Scenario-based dynamic negotiation for the coordination of multi-enterprise supply chains under uncertainty

1 Scenario-Based Dynamic Negotiation for the Coordination of Multi-Enterprise Supply Chains under Uncertainty Kefah Hjaila1, José M. Laínez-Aguirre2,Luis Puigjaner1 and Antonio Espuña1* 1Chemical Engineering Department, Universitat Politècnica de Catalunya, ETSEIB., Av. Diagonal 647, 08028 Barcelona, Spain. 2Department of Industrial and Systems Engineering, University at Buffalo, NY, United States. *corresponding author: [email protected] Abstract A novel Scenario-Based Dynamic Negotiation approach is proposed for the coordination of decentralized Supply Chains under uncertainty. The relation between the involved organizations (client, provider and third parties) and their respective conflicting objectives is captured through a non-zero-sum and non-symmetric roles SBDN negotiation. The client (leader) designs coordination agreements considering the uncertain reaction of the provider (follower) resulting from the uncertain nature of the third parties, which is modeled as a probability of acceptance. Different negotiation scenarios are studied: i) Cooperative, and ii) Non-Cooperative and iii) Standalone cases. The use of the resulting models is illustrated through a case study with different vendors around a “leader” (client) in a decentralized scenario. Although the usual cooperation hypothesis will allow higher overall profit expectations, using the proposed approach it is possible to identify non-Cooperative scenarios with high individual profit expectations which are more likely to be accepted by all partners. Keywords: Decentralized Supply Chain; Tactical planning; Uncertainty management; Competitive management. 1. INTRODUCTION Due to the market dynamics, double marginalization, and the volatility of the market, the enterprises decision-makers have to change their way of managing their Supply chains (SCs). Enterprises in the chemical process industry seek “value preservation” to remain competitive and “value growth” to become more innovative (Grossmann, 2004). Many works in the literature propose different procedures to help decision-makers to optimize their SCs, especially at the tactical level, which is the focus of this paper. These works, briefly discussed below, are devoted to the optimization of the whole system from a centralized perspective. However, holding a large scale SC for one enterprise under a centralized decision-maker may not be feasible, thus collaborating with other enterprises may add value to all participating organizations, so that all can remain competitive in the global volatile market. Such collaboration is hard to develop as it depends on the cooperative behavior of the participants. Furthermore, a complexity arises when considering the different (possibly conflicting) objectives of the organizations involved, since they are really trying to optimize its own benefits without considering the risks associated with the uncertain behavior of the other partners. From a centralized perspective, Laínez et al. (2009) develop an integrated strategic and tactical flexible MILP model taking into account all possible feasible links and material flows 2 among the SC facilities. Amaro and Barbosa-Póvoa (2013) develop a close-loop SC tactical model formulation (MILP), coordinating the direct flows (new products) and the reverse flows (recycled) within a centralized closed-loop perspective where the direct and reverse echelons SCs belong to one organization. Zamarripa et al. (2014) propose a LP tactical model for optimizing multi-site multi-product SC networks, coordinating the different steps through the insurance of the consistency of the supply/demand SC. This work has been expanded later by Hjaila et al. (2016) by integrating third parties’ financial perspectives as new elements to be considered in the decision making, thus resulting in different (LP, NLP, MINLP) tactical centralized models. Typical SCM models focus on the single flow of information biased by the decisionmaker of one organization (centralizing player). However, such information is not sufficient to deal with the new market competitive issues resulting from the presence of other partners, such as coordination/collaboration, negotiations, uncertainty. But, the incorporation of third party decisions should be studied in depth. All the above described works focus on the overall objective of the system, resulting from the coordination between the various echelons/partners within a global SC centralized perspective, so that the individual objectives are disregarded, although they are essential, especially when SC superstructure is decentralized and different organizations are involved, including third parties with conflicting objectives and uncertain behavior. The resolution of conflictive goals through negotiations has been slightly covered by the PSE literature. The approaches discussed at the bargaining literature include the use of quantity discounts, minimum commitments, buy backs (returns), penalties, and revenue sharing (Cachon, 2003). It is worth to comment the work by Cao et al. (2013) which suggests a trading method based on “revenue sharing” approach to solve the conflicts between one manufacturer and the various competing retailers under the leading role of the manufacturer. The authors consider the uncertainty of the production and final markets demands; however, in this work the manufacturer provides the initial production plan according to its uncertainty behavior regardless of the uncertain behavior of retailers which can lead to SC disruptions. In order to guarantee some benefits to the follower, Zhao et al. (2013) propose a negotiation method for optimizing a SC manufacturer-retailer network through bi-directional option contracts (call or put). For the call option, the manufacturer must buy a specific amount of products at a specific price while, for the put option the retailer must pay an allowance for the cancellation or refund of an order. Multi-agent systems have been also proposed for optimizing decentralized SC networks. The work of Cao et al. (2007) develop a Pinch Multi-Agent Genetic Algorithm (PMAGA) for network optimization of water-use at the tactical level where stakeholders cooperate to minimize the total used freshwater. Banaszewski et al. (2013) propose an auction protocol tactical model multi-agent for a Brazilian oil SC to identify the oil products transport plan (types, amounts, allocation). However, the multi-agent-based negotiations are oriented to cooperative situations, in which all participating agents cooperate towards a common objective function. This approach disregards individual objectives and their uncertain nature which can affect the performance of the entire system. 