Closing the loop
A heterogeneous agent model of closed loop supply chains in the transition towards a circular economy
Sophie Abrahamse
Abstract
The rising demand and the limited availability increase the urge to move towards a more resource efficient economy. This transition forms a complex adaptive system and can be modeled using a heterogeneous agent modelling approach. In this paper I extend this model on the supply-side by incorporating the effect of reverse logistics and I analyze to what extent this adjustment influences the conditions of a successful transition towards a circular economy. The model results in a fold bifurcation where the long-term steady state depends on behavioral and market factors. An increase of the rate of return of used products stirs up the system towards a long-term steady state where the circular product dominates the market.
Bachelor’s thesis BSc Econometrics
Faculty of Economics and Business University of Amsterdam
Date: June 28, 2017
Supervisor: Saeed Moghayer
This document is written by Sophie Abrahamse who declares to take full responsibility for the contents of this document. I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
Contents
1 Introduction 3
2 Theoretical framework 5
2.1 Modelling a circular economy using a HAM . . . 6
2.2 Closed-loop supply chains . . . 9
2.3 Closed-loop supply chains in a circular economy . . . 13
3 The model 15 4 Results 19 4.1 Investment in collection . . . 20
4.2 Wholesale price . . . 21
4.3 Collection fee . . . 21
4.4 Payment for the consumer . . . 22
5 Analysis 23 5.1 Interpretations . . . 23 5.2 Reflections . . . 25 5.2.1 Limitations . . . 26 5.2.2 Suggestions . . . 27 6 Case study 28 6.1 Tire industry . . . 28 6.2 Method . . . 29 6.3 Results . . . 29 7 Conclusion 30 Bibliography 33
1
Introduction
Lives are finite, as are resources. The world’s population is continuously growing and the rising demand that follows highlights the limited availability of these resources. Put straight, resources are being overused, causing environmental harm, higher price levels, and more volatility in many markets (MacArthur, 2013, p.2). The only way to respond to this challenge is by moving towards a more resource efficient economy. An economy in which today’s goods are tomorrow’s resources; an economy with more re-using, repairing, refurbishing and recycling; a so called circular economy. However, despite its importance, the challenge of moving towards a circular economy has been relatively slow to rise up the agenda of public policy (Moghayer, Boonman, & Husky, 2015, p.1). According to The Ellen MacArthur Foundation’s report on the Economics of a Circular Economy (2013, p.2), however, it is rarely good policies, but the private sector’s ability to adopt and develop new business models that ultimately make such transitions successful.
According to Moghayer et al. (2015), businesses are in the ’driver’s seat’ in the transition to a resource-efficient economy, but they are facing barriers in their way. These can be categorized into institutional, organizational, technological, behavioral and market barriers, but are all interacting in a fully connected web of constraints (Bastein, Koers, Dittrich, Becker, & Lopez, 2014, p.6). However, results from micro-level initiatives point out that under certain circumstances it is possible to make a successful switch to a circular economy (European Commission for Research Innovation, 2015). Since all barriers form an interacting network it is challenging to consider all of them at once.
Focusing only on the interaction of behavioral and market drivers and barriers, Moghayer et al. (2015) analyze the conditions for a successful transition towards a circular economy. They consider this transition as a complex adaptive system and develop a heterogeneous agent model, abbreviated as HAM, used henceforth. As the name suggests, HAMs are based on heterogeneous agents with boundedly rational beliefs that are constantly up-dated as more data become available. In the case of a circular economy agents can choose from two types of goods or services, a circular and a non-circular type. Developing a HAM in this case seems appropriate since HAMs are highly nonlinear as is the world (Brock & Hommes, 1997; cited in Moghayer, et al., 2015, p.2).
Although the model designed by Moghayer et al. (2015) enables us to get a good grasp of the complexity of identifying the conditions for a successful transition towards a circular economy, it is only the beginning. For instance, in their research they focus on the demand-side, whereas on the supply side they apply a simple mechanism. Supply is assumed to be exogenous which in practice is obviously not the case. In fact, there exist supply mechanisms that apply particularly to circular economies. Incorporating this in the existing model could therefore bring along valuable insights.
Savaskan, Bhattacharya and Van Wassenhove (2004) refer to these supply chain mech-anisms in circular economies as closed-loop supply chains (CLSC’s), which are the dis-tribution systems that describe the reverse channel structure for the collection of used products from consumers. Savaskan et al. (2004, p. 240) distinguish three different network structures with the manufacturer having a different option for collecting new products in each of them: (1) manufacturer collects directly from consumers (model M), (2) manufacturer provides the retailer suitable incentives to collect from consumers (model R), (3) collection is outsourced to a third party (model 3P).
