, 2018). Cardoso et al. (2015) studied SCR and proposed a set of SC indicators that could be used to analyse SCR. SC flow complexity was identified as one of the most promising indicators and further studies on this should be performed to confirm such result. Based on these results, the present work focus on the design and planning of SC where decisions taken on the SC network structure are analysed. A design and planning multi-product, multiperiod MILP model is developed where demand uncertainty is considered. Five different supply chain structures are analysed and the associated complexity optimized. The resulted SC structures are subject to a set of disruptive events and their resilience is analysed.
2. Problem and Model Description In order to be able to discuss how different SC networks behave towards resilience, a five echelons supply chain was considered, where reverse flows are also possible to occur. Such SC involves: Raw Material Suppliers; Plants that can also function as Disassembling Centres with end of life products; Warehouses with added value activities as reconditioning non-conforming products; Outsourcing contractors as an alternative to plants production and finally Markets. In the plants and warehouses, technologies can be installed, which influence production, assembly and disassembly processes. These technologies can be fitted to the entities, or upgraded, to provide better performance. Based on this generic SC structure five different SC cases are studied where different SC structures are considered and allow to compare and construe results on SC resilience: Case A - a forward supply chain; Case B - similar to A, but now integrating also reverse flows between consecutive echelons; Case C - similar to B, but plants and markets can directly exchange products, thus bypassing the warehouses; Case D - similar to B, but with the possibility of transhipment at plants, disassembling centres and warehouses; Case E - the most general case, encompassing all the previous ones, forming a closed-loop supply chain where plants send directly products to markets and can also receive directly from markets the end-of-life products. Transhipment is allowed at plants, warehouses and disassembling centres. The MILP model developed by Cardoso et al. (2015) is taken as a base and was adapted to this work goals, providing a new objective function and a set of constraints to study SC flow complexity. Uncertainty was considered in the SC demand and on Disruptions. A scenario tree is constructed combining the two sources of uncertainty. Demand variability is introduced by generating a scenario on each period from a set of three possibilities (Pessimistic, Realistic or Optimistic). The result probabilistic nodes are then combined with the variability from the disruption that can only assume two options, or it occurs or it does not occur on a specific time period to consider. With this, each scenario probability is given by the probabilities of the path, with all stages, between the root node and each final leaf node. 2.1. Objective Function Two objective functions are studied, Equations 1 and 2. A first one considers the maximization of the network flow complexity (Equation 1), as this would return a network configuration with maximum flow complexity (FC) under the feasibility space generated by problem constraints, being FCt the summation of all positive flows present in the SC for each time period.
Max ∑ FCt
(1)
t
This model formulation, although returning a SC with the maximum amount of feasible possible flows does not take into consideration economic concerns, leading to solutions that may have a
817
Modelling and Analysing Supply Chain Resilience Flow Complexity
low performance in financial terms. This issue can, however, be tackled by setting additional constraints in the model, as is the case of establishing a minimum profit that must be obeyed. However, this method was not followed due to two reasons. First, restrictions had to apply to all cases and scenarios, which involve setting up conditions that cannot interfere with the feasibility of the model. Second, by setting up new conditions there is the possibility of endangering the established relationship and compatibility with the original model. Therefore, a two-step approach is followed. Primarily the model is run based on Equation 1 to retrieve the SC with maximum flow complexity within the model feasibility. The second step is used to retrieve the obtained network configuration and then study how much such network configuration maximizes the economic return. The economic return is based on the Expected Net Present Value, Equation 2 (where CF stands for the Cash flow for each scenario and time period, and ir for a defined interest rate). Trough this method it is ensured a network with maximum flow complexity and with the most advantageous economic performance to the company.
MaxENPV = ∑ pbs × NPVs s
pbs = Probability scenarios
NPVs = ∑ t
CFst (2) (1 + ir)t
By fixing the network configuration there is no capability for the SC network to change, however, it can adapt to the variability introduced in each situation by investing in new technologies, or upgrades to the existing facilities as well as optimize the supply chain flows.
