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Scenario-Based Price Negotiations vs. Game Theory in the Optimization of Coordinated Supply Chains
Krist V. Gernaey, Jakob K. Huusom and Rafiqul Gani (Eds.), 12th International Symposium on Process Systems Engineering and 25th European Symposium on Computer Aided Process Engineering. 31 May – 4 June 2015, Copenhagen, Denmark © 2015 Elsevier B.V. All rights reserved.
Scenario-Based Price Negotiations vs. Game Theory in the Optimization of Coordinated Supply Chains Kefah Hjaila, Luis Puigjaner and Antonio Espuña Chemical Engineering Department, Universitat Politècnica de Catalunya, ETSEIB, Av. Diagonal 647, 08028 Barcelona, Spain.
Abstract A scenario-based negotiation (SBN) win-to-win approach is proposed for the optimization of coordinated decentralized multi-site multi-product Supply Chains (SCs) in a competitive environment. Based on non-symmetric roles, the leader aims to settle its offer taking into account the uncertain reaction of the follower, which behavior is represented by a probability of acceptance. Different negotiation scenarios, based on considering Standalone, Cooperative, and Non-Cooperative SCs are analyzed for the negotiation, resulting in different MINLP tactical models, which are illustrated using a case study with different “follower” SCs around an industrial production SC “leader”. On the other hand, a Stackelberg non-cooperative bi-level MINLP game model is built and solved for the same case study. The Non-Cooperative Negotiation Scenario (NCNS) proves to be more adequate, leading to higher individual profits expectations. Keywords: Tactical management, Supply Chain coordination, Game Theory
1. Introduction The competitiveness among chemical industries is shifting the interest of Process Systems Engineering (PSE) towards SCs coordination based on individual and global benefits. Many works have been carried out to analyze different ways of coordination among SCs, such as the integration of different SCM levels (Varma et al., 2007); or the coordination of suppliers’ and producers’ SCs at the tactical level (Hjaila et al., 2014). But, these works support decisions through the use of centralized objectives, disregarding the goals of individuals SCs, and thus conflicts of interests may arise. Solving these conflicts by negotiations has been studied through Game Theory (GT), and specially through the “revenue sharing” based on Stackelberg’s-game for one manufacturer and many competing retailers (Cao et al., 2013), or through developing a bi-level MINLP design and planning model under the leading role of the manufacturer (Yue & You, 2014). Price negotiations as a way to prepare a coordination agreement has been also proposed as a form of “timing” between producer and customer (Moon et al., 2011). Nevertheless, most of the negotiation mechanisms focus on the competitiveness among the retailers disregarding the supplier’s competitive behavior. Furthermore, the aforementioned approaches are based on dominance leadership, without considering the uncertain behavior of the other partner/s, leading to insufficient coordination. Accordingly, this work aims to establish the best conditions for the coordination contract through quantitative negotiations built on win-to-win principles considering the uncertain behavior of the follower conditions when optimizing the leader SC. A
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scenario-based negotiation approach is developed taking into account the individual and global profits at the tactical level. Furthermore, a Stackelberg-game model is also developed to solve the same negotiation problem.
2. Problem statement 2.1. Scenario-Based Negotiation (SBN) Based on non-symmetric roles, the SBN is held between two independent SCs: supplier SC (follower), and client SC (leader); actually, both have been considered production SCs with their own independent suppliers/markets. The leader decides to improve its benefits by buying internal product/s (negotiation item) from the follower SC. The negotiation procedure is divided into two main steps: i) analyzing the negotiation scenarios, and ii) the coordination agreement. 2.1.1. Analyzing the negotiation scenarios Standalone Scenario (SS)”pre-negotiation”: based on the individual objectives, this step aims to establish benchmarks for all negotiation methods. Non-cooperative negotiation scenario (NCNS): based on individual objectives, this scenario considers the contract to be offered to maximize the profit of the leader SC. Cooperative negotiation scenario (CNS): based on establishing a global objective. 2.1.2. The coordination agreement In order to push the negotiation towards a win-to-win policy, the benefits of any reduction in the uncertainty of the production scenario associated to the signature of a collaboration agreement are considered. This includes the calculation of a probability of acceptance of this agreement by the follower SC, taking into account the risk associated to the uncertain behavior of the external conditions. Then, the contract proposed by the leader will be the one driving to the most profitable leader’s expected profit. 2.2 Game Theory (GT) The interaction between the leader and the follower is modelled as a single-leader– single-follower no-cooperative non-zero-sum Stackelberg-game, resulting in a bi-level MINLP model. The idea of the bi-level is that the follower (lower-level SC) objective function is represented as constraints in the leader problem (upper-level SC). In this paper, the bi-level model is solved by building the Stackelberg-payoff matrix considering constraints in both leader and follower SCs. The reaction function is identified (price vs. quantity) and, based on complete information “dynamic game”, the leader designs its moves by offering prices, and the follower responds by offering the amounts to be supplied according to its best conditions.