3 Many works were carried out to optimize decentralized SCs through Game Theory (GT), based on cooperative and non-cooperative cases. For the cooperative case, Hennet and Areda (2008) develop a coordination agreement for a producer and supplier SC through cooperative games based on sharing the backorder costs and capacity reservation in order to maintain supply flows. Zhao et al. (2010) develop a cooperative game model for the optimization of a decentralized manufacturer-retailer SC based on option-contracts under the condition that the manufacturer maximum production coincides with the retailer reserved quantities. Whereas individual goals through non-cooperative SCs have been studied so far, the proposed approach is based on very simplified SC structures such as in the work of Li et al. (2013). They propose a coordination contract agreement based on “shortage penalty” between one supplier and one buyer (no external markets), so that the follower is obliged to sell which gives a high dominance to the leader. Yue and You (2014) consider more complex structures, in which different competing suppliers and retailers participate. They meet the competition between the different suppliers and retailers through cooperative games based on Nash Equilibrium, while the interactions between the manufacturer and the suppliers/retailers are modeled as non-cooperative Stackelberg games. However, as a cooperative play, competitive suppliers are considered obliged to sell to the manufacturer disregarding the competition among different customers. This gives again a dominant leadership to the customer. Furthermore, in the proposed non-cooperative Stackelberg game, the supplier SC model has been simplified (as LP) in order to be represented as constraints in the manufacturer optimization model (bi-level model), which cannot be resolved if the supplier SC model is a non-convex MINLP (Colson et al. 2007). This approach would require the use of non-realistic linearizing simplifications if the supplier SC should consider aspects like pricing policies, re-design decisions, etc. Moreover, the uncertain behaviors of the followers SCs (suppliers and retailers) are not considered by the leader. In summary, most of the literature about decentralized SCs tactical decision-making, either for cooperative or non-cooperative cases, focuses on simple SC networks, where the follower is forced to cooperate with the leader, and/or proposes linearized models to represent the behavior of some of the actors which can lead to losing some practicality. Current negotiation methods based on non-cooperative SCs allow to provide individual decisions based on static cases without addressing the full SC picture, which should include how partners may react, thus resulting in incomplete negotiations, especially when the negotiating partners (and their third parties) are subject to risk as the result of external uncertainty sources. Moreover, none of the literature work on decentralized SCs optimization evaluates the negotiation outcome based on the benefits probabilities in order to help the negotiating partners to make a final decision. Thus, effective negotiations able to incorporate the conflicting goals of all participants (including third parties) in tactical models are needed to improve the overall performance of decentralized SC networks and to avoid SCs disruptions. Consequently, this paper aims to develop a novel Scenario-Based Dynamic Negotiation method (SBDN) as a tool for decision support to provide the best conditions for coordination 4 between independent production-distribution SCs with conflicting objectives within decentralized SC. The use of this approach to support negotiations, taking into account the competition between different suppliers/markets and their uncertain nature, will improve the capacity to identify and manage new win-to-win scenarios, thus expanding the boundaries of the SC of interest. Such expansion covers both customers and providers, with their respective production-distribution SCs, as part of the overall system. In summary, the objectives of this work can be summarized in the following points: - To analyze cooperative and non-cooperative decentralized SC through a negotiation oriented approach. - To incorporate in the system the uncertain nature of the different involved parties, and to summarize it in a single behavioral expression associated with the follower reaction which is considered in the leader SC objective function. - To represent all the involved partners in a complete production-distribution SCs. - To propose a decision-support strategy to evaluate the overall outcome, based on the risk behavior and the expected benefits of the partners. - To represent the variations between the profits scenarios in one single approach through the probability of acceptance. - To create a generic and flexible enough framework by implementing the resulting strategy, able to be used in real-sized cases of centralized/decentralized SCs with simple/complex structures. 2. Problem Statement The main SC of this work produces several products to final customers using resources from different competing providers. In order to improve its individual profits, the main organization (as a client) may consider to collaborate with other production SCs, which are recognized as independent organizations, with their own competing providers and markets, on the basis of a buying/selling resource which from now on will be considered an “inner component“ (Figure 1). Since the value of this inner component is an income for the main provider and a cost for the main client, a conflict of interests arises to identify the inner component flows (physical/economic) along the tactical time horizon in this complex competitive environment. In order to solve this conflict, a coordination compromise is usually proposed, but its negotiation may be complex and may even end without an agreement. 5 Figure 1Decentralized SC network and stakeholders 2.1 SBDN methodology In the Scenario Based Dynamic Negotiation approach (SBDN) proposed in this work, the parties in the negotiation are the client and the provider, both participating as productiondistribution SCs in the decentralized SC of interest. The elements of negotiation are the inner component physical flows between their SCs, and obviously its unit transfer price. Our SBDN novel approach is based on building a coordination/collaboration contract, and since any contract is between pairs of stakeholders, two main negotiating partners are considered for signing the contract: the Client and the Provider. The rest of the participants organizations (e.g. suppliers, customers, external providers, external clients, etc.) interacting with the decentralized SC are considered as 3rd parties (Figure 2). However, all 3rd parties participate in the decision-making by means of their price policies as will be explained later. Based on a non-symmetrical role, the client (as leader) will design a set of coordination contracts based on its best conditions and the provider (as follower) expected response function (Figure 2). This response function is characterized by the uncertain response of the follower 3rd parties to the quantity and the item price offered by the leader at each time slot over the discrete planning time horizon, and will be assessed on the basis of the incomplete knowledge of the follower uncertain behavior and its external conditions (i.e., uncertainty of third parties’ behavior). 