3. Case Study The presented model is tested in a Case Study of an European Chemical Process SC. The values associated are scaled down, due to confidentiality reasons. The initial SC configuration comprises a set of European locations, with one plant in Hamburg, one warehouse in Munich, four raw materials suppliers, 3 suppliers of final products and 18 Europeans cities as markets. In broad terms, the company is studying the existent SC in order to access the investment necessary in technologies for current entities, or the implementation of new facilities, to improve the SC’s resilient capability. Four operational conditions are studied; one reference case with perfect operational conditions and three examples of disruptions. The disruptions were chosen following failure modes defined by Rice and Caniato (2003). Disruption 1 (Production Facilities)- ” 100% decrease in the production capacity of the most important plant (plant Pl3), in time period 2, caused, for example, by a major natural catastrophe”. Disruption 2 (Supply)- ”The most important raw materials suppliers (s3, s5, s8, s9 and s10) have their supply suspended in time period 2, due to an assumed industrial action”. Disruption 3 (Transportation)- ”The 3PL hired to operate those transportation links, between plants and warehouses, that carry the highest quantity of products (links between Pl3 and warehouses W1, W2 and W4), goes out of business in time period 2”. The scenario tree responsible for the uncertainty in the demand is built based on the assumption that the demand in the beginning is known and that there are three possible branches for time period 2 and 3, with the same probability in both periods; Optimistic 0.25, Realistic 0.5 and Pessimistic 0.25. (Time period 2: Optimistic with an increase of 10%; Realistic with an increase of 3%; Pessimistic with a decrease of 2%. Time period 3: Optimistic with an increase of 5%; Realistic with an increase of 2%; Pessimistic with a decrease of 2%) For each SC case, two configurations are established based on the SC network provided by the two objective functions: maximization of ENPV and maximization of flow complexity, when there is no disruption. These network designs are then subject to the disruptions and the results are analysed and discussed. The MILP model is developed using the GAMS software. The results when applying a network configuration for ENPV maximization can be seen in Table 1, whereas the results for a SC with its flow complexity maximized are presented in Table 2.
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Table 1: Combined results for ENPV Maximization Case A Reference Disruption 1 Disruption 2 Disruption 3 Case B Reference Disruption 1 Disruption 2 Disruption 3 Case C Reference Disruption 1 Disruption 2 Disruption 3 Case D Reference Disruption 1 Disruption 2 Disruption 3 Case E Reference Disruption 1 Disruption 2 Disruption 3
Complexity 46 46 44 44 Complexity 89 84 87 87 Complexity 110 109 108 108 Complexity 90 83 89 88 Complexity 106 102 104 104
ENPV 1.96E+07 1.65E+07 1.78E+07 1.83E+07 ENPV 1.91E+07 1.64E+07 1.77E+07 1.79E+07 ENPV 2.05E+07 1.66E+07 1.45E+07 1.84E+07 ENPV 1.91E+07 1.55E+07 1.77E+07 1.79E+07 ENPV 2,05E+07 1,64E+07 1,65E+07 1,84E+07
FCI 7.61E+05 8.10E+05 1.06E+06 7.80E+05 FCI 7.65E+05 7.99E+05 1.04E+06 7.89E+05 FCI 8.45E+05 9.58E+05 9.84E+05 9.31E+05 FCI 7.65E+05 8.28E+05 1.04E+06 7.88E+05 FCI 8,46E+05 9,68E+05 1,00E+06 9,31E+05
Investment 7.32E+05 7.81E+05 1.03E+06 7.52E+05 Investment 7.20E+05 7.56E+05 9.92E+05 7.45E+05 Investment 7.90E+05 9.03E+05 9.30E+05 8.77E+05 Investment 7.20E+05 7.86E+05 9.95E+05 7.44E+05 Investment 7,91E+05 9,14E+05 9,47E+05 8,77E+05
Inventory 1450.707 1084.072 1231.576 1278.613 Inventory 1449.68 1091.136 1229.269 1301.026 Inventory 913.478 791.844 720.256 885.054 Inventory 1452.711 1123.564 1227.958 1301.334 Inventory 913,478 796,152 805,425 885,033
Purchases 342670 356550 373537.712 313616.662 Purchases 334490 346070 302462.827 304995.435 Purchases 380870 377550 374369 457070 Purchases 334880 266442.058 302704.653 304860.924 Purchases 380670 379080 348862,167 4,55E+05
Sales 50563000 43821000 47473000 48435000 Sales 50548000 44301000 47672000 48744000 Sales 52937000 45538000 40396400 51674000 Sales 50586000 42559300 47651000 48747000 Sales 52940000 45463000 44065000 51674000