Savaskan et al. (2004) show that designing closed-loop supply chains can be beneficial to profits and market demands as it reduces costs as a result of (parts of) products being re-used. In particular it follows from their research, that the second mentioned closed-loop structure is the most appropriate. This means it is most effective if the retailer, which is the agent who is closest to the consumers, undertakes the collection of used products from consumers. Effectiveness in this case is measured in terms of positive effects on the retail- and wholesale price, total channel profits and incentives of businesses to invest in used-product collection (Savaskan, et al., 2004, p.243).
From Savaskan’s (2004) research it is clear that designing closed-loop supply chains in businesses has a positive impact on their business results both in terms of money and brand image. However, it is not clear how a closed-loop supply chain ultimately effects the conditions for a successful transition in terms of behavioral and market barriers, as Moghayer et al. (2015) only apply a highly simplified mechanism on the supply side.
The purpose of this paper is to investigate to what extent the reverse channel structure where the collection of used products is done by the retailer, influences the conditions for a successful transition to a circular economy. In order to address this problem the model
of Moghayer et al. (2015) is extended on the supply side by implementing the closed-loop supply chain where the retailer induces collection. To do so several research steps are undertaken. First of all the costs of designing this type of closed-loop is estimated by a model, which will then be implemented in the original model designed by Moghayer et al. To illustrate the effect of using this closed-loop supply chain, the model is applied to a specific case.
In order to answer the central question, the rest of the paper is organized as follows. In the next section, the existing literature on a transition to circular economy and closed-loop supply chains is being discussed. Section 3 is devoted to explaining the model used in this paper. Next, section 4 presents the analytical results of the influence of a reverse channel structure on the conditions for a successful transition towards a circular economy. Section 5 ensues with the analyses of the results. In section 6, a case study is carried out to measure the change in input and output flows as a consequence of an increase of recycled material in products. Finally, forms the conclusion and an outline of the limitations of this work together with suggestions for future research.
2
Theoretical framework
This section discusses some of the main findings on modelling the transition towards a circular economy on the one hand, and current literature on closed-loop supply chains on the other hand. As it is the main purpose of this paper to incorporate a closed-loop supply chain into the transition model, it is necessary to provide a general overview of recent research on both topics.
The first subsection of this section provides some background information on mod-elling a circular economy. As stated earlier in this paper, Moghayer et al. (2015) model the transition towards a circular economy as a complex adaptive system using a hetero-geneous agent modelling approach. It is beyond the scope of this paper to discuss the underlying derivation in detail, but for the sequel it is important to understand at least the basics. Next, the second subsection discusses Savaskan’s (2004) research on closed-loop supply chains, specifically the case where the retailer induces collection. In the last subsection the aforementioned subjects are brought together as this is the main focus of
the research conducted for this paper.
2.1
Modelling a circular economy using a HAM
In a transition to a circular economy, businesses encounter both drivers and barriers. As stated earlier, Bastein et al. (2014, p.6) identify five different categories: institutional, organizational, technological, behavioral and market. In modelling a circular economy, Moghayer et al. (2015) focus on the latter two. Market barriers are defined as external effects on business operations, containing amongst others market pull, market structure and consumer behavior, whereas behavioral barriers focus on attitudes and social val-ues of individuals. They model these barriers in a complex adaptive system using a heterogeneous modelling approach.
According to research conducted by Brock and Hommes (1997), a framework of het-erogeneous agents is appropriate to model actions of agents, since it captures a wide range of behavioral dynamics as it is based on a boundedly rational world view. It thus takes into account that agents constantly learn as more data becomes available. This is known as evolutionary switching behavior. Due to its unlinearity, different structures of outcomes of the model are possible. In order to classify and evaluate these outcomes mathematically, bifurcation analysis is used (Kuznetsov, 2013; cited in Moghayer, et al., 2015, p.2).
Since quantitative research on a transition to a circular model is rather complex and not the way this topic is generally investigated, Moghayer et al. (2015) make some strong assumptions on both the demand-side and the supply-side in order to keep things simplified.
On the supply-side, they consider a monopolistic market with two types of goods: a circular good, denoted by c, and a non-circular good, denoted by b. Here the circular good is defined as ’a product or service that includes or eases the possibility of recycling’ (Moghayer, et al., 2015, p.3), whereas the non-circular good is not being recycled. For the non-circular good, supply is assumed to be exogenous and its price fixed. For the circular product the price is derived using optimization of the cost function. Derivations are done under the condition of complete information.
On the demand-side, Moghayer et al. (2015) distinguish two types of consumers. On the one side there are the ’early adopters’, who start using the circular good as soon as it becomes available. On the other side are the ’followers’ who follow the early adopters as the name suggests. The choice of consumers is assumed to depend on (1) economic incentives, (2) behavioral factors, (3) network externalities and (4) the intensity of choice. Following Brock and hommes’ research (1997; cited in Moghayer, et al., 2015, p.4), the share of the circular product or the demand is modelled as a discrete choice model in order to capture the evolutionary switching behavior.