6 Figure 2SBDN partners Figure 3 illustrates the SBDN context. The SBDN depends on many elements: i) the economic context of the participants, especially at the standalone case, ii) the market situation (e.g. prices, competing partners, etc.,), iii) the main objectives of each enterprise stakeholder, iv) the quality of the shared information between partners, v) the risk propensity of the main enterprise decision-makers, and finally vi) the probability of acceptance of the follower partner to the decisions made by the leader partner. SBDN Economic context Market situation Enterprises objectives Informatio n sharing Risk propensity Probability of acceptance 7 Figure 3SBDN context The proposed SBDN methodology can be considered as divided into two main parts (Figure 4): the analysis of negotiation scenarios (identification of the best scenario to be used for negotiating the final agreement), and the preparation of the final coordination/collaboration agreement. 2.1.1 Negotiation scenarios Different negotiation scenarios are analyzed in this work on the basis of three main situations i) Standalone, ii) Cooperative, and iii) Non-Cooperative circumstances (Figure 4). Standalone Scenario (SS) Cooperative Negotiation Scenario (CNS) Negotiation Scenarios OptimizationGlobal optimization Global Profit Uncertain conditions Probability of acceptance Coordination contract LeaderFollower Expected Profit Final collaboration agreement Expected Profit Probability distribution Leader non-Cooperative Negotiation Scenario (nCNS) Follower Price scenarios Optimization Current Profit Optimal quanti ty Optimization Uncertain conditions Current Profit Expected Profit Expected follower Profit Current conditions Profit Uncertain conditions Expected follower Profit Current conditions Current conditions Improved expected profit Final response (accept/reject) Figure 4SBDN methodology flowchart i) Cooperative Negotiation Scenario (CNS): Both negotiating parties study the situation under a global perspective, as they were part of a coalition to maximize the overall profit of the SC. This will stablish a second benchmark, in the opposite side. Before starting the negotiation procedures, the logical step 8 for the parties is to analyze whether their eventual coordination agreement offers potential benefit expectations (or not). ii) Non-Cooperative Negotiation Scenario (nCNS) The leader designs the first play by assessing a set of prices and quantities for the negotiation elements, based on her/his best terms and taking into consideration the competitive prices of the follower SC external markets (based on dynamic “sequential” negotiations). Both parties independently optimize their own SCs taking into consideration the flow of a bargaining (price vs. quantity) over the planning time horizon. iii) Standalone Scenario (SS): The negotiating partners optimize their individual profits independently, i.e.: without considering the negotiation step. This scenario will establish individual benchmarks for all methods of negotiation. 2.1.2 The coordination agreement Based on the leader contract offers, both trading partners analyze their expected benefits: From the leader side: The benefits of any reduction in the uncertainty associated with the signature of a coordination agreement may be considered. The leader has to forecast to what extent the follower would accept each coordination contract offer by taking into consideration the uncertain reaction associated with the external risk conditions, and the endogenous uncertainty in the follower model. As a result, the probability of acceptance of this agreement by the follower is estimated. Additionally to the non-formal knowledge that each partner has, probably historically accumulated about the rest of partners, this probability of acceptance, may consider set of external feasible scenarios (follower SC) and the subsequent Monte-Carlo sampling approach. Then, the leader may use this probability of acceptance function to calculate the expected profits. The contract proposed by the leader will be that one leading to the most profitable leader’s expectations, which in turn will depend on the manner the leader manages uncertainty (risk-seeking, risk-neutral, or risk-averse). From the follower side: On the basis of the coordination agreement proposed by the leader, the follower will assess the risks associated with the acceptance or rejection of this cooperation agreement. The evaluation will be based on the probability distribution and cumulative curve of its own expected profits. These probability curves may be also obtained by randomly generating and simulating scenarios through a Monte-Carlo approach (e.g.: assuming normal or any other reasonable probability distribution function). The response of the follower will also depend on how the related organization manages uncertainty (risk-seeking, risk-neutral, or riskaverse). 9 3. Mathematical model A generic tactical MINLP has been developed to evaluate different negotiation scenarios. Small changes in the model’s constraints allow to introduce different coordination situations which are useful to assess whether a specific proposal is likely to be accepted or rejected by the counterparts. 3.1 The tactical base model The base model is designed to be flexible enough to accept simultaneously all necessary partners with their respective SCs and 3rd parties, which enables them to play different roles (e.g. client for one SC and provider for another SC) within a global SC network. This is done by considering the partner SC’s as a set in the mathematical formulation. Accordingly, to represent the negotiation strategy, a set of supply chains (sc1, sc2… SC) is considered linking each SC to its corresponding negotiation partner (follower F or leader L). Furthermore, the model formulation includes a set of third parties D: leader external providers (xv), follower external clients (xc), suppliers (s), and customers (m). The model includes a set of resources r (RM, final product, energy, etc.), production plants pl, and warehouses w as well. A subset w’ is considered to represent the warehouses belonging to other partner SCs. Figure 5 illustrates the main interactions between the leader and the follower SCs, including their relations with 3rd parties. The most important variables are illustrated in the figure: r’ represents the specific resource under negotiation (inner component), which can be purchased from external vendors (xv) and/or sold to external clients (xc). , ',r sc t Q ′ represents the quantity of this negotiation item r’ sent by the follower SC (F) to each production plant (pl) of the leader SC (L) along a discrete planning horizon T, at a transfer price per unit ,' r sc p ′ . ', , ', , r w sc xc t C and , , , ',r xv w sc t V′ represent the flows of the same kind of resource r’ sold to the external clients (xc) and purchased from the external vendors (xv) along the planning horizon T, respectively. The terms ,,r xc t pc ′ and ,,r xv t pv ′ represent the applicable prices for selling and purchasing to the external clients (xc) and from the external vendors (xv), respectively. 