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Optimal design and operation of water supply chain networks using scenario-based dynamic negotiation and multiple negotiation terms
Antonio Espuña, Moisès Graells and Luis Puigjaner (Editors), Proceedings of the 27th European Symposium on Computer Aided Process Engineering – ESCAPE 27 October 1st - 5th, 2017, Barcelona, Spain © 2017 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/B978-0-444-63965-3.50322-6
Optimal design and operation of water supply chain networks using scenario-based dynamic negotiation and multiple negotiation terms. Sergio Medina-Gonzáleza, Fengqi Youb, Antonio Espuñaa a
Department of Chemical Engineering, Universitat Politècnica de Catalunya, EEBE. Av. Eduard Maristany, 10-14, Edifici I, Planta 6, 08019 Barcelona. b Robert Frederick Smith School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY 14853, USA * [email protected]
Abstract A negotiation framework is proposed for the optimal design and operation of a decentralized supply chain. A formulation based on a competitive leader-follower environment, in which the leader should propose a set of negotiation contracts and, at the same time, predict the follower response (to accept/reject the contract) is proposed. The impact of the follower design decisions over the leader objective is evaluated by fixing the follower’s decision variables. Then by applying the Scenario Based Dynamic Negotiation method (considering the associated third parties price uncertainties) a set of feasible solutions is generated. Finally, using the Elimination and Choice Expressing Reality-IV method, the set of feasible solutions are evaluated under multiple defined criteria (including economic and environmental) in order to select a unique, optimal negotiation contract and its associated sustainable solution. This solution properly represents the leader’s and follower’s interests under a win-win negotiation partnership despite the uncontrollable/unpredicted behaviours resulted from the follower’s decisions as well as third party changing prices. Keywords: Decentralized environment; Uncertainty; Negotiation; Decision making.
1. Introduction. The market globalization as well as the constant changes in the market dynamics leads to a necessity of strategies that provides stability in the real industries. Therefore, Process System Engineering (PSE) research focus on the development of fast, robust and reliable tools for designing and managing industries worldwide under a volatile market environment. Here, the main challenge is associated to the increasing presence of supplier/producer competition in the industry, leading to a non-cooperative situations and, very often, conflicts of interest (i.e. objective functions) (Zamarripa et al., 2013). Few works have been carried out to analyze the coordination among supply chains (SCs) in competitive environments. Hijla et al. (2016a) propose a framework in order to approach and describe the third-parties’ role/interaction in a polystyrene production/distribution SC. The work was later expanded to evaluate/coordinate the relations between 2 independent SC’s and their associated competitors (third parties) in order to ensure a win-win situation (Hjaila et al., 2016b) using a Scenario-Based Dynamic Negotiation (SBDN). The competitor’s behaviours were described through a representative set of scenarios, nonetheless, the reliability of the final solution is not
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guaranteed due to the simplified uncertainty approach. Therefore, an appropriate uncertainty formulation, like the two-stage stochastic programming framework, has to be included in the SBDN strategy. Regarding the integrated design and operation of a decentralized SCs under a competitive environment, Yue and You (2016) evaluated the role of follower’s discrete decisions in a negotiation leader-follower optimization problem using a novel mixed integer bi-level programming framework. However, the main shortcoming of their formulation is the fact that the follower’s discrete decisions highly depend on the leader decisions, which compromise the applicability of the final design solution after negotiations between the leader and the follower for collaboration. Consequently a more sophisticate strategy that explicitly considers the follower’s design decisions is needed (regardless of the leader's behaviour). Additionally, the current competitive business environment and the growing importance of designing sustainable processes have created an opportunity area. Therefore, negotiation strategies and “Green” engineering can be used together to improve the traditional economic and environmental assessments. Util now, the simultaneous representation of multiple leader and follower objectives in the final solution remains as an open issue in the current literature. In order to properly overcome such an issue a robust multi-criteria decision making tool should be used within a negotiation strategy. Methods such as Analytical Hierarchical Program (AHP) or Preference Ranking Organisation Methods for Enrichment Evaluations (PROMETHEE) have been used as decision making tools. Nevertheless, due to their limitations, Elimination and Choice Expressing RealityIV (ELECTRE-IV) has gain attention as a reliable decision method (Medina-González et al., 2017). In the present work, a negotiation framework is proposed which allows to produce win-win negotiation contracts despite the uncontrollable/unpredicted behaviours (including follower decisions as well as third party changing prices).