According to the above mentioned assumptions, Moghayer et al. (2015) model the fitness measures for strategies c and b respectively as follows:
Utc(pct, nct) = αbh+ αnwξnct+ αppct (1)
Utb(pbt, nbt) = αnwξ(1 − nct) + αppbt (2)
Here pjt is the price of good j with j ∈ (b, c) at time t, αbh is the individual behavioral
parameter, αnw determines the strength of network externalities, ξ(·) the network
exter-nality function (’word of mouth-effect’), αpthe parameter that determines the price effect
and njt the share of product j with j ∈ (b, c) and nct + nbt = 1.
On the demand-side the following discrete choice model is applied:
nct = δct−1+ (1 − δ) exp(βU c t−1(pct−1nct−1)) P j∈(b,c)exp(βU j t−1(p j t−1n j t−1)) (3)
Here njt is the market share of product j ∈ (b, c) at time t, δ is the inertia in the market and β is a factor that measures the intensity of preference., which measures to what extent agents make social choices or use the best predictors. For a detailed explanation I refer to Moghayer et al. (2015).
On the supply-side the following cost function is used:
C(dct) = (dct)2/2sc (4)
Here the demand dc
t is derived using nct, and sc is a technological parameter that captures
the rate of diffusion of new technologies. By minimizing the cost-function with respect to nc
t, the price function is derived:
Solving equation (3) for (5) numerically gives the phase map F that determines the state dynamics:
nct = F (nct−1; µ) (6)
With µ = (αbh, αnw, αp, sc, β, δ)
The outcome of the heterogeneous agent model is analyzed using bifurcation anal-ysis. For simplification only two parameters are varied: the behavioral parameter αbh,
and the intensity of preference β. All other parameters are held fixed. The result is a bifurcation diagram displayed in figure 1 with three different regions each with its own set of outcomes, separated by so called saddle-node bifurcation curves. Depending on the values of the parameters αbh and β the system ends up in one of these regions in the
long term. Region I corresponds to the state of a unique steady state where introduction of the circular product has failed and the non-circular product dominates the market. Next, in region II the outcome is dependent on the initial state, measured in terms of the number of early adopters in the market. If this number takes on a sufficiently high value, the system reaches a steady state in which the circular product succeeds, otherwise a market failure results (Moghayer, et al., 2015). In region III again a unique steady state is reached, but in this case it entails success for the circular product. The phase diagrams corresponding to each region are shown in figure 2.
In order to measure the environmental indicators in the circular market steady state, Moghayer et al. (2015) use an Environmentally Extended Input Output table, abbrevi-ated as EE-IO. This table reflects both direct and indirect production and consumption flows, including environmental effects, as the name suggests.
As stated earlier, the model designed by Moghayer et al. (2015) is a highly simplified representation of the economic reality, but the results enables us to get a good grasp of the dynamics that play a role in the transition towards a circular economy. However, they give rise to explore these dynamics in further detail and expand the model to make it more reliable. One way of doing this is to enrich the supply side of the model, which can be done by implementing a reverse logistics structure in the existing model, where the rate of return of used products is taken into account. More information regarding reverse logistics is provided in the next subsection.
2.2
Closed-loop supply chains
In a closed-loop supply chain, not only the forward supply chain is considered, but also a reverse supply chain is integrated (Govindan, Soleimani, & Kannan, 2015, p.603). The forward supply chain, commonly just known as the supply chain, is the classical process that describes the journey of raw material being transformed to goods by producers and eventually sold to consumers. Reverse supply chains, on the other hand, are the return flows of used products back to producers with the purpose of re-use, repair, refurbishment or recycling (Govindan, et al., 2015, p.603). By integrating a reverse supply chain, both overall costs and environmental impacts are reduced (Krikke, Bloemhof-Ruwaard, & Van Wassenhove, 2003). However, several different designs of reverse supply chains exist with each one having a different effect on the costs and environmental performance dependent on the industry to which it is applied.
Savaskan et al. (2004) investigate the performance of different reverse logistics and their implications on decisions regarding the forward supply chain and the used-product return rate. They distinguish three different decentralized reverse channel formats: (1) manufacturer collects directly from consumers (model M), (2) manufacturer provides the retailer suitable incentives to collect from consumers (model R), (3) collection is out-sourced to a third party (model 3P). A centrally coordinated system (model C) serves as
Figure 2: Phase portraits (Moghayer, et al., 2015, figure 3, p. 8)
a benchmark to contrast the results with and detect inefficiencies resulting from decen-tralization of decision-making.