ECSL 85.7% 63.3% 72.1% 75.7% ECSL 85.6% 63.8% 72.0% 77.0% ECSL 99.4% 83.4% 71.8% 98.4% ECSL 85.8% 65.5% 72.0% 77.0% ECSL 96,4% 83,7% 77,8% 98,4%
3.1. Case A Case A represents a simple SC structure allowing only forward flows. One relevant analysis can be made regarding the delta of ENPV value between the two options, maximizing ENPV versus maximizing complexity. Comparing the results from both configurations, respectively in Tables 1 and 2 it can be seen an increase in service quality (ECSL) and that the loss in ENPV by incrementing complexity (-0.01E7e) is easily compensated by the gains in disruption 1 and 2 (0.15E7e and 0.1E7e), representing gains of 9% and 5% respectively. During Disruption 3 the leaner SC network is able to provide the same economic return than the network with increased complexity, however, it does so with a decreased service quality. 3.2. Case B Case B represents a SC structure where reverse flows are allowed between consecutive echelons adding complexity to the operation. It is expected an increase in flow complexity in order to cope with such requirement. The SC configuration with ENPV maximization has an increased impact from disruptions causing a decrease in ENPV of 14%, 7% and 6% for disruptions 1, 2 and 3 respectively. When no disruption is present a variation of -0.03E7e in ENPV is expected, when the SC shifts to a more complex network the ENPV variation are positive, with a gain more than the double of the cost if no disruption is present. The service quality is also impacted by a more complex configuration with improvements of 21%, 15% and 7% for disruptions 1, 2 and 3 respectively. 3.3. Case C Case C introduces a different kind of flexibility to the network, it allows the same flows as Case B and also allows for plants and markets to exchange products without any warehouse intervention. There is an increased susceptibility to Disruption 2 in Case C and this is much related with the non-existence of transhipment between entities in the same echelon. The leaner SC has a decrease in ENPV of 19%, 30% and 10% for disruptions 1, 2 and 3 respectively, while the more complex
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Table 2: Combined results for Complexity Maximization Case A Reference Disruption 1 Disruption 2 Disruption 3 Case B Reference Disruption 1 Disruption 2 Disruption 3 Case C Reference Disruption 1 Disruption 2 Disruption 3 Case D Reference Disruption 1 Disruption 2 Disruption 3 Case E Reference Disruption 1 Disruption 2 Disruption 3
Complexity 156 156 151 154 Complexity 346 343 341 344 Complexity 495 495 491 493 Complexity 376 373 372 374 Complexity 525 516 520 523
ENPV 1.95E+07 1.80E+07 1.88E+07 1.83E+07 ENPV 1.89E+07 1.75E+07 1.83E+07 1.78E+07 ENPV 2.03E+07 1.89E+07 1.83E+07 1.94E+07 ENPV 1.89E+07 1.75E+07 1.82E+07 1.78E+07 ENPV 2,03E+07 1,89E+07 1,92E+07 1,94E+07
FCI 8.30E+05 9.54E+05 9.56E+05 8.78E+05 FCI 9.01E+05 1.01E+06 1.03E+06 9.41E+05 FCI 1.05E+06 1.22E+06 1.29E+06 1.09E+06 FCI 9.21E+05 1.03E+06 1.07E+06 9.59E+05 FCI 1,07E+06 1,23E+06 1,25E+06 1,10E+06
Investment 7.32E+05 8.56E+05 8.61E+05 7.81E+05 Investment 7.19E+05 8.30E+05 8.47E+05 7.61E+05 Investment 7.90E+05 9.59E+05 1.03E+06 8.29E+05 Investment 7.20E+05 8.28E+05 8.75E+05 7.59E+05 Investment 7,89E+05 9,51E+05 9,80E+05 8,26E+05
Inventory 1451.691 1305.564 1409.266 1392.458 Inventory 1451.139 1320.152 1409.159 1390.301 Inventory 914.547 915.528 918.789 914.66 Inventory 1456.127 1355.382 1381.246 1391.087 Inventory 915,493 916,495 975,706 915,648
Purchases 342800 316095.608 333077.386 328540 Purchases 334770 310323.917 324379.133 320275.72 Purchases 381050 364530 345240 378400 Purchases 335370 314110.778 316696.483 319616.258 Purchases 380820 365270 354997,874 377860
Sales 50572000 48831000 50058000 49883000 Sales 50564000 49012000 50053000 49855000 Sales 52933000 52193000 51382000 52886000 Sales 50607000 49432000 49723000 49853000 Sales 52933000 52210000 51803000 52886000
ECSL 85.8% 76.9% 83.1% 82.2% ECSL 85.7% 76.9% 83.1% 82.1% ECSL 99.4% 95.1% 90.1% 98.9% ECSL 85.9% 79.9% 81.5% 82.1% ECSL 99,4% 95,2% 92,8% 99,0%