2. Problem Statement Consider two different and independent SC’s, being one of them a net wastewater generator and the other one a wastewater treatment and regenerator SC, both working in a non-cooperative environment, in which the wastewater generator and the wastewater regenerator are considered as leader and follower, respectively. Both SCs considered as functional SC’s with their own independent suppliers/markets. Nevertheless, the leader decides to improve its benefits by searching for a suitable wastewater disposal price and at the same time buying recovered water (to and from the follower SC respectively). Hence, in order to push the agreement towards a win-win policy, the systematic search of a profitable collaboration was considered. It is important to highlight that the agreement must consider the uncertain behavior of the external conditions, the follower design decisions, which remains unknown for the leader, as well as multiple efficiency indicators from both leader’s and follower’s perspectives. Therefore, the negotiation may be complex and may even end without an agreement.
3. Mathematical formulation Without loss of generality a generic two-stage stochastic mixed integer linear programming model (SMILP) is developed as a basis to solve the above mentioned problem. It is important to comment, that the use of the two-stage stochastic programming was used as an uncertainty handling option, however its use does not affect the performance of the proposed strategy and another alternative can be applied (such as multi-parametric approach). The main economic equations of the mathematical formulation are next described:
Optimal Design and Operation of Water Supply Chain Networks using ScenarioBased Dynamic Negotiation and multiple negotiation terms.
1923
݈ܵܽ݁ݏ௦ǡ௦ ݎǡǡ௧ ή ݉݁݀ݔǡ௦ǡǡ௧ǡ௦ ௧ ்אאோ אெ
ܥܵܿݏǢ ܿݏᇱ ܨ אǢ ܵ א ݏ
(1)
ᇲǡ௦ ᇲǡ௧ ή ܳ ᇲ௦ ᇲǡ௦ ௧ ்א אோ
Eq. (1) represents the total sales for each SC considering the associated prices for internal and external consumers ( ᇲǡ௦ ᇲǡ௧ and ݎǡǡ௧ , respectively), as well as each uncertain scenario realization (s). Similarly, the cost for each SC includes raw material purchase, transport, storage, production, and the negotiation resource, respectively, as shown in Eq. (2). Besides, Eq. (3) shows the final profit associated to each SC. ݐݏܥ௦ǡ௦ ൌ ൫ܯܴܥ௦ǡ௧ǡ௦ ܴܶܥ௦ǡ௧ǡ௦ ܶܵܥ௦ǡ௧ǡ௦ ܦܴܲܥ௦ǡ௧ǡ௦ ൯ ௧்א
ܥܵ א ܿݏǢ ܿݏᇱ ܮ אǢ ܵ א ݏ
(2)
ᇲǡ௦ ᇲǡ௧ ή ܳ ᇲ௦ ᇲ ǡ௧ǡ௦ ௧ ்א אோ
݂ܲݎ௦ǡ௦ ൌ ݈ܵܽ݁ݏ௦ǡ௦ െ ݐݏܥ௦ǡ௦ ܥܵ א ܿݏ
(3)
It is important to highlight that the negotiation item ( ᇲ௦ ᇲ ௧ ή ܳ ᇲ ௦ ᇲ ௧௦ ) appears in both equations (Sales and Cost), moreover, this formulation is flexible enough to explore/assess multi-item negotiation contracts simultaneously. As commented before, a leader SC has to be defined producing an unpredictable follower behaviour (uncertain decision and parameters). Mathematically, such an uncontrollable behaviour is faced through the two-stage stochastic programming formulation. Therefore the economic objective changes as follows: ݂ݎܲܧ௦ ൌ ൫݈ܵܽ݁ݏ௦ǡ௦ െ ݐݏܥ௦ǡ௦ ൯ ή ܾݎ௦ ܥܵ א ܿݏ
(4)
௦אௌ
where ܾݎ௦ represents the probability of occurrence of scenario s , each of which represents a possible realization of the uncertaint behaviors of the follower 3rd parties ଵ (suppliers, customers, external client). Without loss of generality ܾݎ௦ ൌ ேǤ௦௦. Parallely, the reaction of the follower at each negotiation contract is modelled using the probability of acceptance over a set of scenarios. Such a probability (݁ܿ݊ܽݐ̴ܾ݁ܿܿܽݎ௦ᇱ ሻ is computed by taking into account the number of scenarios that improve the individual results for the follower SC (See Eq.(5)). ݁ܿ݊ܽݐ̴ܾ݁ܿܿܽݎ௦ᇱ ൌ