In contrast to several other researchers, Savaskan et al. (2004, p.240) present their results on a quantitative basis and do so by using a game-theoretic approach to model the independent decision-making process of each supply chain member. The following provides some additional information on the different network structures investigated, an overview of the assumptions that have been made and a description of the research method including more detailed results.
The different network structures being investigated by Savaskan et al. are shown in figure 3. Model C is the benchmark and corresponds to the situation of a single decision-maker. Model M corresponds to the situation where the manufacturer undertakes the used product collection effort. In Model R, the retailer induces collections and receives a fixed amount of the manufacturer per unit recollected. In the 3P model, a third party induces collection through rewards payed out by manufacturers, forming a direct cost in the supply chain for the latter party.
In an attempt to measure the performance of different reverse logistics formats, Savaskan et al. (2004) make several assumptions. The performance is then measured in terms of 1) the return rate, 2) the price and thus the 3) demand, and 4) the profit of the retailer and the manufacturer. After evaluation model R appears to be the most ef-fective reverse logistics format as it scores best on all four aforementioned measurements. This is due to the retailer’s proximity to the market. In the sequel the assumptions and derivations for the case of model R will be described in more detail. For a more detailed explanation of the derivations of the other models, I refer to Savaskan’s research.
Again assume that b refers to the non-circular product, corresponding to a new man-ufactured product, and c refers to the circular product being a remanman-ufactured used product. For simplicity a monopolistic market with a two-echelon supply chain, existing of a manufacturer and a retailer, is considered. All players in the supply chain have access to the same information and decisions are considered for a single period. Decisions are made under the assumption that the manufacturer acts as a Stackelberg leader over the retailer. This means that the manufacturer knows the best reactions of the retailer and uses this in the decision making process. More specifically, in the case of model R, the manufacturer determines the wholesale price w and the retailer determines the rate of return τ as well as the price p of the product. The Stackelberg structure has been widely used (Tayur et al. 1988; cited in Savaskan, et al. 2004, p. 243) in analogous
Figure 3: Supply chain models with remanufacturing (Savaskan, et al., 2004, figure 1, p. 243)
contexts. Next, it is assumed that remanufacturing used products is less costly than manufacturing a new product: cc < cb and ∆ = cb − cc. Therefore, the manufacturer
strictly prefers a higher product return rate to a lower product return rate due to cost reduction through remanufacturing. The rate of return of used products from consumers, τ , is defined as a function of I, the investment in collection activities, and CL, a scaling
parameter: τ =qCI
L ⇔ I = CLτ
2 and 0 ≤ τ ≤ 1. Here, parameter C
L is assumed to be
sufficiently large in order for remanufacturing to be sufficiently costly. For returning a used product, the consumers receives a fixed payment A per unit from the retailer. For A it must hold that A < ∆, otherwise remanufacturing would not be economically viable. In turn, the retailer receives a transfer price b from the manufacturer, for each product it returns to the manufacturer. For the demand D(p) of the product, a linear demand function is used: D(p) = φ − γp, with φ > γcm and D(p) ≥ 0. This is consistent with the
literature (Bulow, Weng, as cited in Savaskan et al., 2004). To find the optimal values for p, τ and w, the profit functions πR and πM for the the retailer and the manufacturer
respectively are derived. For the retailer the following holds:
πR= (φ − γp)[p − w] + bτ (φ − γp) − CLτ2− Aτ (φ − γp) (7)
Solving the first order conditions with respect to p and τ gives the following best response functions for the retailer:
p∗ = φ + γ[w − (b − A)τ ∗] 2γ (8) τ∗ = b − A 2CL (φ − γp∗) (9)
Given the optimal values p∗ and τ∗, the manufacturer optimizes its profit with respect to the wholesale price w:
πM = (φ − γp)[w − cm− ∆τ∗] − bτ∗(φ − γp) (10)
Optimization w by solving the first order conditions with respect to w then yields:
w∗ = φ + γcm 2γ −
(∆ − b)(b − A)(φ − γcm)
2[4CL− γ(∆ − A)(b − A)]
(11)
Substitution of the optimal value of w in the expressions for p∗ and τ∗ then results in a system of two linear equations with two unknowns which can be solved using linear
algebra: τ ∗ = (φ − γcc)(∆ − A) 8CL− 2γ(∆ − A)2 (12) p∗ = [3CL− γ(∆ − A) 2]φ + γC Lcc γ[4CL− γ(∆ − A)2] (13)
Similar derivations are done for the other models being investigated by Savaskan et al., all using the same game-theoretic approach. A comparison of the models with regards to 1) the return rate, 2) the price and thus 3) the demand, and 4) the profit of the retailers and the manufacturer, yields the conclusion of model R to be most effective. The retailer thus appears to be the most effective undertaker of collection of used products. This paper is therefore dedicated to incorporating Model R into the HAM. The next subsection describes how this is to be done.