3. Mathematical Model A generic MINLP tactical model is developed as a basis for this paper. A set of supply chains (sc1, sc2… SC) is considered with their new subsets linking each SC to its corresponding negotiation partner (follower F or leader L). The total sales include internal and external markets (M), at different prices ( pr c, scc,t and prr , m ,t respectively).
SALES sc d ¦ ¦ ¦ prr , m ,t xdemr , sc , m ,t ¦ ¦ pr c, scc,t Qr c, scc,tsc SC ; scc F tT rR mM
tT r cR
(1)
The SC Cost along the planning time horizon T is (RM purchase, transport, storage, production, and the negotiation resource total costs, respectively (Eq. 2). (2) COSTsc ¦ (CRM sc ,t CTRsc ,t CSTsc ,t CPRDsc ,t ) ¦ ¦ pr c, scc,t Qr c, scc,t tT
tT r cR
Scenario-Based Price Negotiations vs. Game Theory in the Optimization of Coordinated Supply Chains
1861
sc SC ; sc ' L PROFsc
SALES sc – COSTsc
sc SC
(3)
3.1. Application of negotiation scenarios: SS: the negotiation resource quantity Qr c, scc,t will be substituted by zero. CNS: the independent SCs seek to optimize the global SC profit ( Tprofit ) (Eq. 4), Tprofit
¦
scSC
PROFsc
(4)
NCNS: the negotiation resource demand is equal to a constant value Er c, scc,t resulted from maximizing the leader SC profit:
r c R; scc L; t T (5) Within the expected leader SC profit expression, ExPROFsc’ , the uncertainty reduction cost is represented as an “abridged” uncertainty risk, to be represented by a probability of acceptance (Eq. 7) sc ' L ExPROFsc ' PROFsc ' uncertainty risk sc ' (6) Qr c, scc,t
probscc
Er c, scc,t
No. of scenarios of improved profitsscc Total No. of scenariosscc
scc F
(7)
3.2. Application of Game Theory Mathematically, the Stackelbergy game forms a bi-level model (Chu and You, 2015), which can be represented in Eqs. (8 &9), where Z and z are the upper-level and lower levels objective functions; X and Y stands for the upper-level and lower-level decision variables; G and H are the upper-level inequality and equality constraints; while g and h are the lower-level inequality and quality constraints. (8) max Z sc 'L ( x, y ) , subject to Gsc 'L ( x, y ) d 0 , and H sc 'L ( x, y ) 0
x X , yY
Where y max z sc 'F ( x, y ) subject to g sc 'F ( x, y ) d 0 ,and hsc 'F ( x, y ) yY
0
(9)
4. Case Study The negotiation models have been implemented and solved for a real data case study (Figure 1) modified from Zamarripa et al. (2014). The partners involved are a production/distribution SC (leader), and the Energy generation SC (follower); the energy supplied/demanded represents the negotiation item.
Figure 1- The decentralized global SC network
5. Results and discussion 5.1. Scenario-Based Negotiations (SBN) The resulting MINLP models have been solved using GloMIQO (Misener & Floudas, 2013). The negotiation starts from the total profit ensuing from the SS (Figure 2 –
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purple line). Obviously, if coordination will not allow improvement over this total profit, there is nothing to negotiate. It is worth noticing that the NCNS leads to 10.77 M€ total profit at the contract price 0.21 €/kWh, with a difference of 8.7% and 3.3% comparing with the SS and the CNS, respectively. Furthermore, the NCNS mathematical formulation is less complex and so allows to identify better solutions with less computational effort (32% less than SS and 63% less than CNS).