ܰǤ ݂ݎܲܧ݃݊݅ݒݎ݉݅ݏ݅ݎܽ݊݁ܿݏ݂௦ᇱ ܿݏԢ ܨ א ݈ܶܰܽݐǤ ݏ݅ݎܽ݊݁ܿݏ݂
(5)
In addition, ݁ܿ݊ܽݐ̴ܾ݁ܿܿܽݎ௦ᇱ represents a decision criteriona other than the expected profit. Finally, the effect of the follower’s design decisions over the projections of the leader’s decisions is evaluated by solving the leader model iterativeley for a defined set of follower designs.
4. Methodology The proposed solution strategy can be summarized in a set of 6 main steps: 1. Definition of different follower designs in terms of complexity/amount of units. 2. Definition of first and second negotiation item values. Each pair of values (first and second term) will constitute a single contract. 3. Identification of the uncertain parameters to be analysed (i.e. Supplier, customer and external client selling/buying prices).
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4. Generate a representative set of scenarios within the upper and lower bounds for those uncertain parameters under a known probability distribution. 5. For each design; 5.1. For each contract; 5.1.1. For each scenario; 5.1.1.1. Solve the problem and calculate the decision variables (i.e. expected profit for each SC, freshwater consumption, etc.). 5.1.1.2. Add the results of each scenario into a blank matrix, henceforth known as “scenario matrix” 5.1.2. From the “scenario matrix”, calculate performance indicators (such as probability of acceptance, financial risk for each actor, etc.). 5.1.3. Add those performance indicators into a blank matrix and generate a new matrix including all those performance indicators for each contract, henceforth known as “Criteria-Contract matrix”. 5.2. Select the solution (or reduced set of solutions) with the best overall performance for all the criteria in “Criteria-Contract matrix” by applying the ELECTRE-IV method. 6. Compare the solution selected at each design to provide the best overall performance for all the follower designs.
5. Illustrative example In order to illustrate the capabilities of the proposed strategy for the water management of a shale gas supply chain, the case presented in Gao and You et al. (2015) is used as a case study (see Figure 1). The gas production and the wastewater treatment sites are considered as two independent SC’s (leader and follower, respectively, as described in Figure 1). Two follower designs were considered taking into account the lower and upper nominal capacities for the treatment sites (henceforth known as conservative and risky designs). 10 wastewater disposal prices and 5 recovered water prices were defined as first and second negotiation item, respectively (giving a total of 50 negotiation contracts). Finally, 100 scenarios representing the third party prices were considered.
Figure 1. Decentralized SC network.
5.1. Results and discussion After running the optimization procedure for the hull negotiation contracts, the leader’s and the follower’s financial behavior were found (See Figure 2). It can be noticed that, the negotiation contract has an important and linear effect on both actors. The range of the expected profit for both actors are of the order of $230,000 and $338,000 for the leader and the follower, respectively, proving that the interaction between partners represent a
Optimal Design and Operation of Water Supply Chain Networks using ScenarioBased Dynamic Negotiation and multiple negotiation terms.
1925
non-zero-sum system. It is assumed that any contract presenting favorable expected profit value for both players can be considered as a feasible option (i.e. higher than its standalone situation, $77.05x106 and $1.11 x106 for leader and follower respectively).