2.3
Closed-loop supply chains in a circular economy
It is the purpose of this paper to incorporate a closed-loop supply chain in the existing HAM. It follows from the research conducted by Savaskan et al. (2004) that model R, where the retailer induces collection, is the most effective. This paper is therefore dedicated to incorporating model R in the circular economy model. However, doing this is not self-evident. Complications arise because the model presented by Savaskan et al. (2004) is static, whereas the HAM is a discrete dynamical system that is constantly updated over time. Hence it is necessary that the dynamical feature of the HAM be linked to the static cost function in some way. There are several ways of doing this. This section describes and discusses different approaches.
The most straightforward way to incorporate a closed loop supply chain (CLSC) would be to multiply the market demand of the product by the market share nt. The optimal
value for the price pt as a (now dynamical) function of ntthen could be derived using the
game-theoretic approach of Savaskan et al. (2004) as described in the previous section. The price pt as a function of nt could then be substituted in equation (3) of section
2.1 and this would ultimately ’close the loop’ between the HAM and the CLSC-model. However, the derivation of p results in a non-linear relation between p and nt, causing
prices. This would change the dynamics of the overall system radically to such extent that it goes beyond this paper to modify the model for it to still be applicable. Therefore different other approaches are to be investigated. These include a modification, and in this case a simplification, of Savaskan’s model by replacing either the original function of τ or the demand function as a function of nt. This gives the following three alternative
approaches:
Alternative 1: Replace the market demand function of the circular product D(p): D(p) = (φ − γp) ⇒ Dt(nt) = c · nt
Alternative 2: Replace the function of the rate of return τ : τ = d · nt, d ∈ [0, 1]
Alternative 3: Replace both the market demand function and the rate of return function:
τ = d · nt, d ∈ [0, 1]
D(p) = (φ − γp) ⇒ Dt(nt) = c · nt
The above mentioned alternatives each individually have their specific consequences for the model regarding its assumptions and applicability, which are now discussed in more detail. Stated earlier, incorporating a closed-loop supply chain into the original HAM without changing the underlying dynamics of the model, requires a simplification. These simplifications come at the expense of the closed-loop supply chain model, as it unables to calculate all optimal values using the game-theoretic approach of Savaskan et al. (2004). For alternative 1, the rate of return τ is calculated using the closed-loop supply chain model, whereas w is taken exogenous and p is calculated by optimizing the total profit function in the HAM. The latter two is because using Savaskan’s approach yield no relevant solutions. Next, alternative 2 assumes that the rate of return τ depends only on the market share of the circular product. A higher market share of the circular products indicates a higher environmentally awareness among consumers and I assume that this translates into a higher incentive to return used products. However, by calculating the optimal value for p and substituting this into the linear demand function results in a demand of zero for all values of p. This is not a realistic neither useful result. Lastly, alternative 3 takes away any possibility to use game theory in calculating optimal values
as both the rate of return τ and the demand are taken exogenous. The only part that is left and used of the initial closed-loop supply chain model is the different cost items. Without calculating any optimal values from the closed-loop supply chain model, the cost function is directly incorporated in the HAM.
Among all three alternatives, alternative 1 seems to be the most appropriate since it is most realistic as it is the only alternative where execution of the game-theoretic approach of Savaskan et al. (2004) is partly possible. Alternative 2 yields no practical results whatsoever, and alternative 3 only uses the cost function structure of the closed-loop supply chain model. Moreover, alternative 2 and 3 both take the rate of return τ as a variable that only depends on the market share ntwhich is plausible but not as interesting
as alternative 1. That is, alternative 1 captures the effects of varying the collection fee b, the investment in collection, and the the price A that the customer receives from the retailer for returning a product. Taking the aforementioned reasoning into consideration, I use alternative 1 in the model that I use in this paper. Next section describes the derivation of this alternative in more detail and presents the model.
3
The model
This section describes the model and its assumptions that is used in this paper, which is drawn upon the research papers discussed in previous section.