16 the decision making of both negotiating partners is considered, and the evaluation of the coordination contracts will be assessed based on the probability of acceptance. The uncertain reaction of the follower partner resulting from the uncertain behavior of its 3rd parties (suppliers s, customers m, external client xv) is projected in the leader SC model as a probability of acceptance. The probability of acceptance sc prob is computed taking into account the expected benefits and the probabilities of occurrence of each generated scenario. In this work a simple ratio between the number of successful scenarios and the total number of scenarios is proposed to calculate the probability of acceptance sc prob (Eq.19). sc prob is estimated on the basis of the expected profits of the follower SC resulting from the different generated scenarios compared with the expected profits resulting from the standalone case (SS) using the same generated scenarios. In this part, a Monte-Carlo sampling method is used to generate random scenarios of the price policies of the 3rd parties (Eqs. (6, 813): ,,r xc t pc ′ , ,,r sc m rp , and ,, ,r s sc t vrm . ' ' ' . . sc sc sc No of scenarios of improved profits prob Total No of scenarios = ' ;'sc SC sc F∀∈ ∈ (19) The leader expected profit 'sc ExPROF is then obtained (Eq. 20) based on the probability of acceptance ' sc prob . ' '' ' '(1 ) if the follower accep sc sc sc sc ts if the follower r scejects ExPROF prob PROF prob PROF= ⋅ +− ⋅ ' ;'sc SC sc L∀∈ ∈ (20) The mathematical model formulation leads to different MINLP models, which can be applied to different configurations of SCs networks with their own competitive 3rd parties. Furthermore, the integration of the 3rd party price polices in the decision making as (Eqs. 6, 7, 8-13), regardless of the added complexity to the model formulation, gives the 3rd parties enough freedom to manage their financial flows, thus allowing them to participate in the decision-making with their uncertain conditions. Subsequently, the equilibrium can be achieved from this negotiation: between the external client (xc) and the leader partner (L) as competing clients to purchase the resource r’, and between the external vendors (xv) and the follower partner as vendors of the resource r’. Furthermore, the developed MINLP model constitutes a flexible decision-support tool to cover all types of SCs negotiations (cooperative/non-cooperative), for centralized/decentralized SC networks. 4. Case study The developed MINLP models have been implemented and solved for a case study based on the centralized SC system proposed by Hjaila et al. (2016). The centralized SC is decentralized by assuming a decentralized SC superstructure in order to illustrate the 17 proposed approach. Additionally, the planning horizon has been reduced from 10 to 6 time periods and the capacities of the energy generation plants have been increased from 5MWe to 6MWe in order to enhance the competitive pressure among partners. The negotiating parties are the polystyrene production-distribution organization (as leader) and the energy generation organization (as follower), so the internal energy supplied/demanded is considered as the item to be negotiated (amount and price). Each SC is assumed to also negotiate with other own suppliers and markets (Figure 6), so both follower and leader have the flexibility to accept or reject the offers of their respective counterpart. The equilibrium will be achieved between the competing partners: i) between the polystyrene production SC enterprise stakeholder and the local Grid and external markets of the energy generation SC (3rd parties), and ii) between the Local Grid (3rd party as external provider to the leader SC) and the energy generation SC enterprise stakeholder. Figure 6Negotiation partners SCs The energy generation SC consists of 6 renewable energy generators (g1, g2... g6) fed by one RM supplier (s1) of 4 alternative competing resources (wood pellets b1, coal b2, petcoke b3, and marc waste b4). It is assumed that the energy RM is stored in the energy generation sites if necessary. The energy generation enterprise SC provides energy to the Local Grid and to two external markets (Figure 7). The SC of production-distribution of the polystyrene consists of 3 manufacturing sites (pl1, pl2 and pl3) producing two different products (A and B) using 4 alternative resources: rm1 and rm2 to produce product A, and rm3 and rm4 to produce product B. They are provided by 4 competitive suppliers (sup1, sup2, sup3, and sup4) and the energy is obtained from the Local Grid. The final products (A and B) are stored in 2 warehouses (w1 and w2) to be distributed later to three polystyrene markets (m1, m2, and m3) (Figure 8). Prices of both SCs external resources follow a piecewise pricing model, as in Hjaila et al. (2016) with an elasticity’s price of demand of (-20) for the raw materials of the polystyrene production-distribution SC, and (-25) for the raw materials of the energy generation SC. 18 Figure 7Follower SC (SS) Figure 8Leader SC (SS) Table 1 and Table 2 list the distances that the polystyrene RMs travel through the leader SC, and the polystyrene production cost using the different RMs. Table 3 lists the energy generation SC production ratio and cost (energy plants). Table 1Distance suppliers/polystyrene production plants (km) (Reference: Hjaila et al., 2016) Polystyrene SC supplier Distance to production plants (km) pl1 pl2 pl3 sup 1 100 150 145 sup 2 200 120 130 sup 3 110 70 80 sup 4 170 220 215 Table 2Polystyrene production unit costs Unit production cost (€/kg) Product A rm1 0.64 rm2 0.62 Product B rm3 0.58 rm4 0.53 Table 3Energy generation plants production ratio and cost Production ratio Production cost g1-g3 g4-g6 g1-g3 g4-g6 b1 0.73 1.50 0.26 0.13 b2 2.00 2.60 0.20 0.14 b3 0.85 1.80 0.21 0.15 b4 0.80 2.00 0.23 0.14 The energy prices and costs to and from the local Grid are given in Table 4 taking into consideration the characteristics of the Spanish public electricity (Ministry of Industry, Energy and Tourism, 2015). These prices vary according to the tariff type and rates in Spain.). 