Figure 2- Negotiation scenarios total profits
In turn within the NCNS scenario the leader designs its final offer taking into account the follower uncertain reaction; then, the follower has to assess this offer based on its probability distribution curves (accept or reject): 5.1.1. From the leader side: The Production SC assesses its expected profit for each contract offer based on the follower probability of acceptance (Figure 3). In general this probability increases as the contract price increases, but at 0.22 €/kWh the leader decides to buy higher energy amounts from the local Grid, resulting in a sudden probability reduction. The difference between the Production SC contract profit and the expected profit represents the uncertainty cost. The total energy amount needed for the Production SC during the established long term planning horizon is 24.71GWh; 36% of this amount (8.84 GWh) is expected to be supplied from the energy SC, while the rest (15.86 GWh) is to be covered by the local Grid. It is worth mentioning that before considering the uncertainty reduction cost, the contract price 0.14€/kWh was the best option for the leader SC (9.24 M€), but after considering the uncertain reaction of the supplier, the leader offers higher price (0.15 €/kWh), resulting in a 15.5 % profit reduction.
Figure 3- Polystyrene SC contract/expected Profit vs. Probability of acceptance
5.1.2. From the follower side: The Energy SC seeks to optimize its expected benefit based on the leader offer (8.84 GWh at 0.15€/kWh). This results in 2.29M€ profit. In spite of an initially calculated SS profit of 2.44 M€, based on the Energy SC profit probability curves (Figure 4), the probability from accepting the contract seems to be higher.
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Figure 4- Cumulative probability curves
5.2. Results of Game Theory The non-cooperative single-leader/single-follower Stackelberg payoff matrix has been built (Table 1), highlighting the follower optimal quantities for each leader offer. 5.2.1. From the leader side: Stackelberg initial point results in 9.16 M€ profit for the Leader, but this solution is not considered (not win-to-win: The Energy SC Profit is 1.57M€). The final point corresponds the leader SC profit of 7.92 M€ (6% profit improvement vs. the SS). The leader Stackelberg strategy then is to buy 24.71GWh at contract price 0.19 €/kWh. Table 1- Stackelberg-Payoff Matrix L (Leader ) ĺ action (€/kWh) F (Follower) response *:K Ļ 0 (…) 12.00 (…) 23.00 24.71
0.14 F
(…)
0.17
L
F
0.19 L
F
0.20 L
F
0.21 L
F
L
2.44 7.47
2.44 7.47 2.44 7.47 2.44 7.47 2.44 7.47
2.10 8.29
2.46 7.93 2.70 7.69 2.82 7.58 2.94 7.45
1.69 9.06 1.57 9.16
2.38 8.37 2.84 7.90 3.07 7.68 3.30 7.45 2.31 8.42 2.81 7.92 3.06 7.67 3.30 7.43
5.2.2. From the follower side: The leader contract results in 2.81 M€ Energy SC profit (13 % higher than SS: 2.44M€). The follower then analyses its expected benefits in order to accept or reject. The expected follower SC profit with the coordination contract is 2.99 M€, 8.4% higher than the expected profit resulting from rejecting the contract (2.74 M€). So the follower is expected to accept the coordination contract. 5.3. Scenario-Based-Negotiations (SBN) vs. Game Theory (GT): Table 2 shows the final SCs coordination contract using the SBN and GT. The SBN results in higher leader SC profit than GT method, with a difference of (74.61 k€). Table 2- Coordination contract Contract price Negotiation method (€/kWh) Scenario-Based (SBN) 0.15 Stackelberg Game 0.19
Contract amount (GWh) 8.84 24.71
Leader profit (M€) 8.00 7.92
Follower profit (M€) 2.29 2.81
6. Conclusions A Scenario-Based Negotiation (SBN) approach is proposed to set the best conditions for the coordination of independent multi-site multi-product SCs in a highly competitive
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environment. Under the leading role of the client SC, different negotiation scenarios have been analyzed based on Standalone, Non-cooperative, and Cooperative SCs. An uncertainty reduction cost is modelled within the expected leader SC profit as a form of probability of acceptance. From the other hand, a single-leader-single-follower Stackelberg Bi-level MINLP model is developed. Both methods have been illustrated using a case study which coordinates different suppliers’ SCs and client “industrial production SC” (leader) through a global scenario. The results show that the NonCooperative Negotiation scenario (NCNS) proves to be the most adequate scenario leading to higher global profits (8.7% and 3.3% than the Standalone and Cooperative scenarios). Furthermore, the SBN results in higher profit (1%) than GT, in favor of the leader SC. The proposed approach allows to contemplate the different mechanisms a SC may use to modify its relationships with its clients and suppliers during the optimization procedure, which can be used for further second stage agreements, in a generic and flexible way, so it can be applied in practice to real cases, including centralized/decentralized simple/global SCs, as illustrated in the presented case study.