The model used in this paper is based primarily on the results of investigations of Moghayer et al. (2015) and Savaskan et al. (2004). Specifically, the model designed by Moghayer et al. (2015) forms the starting point of the model, which is extended with results that follow from the research conducted by Savaskan et al. (2004). Again, a monopolistic market with a two-echelon supply chain consisting of a single manufacturer and a single retailer is considered. The manufacturer produces two types of products: a circular product denoted by c and a non-circular product denoted by b. Products are bought either by ’early adapters’ or ’followers’. Their product choice is affected by 1) economic incentives, (2) behavioral factors, (3) network externalities and (4) the intensity of choice. Consumers are boundedly rational and base their choice for a articular strategy on an evolutionary fitness measure given by past results (Hommes, 2005). Moghayer et
al. (2015) define the following fitness measures for strategies c and b respectively:
Utc(pct, nct) = αbh+ αnwξnct+ αppct (14)
Utb(pbt, nbt) = αnwξ(1 − nct) + αppbt (15)
where pjt is the price of good j with j ∈ (b, c) at time t, αbh is the individual behavioral
parameter, αnw determines the strength of network externalities, ξ(·) the network
ex-ternality function (’word of mouth-effect’), αp the parameters that determines the price
effect and njt the share of product j at time t with j ∈ (b, c) and nct + nbt = 1. On the demand-side the same discrete choice model is applied:
nct = δt−1c + (1 − δ) exp(βU c t−1(pct−1nct−1)) P j∈(b,c)exp( j t−1(p j t−1n j t−1)) (16)
where njt with j ∈ (b, c) is the market share of product j at time t, δ ∈ [0, 1] measures the inertia in the market and β measures the intensity of preference.
On the supply-side a distinction between the non-circular and the circular good is made. For the non-circular good b, its price and supply are assumed to be fixed. For the supply of the circular good, however, the return of used products is taken into account by incorporating a CLSC into the model. The rather simple cost function used by Moghayer et al. (2015) is now replaced by the more realistic cost function derived by Savaskan et al. (2004). Since model R appears to be the most effective reverse logistics format, the model is extended with a cost function that applies to model R, where the retailer induces collection. The complications that arise by merging a static and a dynamical system require simplifications that lead to three different alternatives, as described in previous section. As alternative 1 seems the most appropriate and useful, here the cost function and the price for alternative 1 are derived. In the sequel these derivations are described and the assumptions and applicability of the alternative is discussed in more detail.
Alternative 1 entails changing the initial linear market demand function for a function that enables one to link the closed-loop supply chain model to the HAM. Specifically, the market demand function can be replaced by a function such that is does no longer depend on the price p, but on the market share nt: D(p) = (φ − γp) ⇒ Dt(nt) = c · nt where
product, and nt is the market share of the circular product. The retailer’s profit is now
given by the following formula:
πtR(τt) = nt· c[p − w] + b · τt· nt· c − CLτt2− A · τt· nt· c (17)
here ntis the market share of the circular product, c is the total market demand, p is the
price of the circular product, w is the wholesale price, τt is the rate of return at time t,
CL> 0 is a scaling parameter that scales the activities regarding investment in collection,
and A is the payment that the customer receives for returning a used product.
For the retailer, using the same approach as Savaskan et al., the best-response func-tions of τ and p should now be derived using optimization. However, solving the first order condition for p yields no relevant solution. Only the optimal value for τ can be derived. Optimizing πR
t (τt) with respect to τ yields the following best-response function
for τ :
τ = c · nt· (b − A) 2CL
(18)
For the manufacturer, using the same approach as Savaskan et al., the best-response function of w should now be derived using optimization. However, solving the first order condition for w yields no relevant solution. Therefore, the wholesale price w should be taken exogenous in this model. The expression for τ can be used to define a cost function that only depends on the market share nt of the circular products. The corresponding
profit function subsequently can be optimized to derive an optimal value for p as a function of nt which can be implemented in the HAM. The cost function is defined as follows:
C(nt) = CL· τ2+ A · τ · c · nt+ w · c · nt τ = c · nt· (b − A) 2CL (19)
Optimizing the profit function πtR(nt) = p · c · nt− C(nt) with respect to nt then yields
the following optimal value for pt:
pt =
c · nt· (b2− A2)
2CL
+ w (20)
The link between the closed-loop supply chain model and the HAM can now be made solving equation (15) for (19). This ultimately gives the phase map F that determines the state dynamics:
with µ = (αbh, αnw, αp, c, A, b, CL, w, β, δ). Here abh is the individual behavioral
param-eter, αnw determines the strength of network externalities, ξ(·) the network externality
function (’word of mouth-effect’), p the parameter that determines the price effect, c the market demand of the circular product, A the payment the consumer receives from the retailer, b the collection fee that the retailer receives from the manufacturer, CLa scaling
parameter for investment in collection activities and w the wholesale price.
In order for the results to be useful, the following assumptions should be considered regarding µ.