Figure 2. Negotiation behavior for the conservative follower designs.
The same analysis was performed for the risky design in which similar behaviors were found. Therefore, the following discussion will be focused on the conservative design results. From Figure 2 it can be noticed that all the negotiation contracts produce better expected profits. Therefore, in order to propose the best agreement the leader has to consider as a key factor both the positive impact of its economic performance and the probability that the follower accepts a specific contract. Those factors represent an indirect way to measure the robustness of the proposed contract. Consequently, in order to handle multiple decision criteria, a set of decision maker’s preferences within the framework of the ELECTRE-IV method was used and displayed in Table 1.
Thresholds Indifference Preference Veto *
Table 1. Thresholds values for the considered decision criteria. Selection Criteria ݐ݂݅ݎܲܧ Water Savings** Prob. acceptance ݐ݂݅ݎܲܧ 7.70x107 1.20x106 6.0x105 0.55 7.71x107 1.45x106 6.80x105 0.75 10.0x107 10.0x107 7.00x105 1
Values expressed in $
**
Values expressed in m3
These criteria were assumed based on the standalone situation and any change in them may lead to a different negotiation contract. However, such an assumption does not affect the applicability/flexibility of the selection strategy. Using the data in Table 1 the ELECTRE-IV method produce a comparison among all the solutions and selects a negotiation agreement with the highest positive impact for all the 5 decision criteria and follower designs. The final negotiation contract that performs better disregarding the follower design consists of a reused water price of $0.041 and a disposal cost of $1.88 per m3 of water and wastewater respectively. The position of this negotiation contract within the feasible financial behavior was presented in Figure 2. Such a negotiation contract has an associated specific design and coordination plan for the decentralized SC network. Therefore, the optimal values of the main decision variables for the leader and the follower SCs’ are presented in Table 2. Disregarding the unpredictable design of the follower, in this specific case the leader is able to propose a negotiation contract that is significantly acceptable for the follower leading to a more sustainable solution. It can be also noticed that the follower is mainly affected by the changes of its design decisions.
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Table 2. Optimal criteria values for each player within the selected negotiation contract. ݐ݂݅ݎܲܧ * ݐ݂݅ݎܲܧி * **ݎ݁ݐܹ݄ܽݏ݁ݎܨProb. Acceptance Conservative 0.73 77.085 x106 1.272 x106 0.820 x106 Risky 0.63 77.085 x106 1.192 x106 0.820 x106 Standalone N/A 77.005 x106 1.117 x106 1.253 x106 6 0.155 x10 Improvement 0.080 x106 0.433 x106 0.075 x106 *
Values expressed in $
**
Values expressed in m3
Conclusions A systematic strategy that allows designing and coordinating a decentralized supply chain through production of an attractive negotiation contract among two independent SC’s was presented. It was demonstrated that the resulting negotiation contract has a positive impact on the economic and environmental performances of all the participants. The proposed strategy used a proper uncertainty formulation, increasing the reliability of the resulting design and planning decisions associated to each negotiation contract. Additionally, the use of ELECTRE-IV method as a decision making tool not only expedited the selection of a unique and reliable negotiation contract but also increased the flexibility of the strategy, being able to consider multiple negotiation items and multiple decision criteria.
Acknowledgements The authors would like to thank the financial support received from the Spanish Ministry of Economy and Competitiveness and the European Regional Development Fund, both funding the Project ECOCIS (DPI2013-48243-C2-1-R), the Generalitat de Catalunya (project 2014-SGR-1092-CEPEiMA), and the Mexican “Consejo Nacional de Ciencia y Tecnología (CONACYT).