SC shows improvements of 14%, 27% and 5% for disruptions 1, 2 and 3 respectively. In terms of service quality it is perceptible an increase in ECSL for the more complex structure, maintaining levels of above 90% even during disruptions. 3.4. Case D Case D allows forward and reverse flows between consecutive echelons and adds a new set of possibilities by allowing transhipment at plants, disassembling centres and warehouses. Applying the leaner configuration, disruptions cause an ENPV decrease of 19%, 7% and 6% for disruptions 1, 2 and 3 respectively. These results can be improved by 13% and 3% for disruptions 1 and 2 respectively, if a more complex network is deployed. In terms of ECSL the leaner configuration leads to a decrease of 24%, 16% and 10% for disruptions 1, 2 and 3 respectively, the more complex network allows for a steady service level of around 80%, improving the alternative configuration by 22%, 13% and 7% for disruptions 1, 2 and 3 respectively. 3.5. Case E Case E represents a network that includes all the possibilities from previous cases. This closed loop SC can perform transhipment at all levels, except for markets, and flows bypassing intermediate entities are also allowed. ENPV variations between steady-state operation and disruptive scenarios are visible, resulting in a decrease of 20%, 20% and 10% for disruptions 1, 2 and 3 respectively on the network provided by the ENPV maximization. On the other hand, applying the more complex network the results of ENPV during the disruptive events are improved by 15%, 16% and 5% for disruptions 1, 2 and 3 respectively. With the maximization of complexity, the SC can return ECSL higher than 90% in all scenarios, even when a disruption does occur. When a leaner network is implemented disruptive scenarios cause a decrease in service level of 13% and 19% for disruptions 1 and 2 respectively. Applying the network with a higher amount of permitted flows leads to an improvement of 14%, 19% and 1% for disruptions 1, 2 and 3 respectively.
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4. Conclusions and Discussion From the above study, it can be concluded that the obtained results vary not only with the SC complexity but also with the SC structure (e.g. forward or closed-loop) as well with the different types of disruptions. Different disruptions cause different results and so decision makers should have enough information to make the most acceptable decision considering model results and available information. It is in this line that, studying SC Resilience factors gain importance, as it allows the development of better models to aid decision making. Considering the behaviour on ENPV caused by the increased complexity, when no disruption occurs, is observed an increment on costs, due to the obligations that come from opening and maintaining more facilities and flows. However, if disruptions occur, there is an evident benefit of operating a more complex SC. The difference in ENPV in disruptive scenarios between the more complex and a leaner SC is always positive, in comparison with not investing in preventive strategies. There is a more evident benefit from deploying a more complex SC in terms of ECSL. The notable shift is made possible by the increased flexibility and redundancy allowed by the higher amount of entities and flows involved resulting in an increased SC responsiveness. The investment made in increasing complexity is completely overcome by the resilience created in the supply chain structures as they are able to better react to disruptions guaranteeing higher service levels and higher profit values. However, this characteristic should be always met by a specific analysis of each SC and to its, perceptible, vulnerabilities. As a final analysis, it is relevant to compare the results of this paper with those from the original publication of Cardoso et al. (2015), aimed at maximizing ENPV for each SC structure and scenario. As expected, our results produce a network with lower ENPV but with a trade-off for better ECSL. As main conclusions, it can be said that investing in proactive resilient Supply Chain Design can reduce losses, generate value to companies and reduce the need for reactive strategies, in case of facing a disruptive event. With this work, we are also capable of attesting the positive correlation between the increased SC complexity with a positive outcome in case of some disruptions, as suggested by Cardoso et al. (2015) in their study. Acknowledgements The authors acknowledge the project DPI2015-67740-P (MINECO/FEDER)
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