0 ≤ τ ≤ 1 The rate of return should be positive but cannot exceed one:
1
2 c · (b − A) ≤ CL
A ≤ b ≤ w The price A ≥ 0 that the retailer pays to the consumers for returning a product, should be less then the collection fee b the retailer
receives from the manufacturer for inducing collection, otherwise the retailer will not have any incentive to carry out such activities. The collection fee b in turn, cannot exceed the wholesale prices, as otherwise the manufacturer would not consider remanufacturing products at all.
pt(nt)0 < 0 From an economic point of view it is to expect that there
is a negative relation between the price pt of the circular profit
and its market share nt such that pt(nt)0 < 0. An increase of the
market share is expected to open doors for a less expensive way of remanufacturing used products, and would therefore cause the price of the circular product to drop. However, the only way this
condition holds is that A > b, which is in conflict with the second
condition. An explanation for this is that this is the case of a monopoly, where an increase in demand will be answered with a higher
c fixed I assume that the level of the absolute total demand of both the circular and the non-circular product does not affect the overall dynamics of the system. For practical purposes I therefore fix parameter c
4
Results
In this section some outcomes of the model that was derived and explained in the previous section are presented. For different values of the parameters, the outcomes are shown by bifurcation diagrams and their corresponding phase portraits.
In order to be able to make a comparison between the initial model as developed by Savaskan et al. (2015) and the model as described in previous section, I fix the same parameters αnw, αp and δ. In line with the assumptions made in the previous section, I
additionally fix parameter c. First I fix all parameters, while I make sure that they satisfy the assumptions made in the previous section, and generate the results. Next, in order to get a grasp of the effect of the characteristics of the closed-loop supply chain as part of the HAM, I vary the remainder of the parameters, respectively A, b, CL and w, one by
one and evaluate their effects individually. The outcomes are again shown graphically by bifurcation diagrams, with the behavioral parameter αbh on the vertical axis and the
intensity of preference parameter β on the horizontal axis. The behavioral parameter in this case is interpreted as product-specific factors that influence the willingness to choose or not choose the circular product. Parameter β measures the willingness to switch to the circular product. Next I perform a bifurcation analysis of the phase map nt= F (nct−1; µ)
by varying the behavioral parameter αbhand the parameter β that measures the intensity
of preference. The outcomes are shown by phase portraits, displaying the steady states for different regions of the bifurcation diagrams.
Figure 5: Bifurcation diagram for different values of the scaling parameter CL
In figure 4 the calculated bifurcation diagram of the CLSC/HAM-model is shown. The parameter values that correspond to this diagram are taken as a starting point. The original bifurcation diagram that results from the initial model of Moghayer et al. (2015) is represented by the dotted line. The bifurcation diagram of the ’CLSC/HAM-model’ is shifted to the left compared to the one of the initial HAM-model. However the dynamics are similar. Varying β again results in a saddle-node bifurcation, or fold bifurcation, such that the diagram is again partitioned into three regions. Region I leads to a steady state where the non-circular product dominates the market and introduction of the circular product has failed. In region II, the (un)success of the circular product depends on the initial state, measured in terms of ’early adopters’. If the number of early adopters is sufficiently high, the steady state of domination of the circular product is achieved, otherwise market failure results. Lastly, region III corresponds to the situation of a unique steady state where the circular product is successfully introduced in the market. In the sequel the parameters A, b, CLand w are varied one by one and their effects compared to
the ’starting point’ situation are evaluated individually.
4.1
Investment in collection
In figure 5 the calculated bifurcation diagrams for different values of the scaling parameter CL are shown. It can be seen that an increase of the scaling parameter CL causes the
shrink. This is somewhat contrary to my intuition as I expect that an increase of CL,
and thus a decrease of τ , minimizes the chance of success for the circular product. In the light of this reasoning I would have expected the opposite effect of the diagram shifting upward.
4.2
Wholesale price
In figure 6 the bifurcation diagrams for different values of the wholesale price w are shown. An increase of the wholesale price causes the price of the circular product to rise. From the figure it can be seen that this leads the diagram to shift upward and thus an enlargement of region I.
4.3
Collection fee
Figure 7 displays the bifurcation diagrams for different values of the collection fee b that the retailer receives from the manufacturer for inducing collection. The higher the collection fee, the larger region I. Intuitively, this seems not right. Because the function for τ is increasing in b, I expect that this positively affects the introduction of the circular product. An economic view on this situation confirms this, because a higher collection fee motivates the retailer to invest in collection of used products, enlarging the chance of success for the circular product.
Figure 7: Bifurcation diagram for different values of the collection fee b
Figure 8: Bifurcation diagram for different values of the payment for the consumer A
4.4
Payment for the consumer
In figure 8 the bifurcation diagrams for different values of the payment for the consumer A are shown. From the diagram it can be seen that an increase of the payment for the consumer causes region I to shrink. Receiving a greater amount for returning a used products, gives the consumer a higher incentive to participate in these activities and thus causes the rate of return to rise. I expect that an increase of the rate of return translates into a greater chance of success for the circular product, and therefore a size reduction of region I.
5
Analysis
This section analyzes the results that are established in the previous section. More specifically, the influence of incorporating a CLSC in the original HAM is being discussed. The analysis is done by means of the bifurcation diagrams and phase portraits. First the interpretation of the results is discussed, which is then followed by some reflections.