References Gao J. and You F. (2015). “Optimal Design and Operations of Supply Chain Networks for Water Management in Shale gas Production: MILFP Model and Algorithms for the Water-Energy Nexus” AIChE Journal 61: 1184-1208. Hjaila K., Laínez-Aguirre J.M., Zamarripa M., Puigjaner L. and Espuña A. (2016a). “Optimal integration of third-parties in coordinated supply chain management environment.” Comput. Chem. Eng. 86: 48–61. Hjaila K., Laínez-Aguirre J.M., , Puigjaner L. and Espuña A. (2016b). “Scenario-based dynamic negotiation for the coordination of multi-enterprise supply chains under uncertainty” Comput. Chem. Eng. 91: 445–470. Medina-González S.A., Graells M., Guillén-Gosálbez G., Espuña A., Puigjaner L. (2017). “Systematic Approach for the design of sustainable Supply Chains under quality uncertainty” Energ. Convers Manag. http://dx.doi.org/10.1016/j.enconman.2017.02.060 Zamarripa M.A., Aguirre A.M., Méndez C.A., Espuña, A. (2013). “Mathematical Programming and game theory optimization-based tool for supplying chain plannning in cooperative/competitive environments.” Chem. Eng. Res. Des. 91: 1588-1600.
Optimal design and operation of water supply chain networks using scenario-based dynamic negotiation and multiple negotiation terms. Sergio Medina-Gonzáleza, Fengqi Youb, Antonio Espuñaa a
Department of Chemical Engineering, Universitat Politècnica de Catalunya, EEBE. Av. Eduard Maristany, 10-14, Edifici I, Planta 6, 08019 Barcelona. b Robert Frederick Smith School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY 14853, USA * [email protected]
Abstract A negotiation framework is proposed for the optimal design and operation of a decentralized supply chain. A formulation based on a competitive leader-follower environment, in which the leader should propose a set of negotiation contracts and, at the same time, predict the follower response (to accept/reject the contract) is proposed. The impact of the follower design decisions over the leader objective is evaluated by fixing the follower’s decision variables. Then by applying the Scenario Based Dynamic Negotiation method (considering the associated third parties price uncertainties) a set of feasible solutions is generated. Finally, using the Elimination and Choice Expressing Reality-IV method, the set of feasible solutions are evaluated under multiple defined criteria (including economic and environmental) in order to select a unique, optimal negotiation contract and its associated sustainable solution. This solution properly represents the leader’s and follower’s interests under a win-win negotiation partnership despite the uncontrollable/unpredicted behaviours resulted from the follower’s decisions as well as third party changing prices. Keywords: Decentralized environment; Uncertainty; Negotiation; Decision making.
1. Introduction. The market globalization as well as the constant changes in the market dynamics leads to a necessity of strategies that provides stability in the real industries. Therefore, Process System Engineering (PSE) research focus on the development of fast, robust and reliable tools for designing and managing industries worldwide under a volatile market environment. Here, the main challenge is associated to the increasing presence of supplier/producer competition in the industry, leading to a non-cooperative situations and, very often, conflicts of interest (i.e. objective functions) (Zamarripa et al., 2013). Few works have been carried out to analyze the coordination among supply chains (SCs) in competitive environments. Hijla et al. (2016a) propose a framework in order to approach and describe the third-parties’ role/interaction in a polystyrene production/distribution SC. The work was later expanded to evaluate/coordinate the relations between 2 independent SC’s and their associated competitors (third parties) in order to ensure a win-win situation (Hjaila et al., 2016b) using a Scenario-Based Dynamic Negotiation (SBDN). The competitor’s behaviours were described through a representative set of scenarios, nonetheless, the reliability of the final solution is not
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guaranteed due to the simplified uncertainty approach. Therefore, an appropriate uncertainty formulation, like the two-stage stochastic programming framework, has to be included in the SBDN strategy. Regarding the integrated design and operation of a decentralized SCs under a competitive environment, Yue and You (2016) evaluated the role of follower’s discrete decisions in a negotiation leader-follower optimization problem using a novel mixed integer bi-level programming framework. However, the main shortcoming of their formulation is the fact that the follower’s discrete decisions highly depend on the leader decisions, which compromise the applicability of the final design solution after negotiations between the leader and the follower for collaboration. Consequently a more sophisticate strategy that explicitly considers the follower’s design decisions is needed (regardless of the leader's behaviour). Additionally, the current competitive business environment and the growing importance of designing sustainable processes have created an opportunity area. Therefore, negotiation strategies and “Green” engineering can be used together to improve the traditional economic and environmental assessments. Util now, the simultaneous representation of multiple leader and follower objectives in the final solution remains as an open issue in the current literature. In order to properly overcome such an issue a robust multi-criteria decision making tool should be used within a negotiation strategy. Methods such as Analytical Hierarchical Program (AHP) or Preference Ranking Organisation Methods for Enrichment Evaluations (PROMETHEE) have been used as decision making tools. Nevertheless, due to their limitations, Elimination and Choice Expressing RealityIV (ELECTRE-IV) has gain attention as a reliable decision method (Medina-González et al., 2017). In the present work, a negotiation framework is proposed which allows to produce win-win negotiation contracts despite the uncontrollable/unpredicted behaviours (including follower decisions as well as third party changing prices).