Acknowledgements Financial support received from the Spanish Ministry of Economy and Competitiveness and the European Regional Development Fund, both funding the Project SIGERA (DPI2012-37154-C02-01), and from the Generalitat de Catalunya (AGAUR FI program and grant 2014-SGR-1092-CEPEiMA), is fully appreciated.
References D. Yue, & F. You, 2014, Game-Theoretic Modeling and Optimization of Multi-echelon Supply Chain Design and Operation under Stackelberg Game and Market Equilibrium, Comp & Chem Eng, 71, 347–361. E. Cao, C. Wan, M. Lai, 2013, Coordination of a supply chain with one manufacturer and multiple competing retailers under simultaneous demand and cost disruptions, Int J. Prod Econ, 141, 425–433. K. Hjaila, M. Zamarripa, A. Shokry, A. Espuña, 2014, Application of Pricing Policies for Coordinated Management of Supply Chains, Comp Aided Chem Eng, 33, 475–480. M. Zamarripa, K. Hjaila, J. Silvente, A. Espuña, 2014, Tactical management for coordinated supply chains, Comp & Chem Eng, 66, 110-123. R. Misener, Ch. Floudas, 2013, GloMIQO: Global mixed-integer quadratic optimizer, J Glob Optim, 57,3–50. V.A. Varma, G.V. Reklaitis, G. E. Blau, J. F. Pekny, 2007, Enterprise-wide modelling & optimization—An overview of emerging research challenges and opportunities, Comp & Chem Eng, 31,692–711 Y. Chu, F. You, J.M. Wassick, A. Agarwal, 2015, Integrated planning andscheduling under production uncertainties: bi-level model for-mulation and hybrid solution method, Comp. & Chem. Eng., 72, 255–272. Y. Moon, T. Yao, S. Park, 2011, Price negotiation under uncertainty, Int J. Prod Econ, 134, 413– 423.
Scenario-Based Price Negotiations vs. Game Theory in the Optimization of Coordinated Supply Chains Kefah Hjaila, Luis Puigjaner and Antonio Espuña Chemical Engineering Department, Universitat Politècnica de Catalunya, ETSEIB, Av. Diagonal 647, 08028 Barcelona, Spain.
Abstract A scenario-based negotiation (SBN) win-to-win approach is proposed for the optimization of coordinated decentralized multi-site multi-product Supply Chains (SCs) in a competitive environment. Based on non-symmetric roles, the leader aims to settle its offer taking into account the uncertain reaction of the follower, which behavior is represented by a probability of acceptance. Different negotiation scenarios, based on considering Standalone, Cooperative, and Non-Cooperative SCs are analyzed for the negotiation, resulting in different MINLP tactical models, which are illustrated using a case study with different “follower” SCs around an industrial production SC “leader”. On the other hand, a Stackelberg non-cooperative bi-level MINLP game model is built and solved for the same case study. The Non-Cooperative Negotiation Scenario (NCNS) proves to be more adequate, leading to higher individual profits expectations. Keywords: Tactical management, Supply Chain coordination, Game Theory
1. Introduction The competitiveness among chemical industries is shifting the interest of Process Systems Engineering (PSE) towards SCs coordination based on individual and global benefits. Many works have been carried out to analyze different ways of coordination among SCs, such as the integration of different SCM levels (Varma et al., 2007); or the coordination of suppliers’ and producers’ SCs at the tactical level (Hjaila et al., 2014). But, these works support decisions through the use of centralized objectives, disregarding the goals of individuals SCs, and thus conflicts of interests may arise. Solving these conflicts by negotiations has been studied through Game Theory (GT), and specially through the “revenue sharing” based on Stackelberg’s-game for one manufacturer and many competing retailers (Cao et al., 2013), or through developing a bi-level MINLP design and planning model under the leading role of the manufacturer (Yue & You, 2014). Price negotiations as a way to prepare a coordination agreement has been also proposed as a form of “timing” between producer and customer (Moon et al., 2011). Nevertheless, most of the negotiation mechanisms focus on the competitiveness among the retailers disregarding the supplier’s competitive behavior. Furthermore, the aforementioned approaches are based on dominance leadership, without considering the uncertain behavior of the other partner/s, leading to insufficient coordination. Accordingly, this work aims to establish the best conditions for the coordination contract through quantitative negotiations built on win-to-win principles considering the uncertain behavior of the follower conditions when optimizing the leader SC. A