19 Table 4Current external energy prices Energy price (€/kWh) Energy price to the fixed energy markets 0.20 Energy price to Local Grid (demand <2GWh) 0.21 Energy price to Local Grid (2GWh<demand< 4GWh) 0.20 Energy price to Local Grid (4GWh<demand < 6GWh) 0.19 Local Grid energy price to energy markets 0.22 Local Grid energy price to Polystyrene SC (demand>2GWh) 0.22 Local Grid energy price to Polystyrene SC (2GWh<demand<4GWh) 0.21 Local Grid energy price to Polystyrene SC (4GWh<demand<8GWh) 0.20 Figure 9Decentralized SC network 5. Results and discussion As a first step, the MINLP tactical models of both negotiating partners are optimized as standalone cases, so that the standalone (SS) individual profits are obtained. Then, for both CNS and nCNS cases (see Figure 9 Decentralized SC), the negotiation is held to identify the internal energy flows (negotiation item) over the whole planning time horizon. The leader may offer several prices for the internal energy in this case varying from 0.14 to 0.22 €/kWh (contract prices ,' contract r sc p ′ in the mathematical model). These prices are estimated based on the electrical energy price variations in Spain during the last ten years. The leader may also offer lower prices, but this would result in the rejection of the contract by the follower partner. So, these offers depend on the knowledge that the leader has about the follower and the 3rd parties price variations (local Grid purchase prices from the follower, local Grid selling price 20 to external markets, and the renewable energy price to the external markets). For the CNS and nCNS, the total and individual expected profits are obtained for each energy price offer to be considered. The proposed SBDN resulted in the different MINLP models for the different proposed cases (Standalone - SS, Cooperative Negotiation - CNS and Non-Cooperative Negotiation - nCNS). They have been implemented using the General Algebraic Modeling System GAMS 24.2.3, and solved over the planning time horizon (6 time periods; 1000 working hours each) on a Windows 7 computer with an Intel® Core™ i7-2600 CPU 3.40GHz processor with 16.0 GB of RAM, using the Global mixed-integer quadratic optimizer “GloMIQO” (Misener & Floudas, 2013). The models statistics show that the nCNS mathematical formulation is less complex as it allows to identify better solutions in less computational efforts; 32% less than the SS and 63% less than the CNS scenarios, respectively (Table 5). Table 5Models statistics Single equations Single variables Discret variables CPU (sec) Standalone Scenario (SS) 2,166 2,942 306 15.6 Cooperative Negotiation Scenario (CNS) 2,165 2,926 306 31.6 Non-Cooperative Negotiation Scenario (nCNS) 2,166 2,942 306 11.8 The tactical decisions achieved are the expected RM acquisition, internal product flows and prices (contract terms), and expected production, inventory, and distribution levels for each partner. In the next subsections, the resulting SC individual and global profits for each coordination contract are discussed, and the effects of the uncertain reaction of the follower on the tactical decisions of the decentralized SC are analyzed, as well as the effects of the follower response on the leader SC tactical and economic decisions. 5.1 Negotiation Scenarios On the one hand, considering a deterministic situation based on the current market energy prices (Table 4), the total and individual SC Profits (nominal) resulting from the different leader coordination contract offers are obtained (Figures 10 & 11). The purple line represents the SC nominal profits ensuing from the leader SC (Figure 10) and the Follower SC (Figure 11) standalone scenarios (SS); so the negotiation only makes sense when the profits exceed these lines. From the leader side (Figure 10), it seems that the nCNS leads to better solutions than the CNS at all negotiation prices offers, although the CNS leads to higher overall profits (Figure 12). 21 Figure 10Leader SC nominal profit vs. negotiation price From the follower side, it is noticed that for negotiation prices above 0.17 €/kWh the CNS would lead to better profits (Figure 12), if the risks associated with its SC uncertain external conditions are not considered. Figure 11Follower SC Profit vs. negotiation price Figure 12Overall SC Profit 5.2 Monte-Carlo sampling The use of Monte-Carlo sampling as part of the optimization procedure is a practical way to reduce the complexity of the model formulation, by considering a set of realizations of the uncertain variables as representative of the global system behaviour. It helps in obtaining the probability of acceptance of the different offers, the probability distribution of expected profits and the cumulative probability curves. In this case, in order to obtain the probability of acceptance of each of the different contract offers (flows and prices), the proposed MINLP 22 tactical model of the follower is solved for each contract offer at the different generated scenarios, in order to obtain each one emulating a realization of the external energy prices of the 3rd parties around the follower SC as follows (Figure 13). Each scenario includes specific random values of: (a) the local Grid energy price to the external markets (Figure 13a), (b) the renewable energy price from the follower to local Grid at price zone 1 (Figure 13b), (c) the renewable energy price from the follower to local Grid at price zone 2 (Figure 13c), (d) the renewable energy price from the follower to local Grid at price zone 3 (Figure 13d), (e) the renewable energy price from the follower to the external markets (Figure 13e). a) b) c) d) 23 e) Figure 13Energy prices generation (Monte-Carlo) For simplicity, the generation of price scenarios is based on a normal distribution. The standard deviation of prices generated (σ) is assumed to be 0.03 € / kWh for all price ranges, while the average (μ) for each price generation is equal to its current nominal price, as shown in Table 4. Indeed, a correlation between these prices is assumed, so that for the first price (a: local grid to external markets) a normal distribution is generated (Figure 13a), and then the remainder distributions are generated assuming a significant correlation with this first one. The variations in these price predictions are justified by the volatile changes in the energy prices, so their computation should be based on the perception of the market volatility by the leader decision maker. The values assumed in this work are based on the perception of the energy price volatility in the Spanish market by the authors; obviously this perception significantly affects the specific results obtained in the presented case study, although this does not compromise the usefulness of the presented methodology: from the different generated scenarios, the corresponding reactions from the follower can be anticipated. 5.3 Coordination Contract In the nCNS negotiation scenario, the leader would design the final coordination contract considering the uncertain reaction of the follower in order to estimate its SC expected benefits. Then the results will be analyzed from both leader and follower sides. 