2. Problem Statement Consider two different and independent SC’s, being one of them a net wastewater generator and the other one a wastewater treatment and regenerator SC, both working in a non-cooperative environment, in which the wastewater generator and the wastewater regenerator are considered as leader and follower, respectively. Both SCs considered as functional SC’s with their own independent suppliers/markets. Nevertheless, the leader decides to improve its benefits by searching for a suitable wastewater disposal price and at the same time buying recovered water (to and from the follower SC respectively). Hence, in order to push the agreement towards a win-win policy, the systematic search of a profitable collaboration was considered. It is important to highlight that the agreement must consider the uncertain behavior of the external conditions, the follower design decisions, which remains unknown for the leader, as well as multiple efficiency indicators from both leader’s and follower’s perspectives. Therefore, the negotiation may be complex and may even end without an agreement.
3. Mathematical formulation Without loss of generality a generic two-stage stochastic mixed integer linear programming model (SMILP) is developed as a basis to solve the above mentioned problem. It is important to comment, that the use of the two-stage stochastic programming was used as an uncertainty handling option, however its use does not affect the performance of the proposed strategy and another alternative can be applied (such as multi-parametric approach). The main economic equations of the mathematical formulation are next described:
Optimal Design and Operation of Water Supply Chain Networks using ScenarioBased Dynamic Negotiation and multiple negotiation terms.
1923
݈ܵܽ݁ݏ௦ǡ௦ ݎǡǡ௧ ή ݉݁݀ݔǡ௦ǡǡ௧ǡ௦ ௧ ்אאோ אெ
ܥܵܿݏǢ ܿݏᇱ ܨ אǢ ܵ א ݏ
(1)
ᇲǡ௦ ᇲǡ௧ ή ܳ ᇲ௦ ᇲǡ௦ ௧ ்א אோ
Eq. (1) represents the total sales for each SC considering the associated prices for internal and external consumers ( ᇲǡ௦ ᇲǡ௧ and ݎǡǡ௧ , respectively), as well as each uncertain scenario realization (s). Similarly, the cost for each SC includes raw material purchase, transport, storage, production, and the negotiation resource, respectively, as shown in Eq. (2). Besides, Eq. (3) shows the final profit associated to each SC. ݐݏܥ௦ǡ௦ ൌ ൫ܯܴܥ௦ǡ௧ǡ௦ ܴܶܥ௦ǡ௧ǡ௦ ܶܵܥ௦ǡ௧ǡ௦ ܦܴܲܥ௦ǡ௧ǡ௦ ൯ ௧்א
ܥܵ א ܿݏǢ ܿݏᇱ ܮ אǢ ܵ א ݏ
(2)
ᇲǡ௦ ᇲǡ௧ ή ܳ ᇲ௦ ᇲ ǡ௧ǡ௦ ௧ ்א אோ
݂ܲݎ௦ǡ௦ ൌ ݈ܵܽ݁ݏ௦ǡ௦ െ ݐݏܥ௦ǡ௦ ܥܵ א ܿݏ
(3)
It is important to highlight that the negotiation item ( ᇲ௦ ᇲ ௧ ή ܳ ᇲ ௦ ᇲ ௧௦ ) appears in both equations (Sales and Cost), moreover, this formulation is flexible enough to explore/assess multi-item negotiation contracts simultaneously. As commented before, a leader SC has to be defined producing an unpredictable follower behaviour (uncertain decision and parameters). Mathematically, such an uncontrollable behaviour is faced through the two-stage stochastic programming formulation. Therefore the economic objective changes as follows: ݂ݎܲܧ௦ ൌ ൫݈ܵܽ݁ݏ௦ǡ௦ െ ݐݏܥ௦ǡ௦ ൯ ή ܾݎ௦ ܥܵ א ܿݏ
(4)
௦אௌ
where ܾݎ௦ represents the probability of occurrence of scenario s , each of which represents a possible realization of the uncertaint behaviors of the follower 3rd parties ଵ (suppliers, customers, external client). Without loss of generality ܾݎ௦ ൌ ேǤ௦௦. Parallely, the reaction of the follower at each negotiation contract is modelled using the probability of acceptance over a set of scenarios. Such a probability (݁ܿ݊ܽݐ̴ܾ݁ܿܿܽݎ௦ᇱ ሻ is computed by taking into account the number of scenarios that improve the individual results for the follower SC (See Eq.(5)). ݁ܿ݊ܽݐ̴ܾ݁ܿܿܽݎ௦ᇱ ൌ