1860
K. Hjaila et al.
scenario-based negotiation approach is developed taking into account the individual and global profits at the tactical level. Furthermore, a Stackelberg-game model is also developed to solve the same negotiation problem.
2. Problem statement 2.1. Scenario-Based Negotiation (SBN) Based on non-symmetric roles, the SBN is held between two independent SCs: supplier SC (follower), and client SC (leader); actually, both have been considered production SCs with their own independent suppliers/markets. The leader decides to improve its benefits by buying internal product/s (negotiation item) from the follower SC. The negotiation procedure is divided into two main steps: i) analyzing the negotiation scenarios, and ii) the coordination agreement. 2.1.1. Analyzing the negotiation scenarios Standalone Scenario (SS)”pre-negotiation”: based on the individual objectives, this step aims to establish benchmarks for all negotiation methods. Non-cooperative negotiation scenario (NCNS): based on individual objectives, this scenario considers the contract to be offered to maximize the profit of the leader SC. Cooperative negotiation scenario (CNS): based on establishing a global objective. 2.1.2. The coordination agreement In order to push the negotiation towards a win-to-win policy, the benefits of any reduction in the uncertainty of the production scenario associated to the signature of a collaboration agreement are considered. This includes the calculation of a probability of acceptance of this agreement by the follower SC, taking into account the risk associated to the uncertain behavior of the external conditions. Then, the contract proposed by the leader will be the one driving to the most profitable leader’s expected profit. 2.2 Game Theory (GT) The interaction between the leader and the follower is modelled as a single-leader– single-follower no-cooperative non-zero-sum Stackelberg-game, resulting in a bi-level MINLP model. The idea of the bi-level is that the follower (lower-level SC) objective function is represented as constraints in the leader problem (upper-level SC). In this paper, the bi-level model is solved by building the Stackelberg-payoff matrix considering constraints in both leader and follower SCs. The reaction function is identified (price vs. quantity) and, based on complete information “dynamic game”, the leader designs its moves by offering prices, and the follower responds by offering the amounts to be supplied according to its best conditions.
3. Mathematical Model A generic MINLP tactical model is developed as a basis for this paper. A set of supply chains (sc1, sc2… SC) is considered with their new subsets linking each SC to its corresponding negotiation partner (follower F or leader L). The total sales include internal and external markets (M), at different prices ( pr c, scc,t and prr , m ,t respectively).
SALES sc d ¦ ¦ ¦ prr , m ,t xdemr , sc , m ,t ¦ ¦ pr c, scc,t Qr c, scc,tsc SC ; scc F tT rR mM
tT r cR
(1)
The SC Cost along the planning time horizon T is (RM purchase, transport, storage, production, and the negotiation resource total costs, respectively (Eq. 2). (2) COSTsc ¦ (CRM sc ,t CTRsc ,t CSTsc ,t CPRDsc ,t ) ¦ ¦ pr c, scc,t Qr c, scc,t tT
tT r cR
Scenario-Based Price Negotiations vs. Game Theory in the Optimization of Coordinated Supply Chains
1861
sc SC ; sc ' L PROFsc
SALES sc – COSTsc
sc SC
(3)
3.1. Application of negotiation scenarios: SS: the negotiation resource quantity Qr c, scc,t will be substituted by zero. CNS: the independent SCs seek to optimize the global SC profit ( Tprofit ) (Eq. 4), Tprofit
¦
scSC
PROFsc
(4)
NCNS: the negotiation resource demand is equal to a constant value Er c, scc,t resulted from maximizing the leader SC profit:
r c R; scc L; t T (5) Within the expected leader SC profit expression, ExPROFsc’ , the uncertainty reduction cost is represented as an “abridged” uncertainty risk, to be represented by a probability of acceptance (Eq. 7) sc ' L ExPROFsc ' PROFsc ' uncertainty risk sc ' (6) Qr c, scc,t
probscc
Er c, scc,t
No. of scenarios of improved profitsscc Total No. of scenariosscc
scc F
(7)
3.2. Application of Game Theory Mathematically, the Stackelbergy game forms a bi-level model (Chu and You, 2015), which can be represented in Eqs. (8 &9), where Z and z are the upper-level and lower levels objective functions; X and Y stands for the upper-level and lower-level decision variables; G and H are the upper-level inequality and equality constraints; while g and h are the lower-level inequality and quality constraints. (8) max Z sc 'L ( x, y ) , subject to Gsc 'L ( x, y ) d 0 , and H sc 'L ( x, y ) 0
x X , yY
Where y max z sc 'F ( x, y ) subject to g sc 'F ( x, y ) d 0 ,and hsc 'F ( x, y ) yY
0
(9)
4. Case Study The negotiation models have been implemented and solved for a real data case study (Figure 1) modified from Zamarripa et al. (2014). The partners involved are a production/distribution SC (leader), and the Energy generation SC (follower); the energy supplied/demanded represents the negotiation item.