5.3.1 The leader offer The leader estimates its expected SC benefits at each negotiation price, based on the follower probability of acceptance values. To calculate the probability of acceptance at each negotiation price, the follower nCNS model is solved for the 500 generated scenarios, and the number of favorable scenarios is obtained (the expected benefits that exceed the Standalone SS expected benefits). Then the probability of acceptance (Eq. 19) is calculated for each negotiation price (Table 6). It is noticed that the probability of acceptance is zero if the offered contract prices are in the range (0.14-0.16 €/kWh), while it increases from offers above (0.17 24 €/kWh), till reaching the highest value (100 %) at contract price 0.22 €/kWh (see also Figure 11). Table 6Probability of acceptance 0.14 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 No of scenarios where the follower obtains improved Profit (contract vs. SS) 0 0 0 89 314 393 440 477 498 Probability of Acceptance 0 0 0 0.18 0.63 0.79 0.88 0.95 1.00 Based on these probabilities of acceptance, the leader assesses its SC expected benefits (Eq. 20) considering its SC benefits in case that the follower accepts or rejects each contract offer (Table 7 and Figure 14). Figure 14 shows the leader production-distribution SC expected benefits vs. the probability of acceptance. It can be noticed that 24.71 GWh of total energy is needed for the leader SC production in order to fulfill the final markets demands. From Table 7, it is demonstrated that is better for the leader to purchase this amount from the follower at all contract prices, except at 0.22 €/kWh, where is better for the leader to purchase a large part from the Local Grid (21.96 GWh) at lower price, between 0.20 and 0.22 €/kWh (see Table 4). Table 7Coordination contracts and Leader expected benefits Contract price (€/kWh) Internal energy (GWh) Energy from Grid (GWh) Profit if the follower accepts (M€) Profit if the follower rejects (M€) Probability of acceptance Expected profit (M€) 0.14 24.71 0 9.25 7.47 0 7.47 0.15 24.71 0 8.99 7.47 0 7.47 0.16 24.71 0 8.74 7.47 0 7.47 0.17 24.71 0 8.48 7.47 0.18 7.65 0.18 24.71 0 8.23 7.47 0.63 7.95 0.19 24.71 0 7.99 7.47 0.79 7.88 0.20 24.71 0 7.77 7.47 0.88 7.74 0.21 24.71 0 7.51 7.47 0.95 7.50 0.22 2.75 21.96 7.47 7.47 1.00 7.47 25 Figure 14Leader expected Profits vs. Probability of acceptance It is worth to emphasize the importance of the Grid energy price-quantity constraints. For example, the Local Grid is offering the leader 0.20 €/kWh just when the energy demand exceeds 4GWh each planning time period, but it might be worth for the Leader to maintain its contract with the follower, as it is more evident from Table 8, where the schedule of energy purchase levels from the follower (in case it accepts) along the planning time horizon is explicit. Then, purchasing 24.71 GWh from the follower at the price of 0.21€/kWh costs the leader 5.19 M€, but if the leader purchases these amounts from the Local Grid, this will imply a cost of 5.38 M€. Table 8Internal energy purchase levels at price 0.21 €/kWh t1 t2 t3 t4 t5 t6 P1 1.47 1.47 1.59 1.47 0.75 1.47 P2 2.56 1.53 2.56 1.53 0.95 1.31 P3 1.53 0.67 1.53 0.67 0.67 0.98 It is worth noticing that the coordination contract offered by the leader results from the anticipation of the follower’s response, which in turn depends on the quality of the knowledge he/she has about the other participants, 3rd parties included, and the way how she/he predicts the market prices. Within the context of the presented case-study, the leader’s expected profit (where the follower's uncertain reaction is projected) is considered as the key reference for selecting the coordination contract. The leader's decision-making may have different criteria that can lead to different decisions. Here, we will analyze three options according to the SBDN criteria, which depend on the risk-behaviour of the decision-maker. From Table 7 it results that, if the leader offers the lowest prices 0.14-0.16 €/kWh, she/he would face a 0 % probability of acceptance resulting from the high frequency of negative profit scenarios. This means that the leader should not choose these prices although the potential benefits are higher. However, an option with a very high probability of acceptance by the follower is not always the smartest decision for the leader, since the coordination might be even unprofitable as the price to be paid to the follower is very high, even higher than the one offered by the local electricity grid (so leader SC should return to its standalone case). For example, for the 32 cases (3,450 tons) and the total production is also the same (3,380 tons), as the leader decision is to fulfill the total polystyrene market demands. It is noticed that using the riskneutral nCNS coordination contract results in 7% improvements in the total inventory, in comparison with the SS case, while leading to 5 % increase in the total distribution levels, for the same reasons explained before. Table 12Leader tactical decisions-breakdown (risk-neutral) nCNS SS RM purchase (tons) 3,449.75 3,449.75 Energy from Grid (GWh) 0 24.71 Internal Energy (GWh) 24.71 0 Production (tons) 3,380.40 3,380.40 Distribution (k.tons.km) 1,332.07 1,271.50 Inventory (tons.h) 495.00 530.18 Figure 21 illustrates the economic decisions breakdown of the leader in case of using the riskneutral strategy. Using the nCNS risk-neutral strategy leads to 17% improvements in the total energy purchase cost (0.75 M€ savings); 1 % improvements in the RM purchase cost (25.72 k€ savings); and 2 % improvements in the total polystyrene production cost (42.24 k€), when compared with its Standalone SS case. Figure 21Leader economic decisions (risk-neutral) Table 13 summarizes the final economic decisions of the leader in case of using the risk-neutral strategy, in comparison with its SC standalone case (SS). Considering that the decision in both cases is to fulfill the final market demands, it results in 18.59 M€ total sales, with 10 % improvements in the leader SC benefits. Table 13Leader SC economic summary (risk-neutral) nCNS SS Cost (M€) 10.36 11.12 Sales (M€) 18.59 18.59 Profit (M€) 8.23 7.47 5.4.3 Leader risk-averse strategy 33 Table 14 summarizes the tactical decisions of the leader in case of deciding to avoid risk (coordination contract: 24.71 GWh at 0.19€/kWh), compared with its SC standalone case. It is to be noticed that using the risk-averse nCNS coordination contract results in an improvement of 13 % in the total inventory levels, while leading to 4.3 % increase in the total distribution levels, in comparison with the SS case. Table 14Leader tactical decisions-breakdown (risk-averse) nCNS SS RM purchase (tons) 3,449.75 3,449.75 Energy from Grid (GWh) 0 24.71 Internal Energy (GWh) 24.71 0 Production (tons) 3,380.40 3,380.40 Distribution (k.tons.km) 1,328.19 1,271.50 Inventory (tons.h) 468.90 530.18 Figure 22 illustrates the economic decisions of the leader in case of using the risk-averse strategy, leading to 11% improvements in the total energy purchase cost (0.51 M€ savings); 1 % in the RM purchase cost (26.79 k€ savings); and 2 % in the total