ܰǤ ݂ݎܲܧ݃݊݅ݒݎ݉݅ݏ݅ݎܽ݊݁ܿݏ݂௦ᇱ ܿݏԢ ܨ א ݈ܶܰܽݐǤ ݏ݅ݎܽ݊݁ܿݏ݂
(5)
In addition, ݁ܿ݊ܽݐ̴ܾ݁ܿܿܽݎ௦ᇱ represents a decision criteriona other than the expected profit. Finally, the effect of the follower’s design decisions over the projections of the leader’s decisions is evaluated by solving the leader model iterativeley for a defined set of follower designs.
4. Methodology The proposed solution strategy can be summarized in a set of 6 main steps: 1. Definition of different follower designs in terms of complexity/amount of units. 2. Definition of first and second negotiation item values. Each pair of values (first and second term) will constitute a single contract. 3. Identification of the uncertain parameters to be analysed (i.e. Supplier, customer and external client selling/buying prices).
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4. Generate a representative set of scenarios within the upper and lower bounds for those uncertain parameters under a known probability distribution. 5. For each design; 5.1. For each contract; 5.1.1. For each scenario; 5.1.1.1. Solve the problem and calculate the decision variables (i.e. expected profit for each SC, freshwater consumption, etc.). 5.1.1.2. Add the results of each scenario into a blank matrix, henceforth known as “scenario matrix” 5.1.2. From the “scenario matrix”, calculate performance indicators (such as probability of acceptance, financial risk for each actor, etc.). 5.1.3. Add those performance indicators into a blank matrix and generate a new matrix including all those performance indicators for each contract, henceforth known as “Criteria-Contract matrix”. 5.2. Select the solution (or reduced set of solutions) with the best overall performance for all the criteria in “Criteria-Contract matrix” by applying the ELECTRE-IV method. 6. Compare the solution selected at each design to provide the best overall performance for all the follower designs.
5. Illustrative example In order to illustrate the capabilities of the proposed strategy for the water management of a shale gas supply chain, the case presented in Gao and You et al. (2015) is used as a case study (see Figure 1). The gas production and the wastewater treatment sites are considered as two independent SC’s (leader and follower, respectively, as described in Figure 1). Two follower designs were considered taking into account the lower and upper nominal capacities for the treatment sites (henceforth known as conservative and risky designs). 10 wastewater disposal prices and 5 recovered water prices were defined as first and second negotiation item, respectively (giving a total of 50 negotiation contracts). Finally, 100 scenarios representing the third party prices were considered.
Figure 1. Decentralized SC network.
5.1. Results and discussion After running the optimization procedure for the hull negotiation contracts, the leader’s and the follower’s financial behavior were found (See Figure 2). It can be noticed that, the negotiation contract has an important and linear effect on both actors. The range of the expected profit for both actors are of the order of $230,000 and $338,000 for the leader and the follower, respectively, proving that the interaction between partners represent a
Optimal Design and Operation of Water Supply Chain Networks using ScenarioBased Dynamic Negotiation and multiple negotiation terms.