Figure 1- The decentralized global SC network
5. Results and discussion 5.1. Scenario-Based Negotiations (SBN) The resulting MINLP models have been solved using GloMIQO (Misener & Floudas, 2013). The negotiation starts from the total profit ensuing from the SS (Figure 2 –
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purple line). Obviously, if coordination will not allow improvement over this total profit, there is nothing to negotiate. It is worth noticing that the NCNS leads to 10.77 M€ total profit at the contract price 0.21 €/kWh, with a difference of 8.7% and 3.3% comparing with the SS and the CNS, respectively. Furthermore, the NCNS mathematical formulation is less complex and so allows to identify better solutions with less computational effort (32% less than SS and 63% less than CNS).
Figure 2- Negotiation scenarios total profits
In turn within the NCNS scenario the leader designs its final offer taking into account the follower uncertain reaction; then, the follower has to assess this offer based on its probability distribution curves (accept or reject): 5.1.1. From the leader side: The Production SC assesses its expected profit for each contract offer based on the follower probability of acceptance (Figure 3). In general this probability increases as the contract price increases, but at 0.22 €/kWh the leader decides to buy higher energy amounts from the local Grid, resulting in a sudden probability reduction. The difference between the Production SC contract profit and the expected profit represents the uncertainty cost. The total energy amount needed for the Production SC during the established long term planning horizon is 24.71GWh; 36% of this amount (8.84 GWh) is expected to be supplied from the energy SC, while the rest (15.86 GWh) is to be covered by the local Grid. It is worth mentioning that before considering the uncertainty reduction cost, the contract price 0.14€/kWh was the best option for the leader SC (9.24 M€), but after considering the uncertain reaction of the supplier, the leader offers higher price (0.15 €/kWh), resulting in a 15.5 % profit reduction.
Figure 3- Polystyrene SC contract/expected Profit vs. Probability of acceptance
5.1.2. From the follower side: The Energy SC seeks to optimize its expected benefit based on the leader offer (8.84 GWh at 0.15€/kWh). This results in 2.29M€ profit. In spite of an initially calculated SS profit of 2.44 M€, based on the Energy SC profit probability curves (Figure 4), the probability from accepting the contract seems to be higher.