production cost (40.71 k€), when compared with its SC standalone case. Figure 22Leader tactical decisions (risk-averse) Table 15 summarizes the final economic decisions of the leader in case of using the risk-averse strategy, compared with its SC standalone case (SS), resulting in 7 % improvements in the leader SC benefits. Table 15Leader SC economic summary (risk-averse) nCNS SS Cost (M€) 10.61 11.12 Sales (M€) 18.59 18.59 Profit (M€) 7.99 7.47 5.5 Follower expected tactical decisions 34 The expected tactical decisions of the follower are analyzed next based on the 500 generated scenarios at the nCNS, in comparison with its SC standalone case. Figure 23 shows the expected energy flows around the follower SC at its standalone case. Figure 23Expected energy flows (SS) The follower expected tactical decisions then will be analyzed for each risk-response the follower could make, comparing with its above-mentioned standalone case. 5.5.1 Follower risk-seeking response In case the follower accepts the leader risk-seeking strategy (coordination contract: 24.71GWh at 0.17€/kWh), the follower SC is expected that will generate 15 % more energy in order to be able to sell the 24.71 GWh to the leader SC (Figure 24), leading to 18% reductions in the expected energy sales to Local Grid, and 20 % reductions in the expected total sales to the external energy markets, in comparison with its expected standalone case. Here, one may say that the follower should sell more energy to the Grid in order to compensate, but in fact, its expected SC total cost is also increasing. Generating those 15 % extra energy leads to 14 % increase in its expected SC total cost, in comparison with its expected standalone case (difference of 2.21 M€), whereas the contract price is still low to compensate the sales of the follower. 35 Figure 24Expected energy flows (risk-seeking) Figure 25 shows the expected energy generation levels along the planning time horizon resulting from accepting the leader risk-seeking strategy (Figure 25a), compared with rejecting it (Figure 25b). It is noticed that the expected energy generation is distributed equally between the energy generation plants (g4, g5, and g6) with 15 GWh energy generation per time period using the risk-seeking strategy (nCNS); 15 % higher than the standalone case (Figure 25b), in order to sell the high amount of energy needed by the leader (24.71 GWh). The rest is to be reduced from the energy sales to the Grid and to the external energy markets. It is worth mentioning that each energy generation plant has a capacity of 6GWh, but in this case, the expected cost of operating up to their full capacity does not compensate the follower. This takes into consideration that generating the energy plants (g1, g2, and g3) is expensive for the follower, due to their lower efficiency (see Table 3). This strategy leads to an 18 % higher of the expected RM purchase amounts, in comparison with the expected standalone case. Figure 25Expected energy generation levels (risk-seeking) a) nCNS b) SS Figure 26 summarizes the follower expected economic decisions according to the leader risk-seeking strategy, in comparison with its expected standalone decisions. It is noticed that the coordination contract (24.71GWh at 0.17 €/kWh) leads to 14 % increase in 36 the expected energy generation cost, resulting in 16 % increase in the expected RM purchase cost, and consequently to 17% decrease in the expected energy sales to the Grid; and 17 % decrease in the expected energy sales to the external markets, compared with its expected standalone case. Figure 26Follower expected tactical decisions (risk-seeking) Table 16 summarizes the follower final expected economic decisions in case of accepting the leader risk-seeking strategy, in comparison with its expected standalone case (SS). Considering all the expected benefits resulted from the 500 risk scenarios (positive and negative cases), the proposed coordination contract results in 10 % reductions in the follower total expected profit. However, as we mentioned before, the follower would risk and accept based on the 22 % expected profits improvements resulting from the 18 % improved probabilities. Table 16Follower expected economic summary (risk-seeking) NCNS SS Cost (M€) 15.38 13.16 Sales (M€) 17.83 15.90 Profit (M€) 2.46 2.74 5.5.2 Follower risk-neutral response It is expected that the follower SC will generate 15 % more energy than the SS (Figure 29) in order to sell the 24.71 GWh to the leader. 63 % of the total energy generation is expected to be sold to the Local Grid, while the rest is expected to be sold to the leader SC (27 %) and to the external energy markets (10 %). This leads to 15 % increase in the expected SC cost (Figure 27 and Figure 28), in comparison with standalone case. 37 Figure 27Expected energy flows (risk-neutral) Figure 28 summarizes the follower's expected economic decisions according to the leader's risk-neutral strategy, compared with the standalone case. The coordination contract, results in a 14 % increase in the expected energy generation cost, ensuing in a 16 % increase in the expected RM purchase cost, and 16 % decrease in the expected energy sales to the Grid, as well an 18 % decrease in the expected energy sales to the external markets, compared with its expected standalone decisions. Figure 28Follower expected economic decisions (risk-neutral) Table 17 summarizes the final expected economic decisions of the follower in case of accepting the leader risk-neutral strategy, in comparison with its expected standalone case. Considering all risk scenarios (the improved 63% and the 37% negative cases), the proposed coordination contract gives similar total expected profits as the expected standalone case. Nevertheless, as we mentioned before, the follower would accept, based on the 12 % expected profit improvement resulting from the 63 % improved probability. Table 17Follower expected economic summary (risk-neutral) NCNS SS Cost (M€) 15.42 13.16 38 Sales (M€) 18.13 15.90 Profit (M€) 2.71 2.74 5.5.3 Follower risk-averse response In this case, the follower SC is expected to generate 15% more energy than the SS (Figure 29), 62 % of the total energy generation is expected to be sold to the Local Grid, while the rest is expected to be sold to the leader SC (28 %) and to the external energy markets (10 %). Figure 29Expected energy flows (risk-averse) Figure 30 summarizes the follower expected economic decisions according to the leader's risk-averse strategy, compared with the expected standalone decisions. The coordination contract results in 16 % increase in the expected RM purchase cost, and accordingly to 14 % increase in the expected total SC cost (Table 18). Figure 30Follower expected economic decisions (risk-averse) Table 18 summarizes the final expected economic decisions of the follower in case of accepting the leader's risk-averse strategy, in comparison with the expected standalone case. Considering all risk scenarios (the improved 79% and the 21 % negative cases), the coordination contract proposed results in an 8 % profit improvement (0.21 M€), compared 39 with the expected standalone benefits. Furthermore, the follower would accept based on the 19 % expected profit improvement, resulting from the 79 % improved probability. Table 18Follower expected economic summary (risk-averse) nCNS SS Cost (M€) 15.38 13.16 Sales (M€) 18.33 15.90 Profit (M€) 2.95 2.74 As a final result, unlike the current negotiation methods, and to be able to capture high competitive situations (external suppliers/markets), the proposed SBDN approach does not give a full dominance to the leader, indeed, the follower has some “embedded” leadership, resulting in reductions in the expected leader benefits. Furthermore, the uncertain nature of the third parties affects the follower's reaction to the leader strategies, and thus plays a important role in the decision-making of decentralized SC and in the negotiation outcome. 