1925
non-zero-sum system. It is assumed that any contract presenting favorable expected profit value for both players can be considered as a feasible option (i.e. higher than its standalone situation, $77.05x106 and $1.11 x106 for leader and follower respectively).
Figure 2. Negotiation behavior for the conservative follower designs.
The same analysis was performed for the risky design in which similar behaviors were found. Therefore, the following discussion will be focused on the conservative design results. From Figure 2 it can be noticed that all the negotiation contracts produce better expected profits. Therefore, in order to propose the best agreement the leader has to consider as a key factor both the positive impact of its economic performance and the probability that the follower accepts a specific contract. Those factors represent an indirect way to measure the robustness of the proposed contract. Consequently, in order to handle multiple decision criteria, a set of decision maker’s preferences within the framework of the ELECTRE-IV method was used and displayed in Table 1.
Thresholds Indifference Preference Veto *
Table 1. Thresholds values for the considered decision criteria. Selection Criteria ݐ݂݅ݎܲܧ Water Savings** Prob. acceptance ݐ݂݅ݎܲܧ 7.70x107 1.20x106 6.0x105 0.55 7.71x107 1.45x106 6.80x105 0.75 10.0x107 10.0x107 7.00x105 1
Values expressed in $
**
Values expressed in m3
These criteria were assumed based on the standalone situation and any change in them may lead to a different negotiation contract. However, such an assumption does not affect the applicability/flexibility of the selection strategy. Using the data in Table 1 the ELECTRE-IV method produce a comparison among all the solutions and selects a negotiation agreement with the highest positive impact for all the 5 decision criteria and follower designs. The final negotiation contract that performs better disregarding the follower design consists of a reused water price of $0.041 and a disposal cost of $1.88 per m3 of water and wastewater respectively. The position of this negotiation contract within the feasible financial behavior was presented in Figure 2. Such a negotiation contract has an associated specific design and coordination plan for the decentralized SC network. Therefore, the optimal values of the main decision variables for the leader and the follower SCs’ are presented in Table 2. Disregarding the unpredictable design of the follower, in this specific case the leader is able to propose a negotiation contract that is significantly acceptable for the follower leading to a more sustainable solution. It can be also noticed that the follower is mainly affected by the changes of its design decisions.
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Table 2. Optimal criteria values for each player within the selected negotiation contract. ݐ݂݅ݎܲܧ * ݐ݂݅ݎܲܧி * **ݎ݁ݐܹ݄ܽݏ݁ݎܨProb. Acceptance Conservative 0.73 77.085 x106 1.272 x106 0.820 x106 Risky 0.63 77.085 x106 1.192 x106 0.820 x106 Standalone N/A 77.005 x106 1.117 x106 1.253 x106 6 0.155 x10 Improvement 0.080 x106 0.433 x106 0.075 x106 *
Values expressed in $
**
Values expressed in m3
Conclusions A systematic strategy that allows designing and coordinating a decentralized supply chain through production of an attractive negotiation contract among two independent SC’s was presented. It was demonstrated that the resulting negotiation contract has a positive impact on the economic and environmental performances of all the participants. The proposed strategy used a proper uncertainty formulation, increasing the reliability of the resulting design and planning decisions associated to each negotiation contract. Additionally, the use of ELECTRE-IV method as a decision making tool not only expedited the selection of a unique and reliable negotiation contract but also increased the flexibility of the strategy, being able to consider multiple negotiation items and multiple decision criteria.
Acknowledgements The authors would like to thank the financial support received from the Spanish Ministry of Economy and Competitiveness and the European Regional Development Fund, both funding the Project ECOCIS (DPI2013-48243-C2-1-R), the Generalitat de Catalunya (project 2014-SGR-1092-CEPEiMA), and the Mexican “Consejo Nacional de Ciencia y Tecnología (CONACYT).
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