Scenario-Based Price Negotiations vs. Game Theory in the Optimization of Coordinated Supply Chains
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Figure 4- Cumulative probability curves
5.2. Results of Game Theory The non-cooperative single-leader/single-follower Stackelberg payoff matrix has been built (Table 1), highlighting the follower optimal quantities for each leader offer. 5.2.1. From the leader side: Stackelberg initial point results in 9.16 M€ profit for the Leader, but this solution is not considered (not win-to-win: The Energy SC Profit is 1.57M€). The final point corresponds the leader SC profit of 7.92 M€ (6% profit improvement vs. the SS). The leader Stackelberg strategy then is to buy 24.71GWh at contract price 0.19 €/kWh. Table 1- Stackelberg-Payoff Matrix L (Leader ) ĺ action (€/kWh) F (Follower) response *:K Ļ 0 (…) 12.00 (…) 23.00 24.71
0.14 F
(…)
0.17
L
F
0.19 L
F
0.20 L
F
0.21 L
F
L
2.44 7.47
2.44 7.47 2.44 7.47 2.44 7.47 2.44 7.47
2.10 8.29
2.46 7.93 2.70 7.69 2.82 7.58 2.94 7.45
1.69 9.06 1.57 9.16
2.38 8.37 2.84 7.90 3.07 7.68 3.30 7.45 2.31 8.42 2.81 7.92 3.06 7.67 3.30 7.43
5.2.2. From the follower side: The leader contract results in 2.81 M€ Energy SC profit (13 % higher than SS: 2.44M€). The follower then analyses its expected benefits in order to accept or reject. The expected follower SC profit with the coordination contract is 2.99 M€, 8.4% higher than the expected profit resulting from rejecting the contract (2.74 M€). So the follower is expected to accept the coordination contract. 5.3. Scenario-Based-Negotiations (SBN) vs. Game Theory (GT): Table 2 shows the final SCs coordination contract using the SBN and GT. The SBN results in higher leader SC profit than GT method, with a difference of (74.61 k€). Table 2- Coordination contract Contract price Negotiation method (€/kWh) Scenario-Based (SBN) 0.15 Stackelberg Game 0.19
Contract amount (GWh) 8.84 24.71
Leader profit (M€) 8.00 7.92
Follower profit (M€) 2.29 2.81
6. Conclusions A Scenario-Based Negotiation (SBN) approach is proposed to set the best conditions for the coordination of independent multi-site multi-product SCs in a highly competitive
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environment. Under the leading role of the client SC, different negotiation scenarios have been analyzed based on Standalone, Non-cooperative, and Cooperative SCs. An uncertainty reduction cost is modelled within the expected leader SC profit as a form of probability of acceptance. From the other hand, a single-leader-single-follower Stackelberg Bi-level MINLP model is developed. Both methods have been illustrated using a case study which coordinates different suppliers’ SCs and client “industrial production SC” (leader) through a global scenario. The results show that the NonCooperative Negotiation scenario (NCNS) proves to be the most adequate scenario leading to higher global profits (8.7% and 3.3% than the Standalone and Cooperative scenarios). Furthermore, the SBN results in higher profit (1%) than GT, in favor of the leader SC. The proposed approach allows to contemplate the different mechanisms a SC may use to modify its relationships with its clients and suppliers during the optimization procedure, which can be used for further second stage agreements, in a generic and flexible way, so it can be applied in practice to real cases, including centralized/decentralized simple/global SCs, as illustrated in the presented case study.
Acknowledgements Financial support received from the Spanish Ministry of Economy and Competitiveness and the European Regional Development Fund, both funding the Project SIGERA (DPI2012-37154-C02-01), and from the Generalitat de Catalunya (AGAUR FI program and grant 2014-SGR-1092-CEPEiMA), is fully appreciated.
References D. Yue, & F. You, 2014, Game-Theoretic Modeling and Optimization of Multi-echelon Supply Chain Design and Operation under Stackelberg Game and Market Equilibrium, Comp & Chem Eng, 71, 347–361. E. Cao, C. Wan, M. Lai, 2013, Coordination of a supply chain with one manufacturer and multiple competing retailers under simultaneous demand and cost disruptions, Int J. Prod Econ, 141, 425–433. K. Hjaila, M. Zamarripa, A. Shokry, A. Espuña, 2014, Application of Pricing Policies for Coordinated Management of Supply Chains, Comp Aided Chem Eng, 33, 475–480. M. Zamarripa, K. Hjaila, J. Silvente, A. Espuña, 2014, Tactical management for coordinated supply chains, Comp & Chem Eng, 66, 110-123. R. Misener, Ch. Floudas, 2013, GloMIQO: Global mixed-integer quadratic optimizer, J Glob Optim, 57,3–50. V.A. Varma, G.V. Reklaitis, G. E. Blau, J. F. Pekny, 2007, Enterprise-wide modelling & optimization—An overview of emerging research challenges and opportunities, Comp & Chem Eng, 31,692–711 Y. Chu, F. You, J.M. Wassick, A. Agarwal, 2015, Integrated planning andscheduling under production uncertainties: bi-level model for-mulation and hybrid solution method, Comp. & Chem. Eng., 72, 255–272. Y. Moon, T. Yao, S. Park, 2011, Price negotiation under uncertainty, Int J. Prod Econ, 134, 413– 423.