6. Conclusions Due to the volatility of the market, enterprises seek to change their way in managing their SCs by collaborating with other partner SCs in order to enhance their benefits. In this framework, and in order to avoid double marginalization of the markets, a contract is a must; and since any contract is between two organizations, the other participants in the decentralized SC systems must be considered as third parties. So in this work, a novel Scenario-Based Dynamic Negotiation (SBDN) approach has been proposed in this work aiming to help the SC managers to make efficient decisions for global decentralized multi-site, multi-product SCs subjected to uncertain competitive conditions in the presence of third partners. The proposed approach is based on establishing the best conditions for the coordination/collaboration contracts between partners with conflicting objectives through negotiations built on expected win-to-win principles. The interaction between the partners (client and provider, both represented as full SCs, and third parties) is captured through noncooperative dynamic SBDN negotiation with non-zero-sum non-symmetric roles. The client, “as leader”, designs a set of offers (coordination/collaboration contracts) taking into account the uncertain reaction of the provider (“follower”) resulting from the uncertain nature of the follower SC behavior and its third parties, which is modeled as a probability of acceptance. Here, the probability of acceptance is able to capture the variations between the profits scenarios resulted from a Monte-Carlo simulation method. As a result, different negotiation scenarios can be analyzed based on individual and global objectives: i) Cooperative Negotiation Scenario (CNS), and ii) Non-Cooperative Negotiation Scenario (nCNS), and iii) Standalone Scenario (SS). Furthermore, a final decision-making methodology is proposed to help both the leader and the follower to evaluate the final coordination contract, based on different risk strategies (risk-seeking, risk-neutral, and riskaverse). 40 The proposed approach has been implemented through the formulation and combination of different tactical MINLP flexible models, which have been applied to a case study of a decentralized large-scale SC composed by different providers’ SCs around an industrial production/distribution SC (“leader”). The results show how the uncertain nature of the third parties is expected to affect the follower reaction to the leader strategies, and thus affects the tactical decisions of the leader as well as the expected tactical reactions of the follower. Using the proposed SBDN approach, it is possible to manage non-Cooperative Negotiation Scenarios (nCNS) in order to identify and manage high individual profit expectations likely to be accepted by all partners/players. The third parties participate in the decision-making through their price policies, influencing the management of the SC financial flows and helping to stay competitive. Furthermore, the third parties (external providers/clients) are competing with other negotiating partners which might be part of a different SC functioning as standalone case. This flexibility to accept/reject the coordination, which counts as added value of the proposed approach, is based on the estimation of the price policies of the competing parties, which are integrated into the model formulation. By doing so, equilibrium situations result between the negotiating partners and the 3rd parties. The characteristics of this equilibrium will be further investigated in the future works. The proposed approach identifies situations where the coordination may lead to higher expected benefits for all partners, proposing a flexible procedure able to cope with the different risk behaviours of the decision makers, which can be applied to real cases when different enterprises seek to collaborate under uncertain conditions. Using the proposed SBDN systematic, the decision-makers will be able to evaluate the effects of their decisions and the other partners’ decisions on their choice. The use of Monte-Carlo sampling method adds value to the proposed approach, as both leader and follower are able to assess their decisions based on methodically generated data and, unlike other PSE literature approaches, taking into consideration the variability between generated profits scenarios. Finally, the proposed decision support procedures enable the decentralized SCs organizations to modify their relationships during the optimization procedure, which can be used for further second-stage agreements. Furthermore, the proposed generic models are flexible enough to be applied in practice to real cases, including simple/global SCs centralized/decentralized, as illustrated in the presented case study. Acknowledgement Financial support received from the “Agència de Gestió d'Ajuts Universitaris i de Recerca AGAUR”, 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 (2014-SGR-1092-CEPEiMA), is fully appreciated. 41 Acronyms CNS Cooperative-Negotiation Scenario CPU Central Processing Unit EWO Enterprise-Wide Optimization GAMS The General Algebraic Modeling System GHz Gigahertz GloMIQO Global Mixed-Integer Quadratic Optimizer GT Game Theory LP Linear Programming MINLP Mixed Integer Non-Linear Programming MILP Mixed Integer Linear Programming MW Megawatt nCNS Non-Cooperative-Negotiation Scenario NE Nash Equilibrium NLP Non-Linear Programming PMAGA Pinch Multi-Agent Genetic Algorithm PSE Process System Engineering RM Raw Material SBDN Scenario-Based Dynamic Negotiations SC Supply Chain SCM Supply Chain Management SS Standalone Scenario µ Mean σ Standard deviation Nomenclature Indexes D 3 rd party M Final customers N number of Piecewise price and quantity zones of 3 rd parties PL Production plant R resource (raw materials, intermediate/final products, energy,…) SC supply chain T time period W warehouse Sets F follower SC L leader SC m final consumers n piecewise pricing zone of 3 rd parties