By incorporating a CLSC in the original HAM, the overall dynamics of the system does not change, as can be seen in the bifurcation diagram of figure 4. This diagram captures the joint effect of the behavioral parameter αbh and the intensity of choice parameter β.
The system again undergoes a flip bifurcation point for specific values of the parameters β and αbh. The steady states of the different regions of the bifurcation diagram can be
analyzed using phase portraits. By fixing β to a specific value (here β = 0.1) and varying αbh, phase portraits corresponding to each region can be generated. The phase portraits
that belong to the bifurcation diagram of figure 4, are shown in figure 9. It can be seen that the CLSC/HAM-model yields less extreme results than the original HAM-model: the steady state of region I and III correspond to respectively a greater and a smaller steady state market share of the circular product. Besides, in region II a significantly higher amount of initial adopters (> 60%) is needed for successful introduction of the circular product. Due to the presence of many parameters that each have their individual effects but at the same time are all interacting in a fully connected web, it goes beyond this paper to find a detailed explanation for this. However, it is possible to give a slight idea of the underlying dynamics of the model. In the sequel I analyze the results presented in the previous section for different values of the parameters CL, w, b, A underlying in the
CLSC-model.
5.1
Interpretations
I start off with evaluating the effect of varying the scaling parameter CL. Stated in
the previous section, the effect is somewhat contrary to my intuition. Considering the structure of the rate of return τ , an increase of the scaling parameter CL causes the
rate of return to decrease, representing a decreased enthusiasm of consumers for circular products. It is reasonable to expect that this has a negative influence on the market
Figure 9: Phase diagrams for β = 0.1 and αbh= −2, 1, 4
share of the circular product and therefore a negative impact on the chance of a successful introduction of the circular product. In this light an enlargement of region I would be expected. However, considering figure 5, an increase of CL appears to have a positive
effect on the market share. This can be explained by evaluating the expression for pt of
nt, which is an increasing function in τ . Therefore, a decrease of τ , will result in a lower
price of the circular product, causing it to be more attracting for consumers. This might be an explanation for the chance of successful introduction of the circular product to rise. Next, I evaluate the effect of varying the wholesale price w. From an economic perspec-tive, this is in line with the expectations, since a retailer normally invoices the consumer for a higher wholesale price. This is confirmed by the price function pt of nt presented in
equation (19). The consumer responses to this increase in the price of the circular prod-uct by a lower demand. The lower the demand, the lower the chance of success of the
circular product. However, the price function ptof ntleads to a contradicting conclusion,
since this function is increasing in nt. A higher wholesale price would therefore lead to
a higher price and a higher market demand. A logical conclusion would be that region I shrinks, but this is not the case. Since all variables are interacting with each other, it is possible that the effects of the other variables surpass the effect of an increase of w.
For the collection fee b again the results contradict with the expectation. I expect that a higher collection fee for the retailer motivates the latter to invest more in collection activities, increasing the environmental awareness among consumers and ultimately driv-ing the market share of the circular product up. The expression for pt of nt confirms this
as a higher collection fee results in a higher price and, because of the positive relation, a higher market demand of the circular product. However, an increase in b causes the diagram to move upward, enlarging the region of a market failure.
Lastly I discuss the effects of varying the payment that the customer receives for returning a used product. An increase of the payment gives the consumer a higher incentive to return used products. The higher the payment, the more the diagram shifts downward. This is reasonable since it makes sense that less pro-environmental values are needed in order for the circular product to succeed, that is; the steady state of a the circular product being successful is reached for lower values of αbh.
Concluding, the outcomes of the model are sometimes somewhat contradictory to either the economic theory or the model. However, the model exists of many parameters which all interact in a fully connected web, making it complicated to explain all outcomes.
5.2
Reflections
This paper seeks to investigate the effects of incorporating a closed-loop supply chain in the existing model that models the transition towards a circular economy. The results that are obtained are highly dependent on the restricted model that was used, which is a extremely simplified representation of the reality. Also due to the absence of real data, the outcomes of the model cannot be used for recommendations. However, the outcomes can prove to be useful in exhibiting the conceptual idea. The aim of this paper is therefore primarily to illustrate the method that is developed, more than to draw conclusions from.
This subsection attempts to sketch a full overview of the limitations of the method used in this paper and lists some suggestions for future research.
5.2.1 Limitations
In this paper an attempt has been done to expand the original incorporate the static model of the closed-loop supply chain, in the existing dynamical discrete choice model. The latter requires the relation between the price ptand the market share ntto be linear.
However, when following the game-theoretic approach of Savaskan et al. (2004), a non-linear relation was derived. This problem was solved changing the demand function, but of course this comes at a cost. The optimal values of both the wholesale price w and the price p now could not be derived any longer with game-theory. In future research, the model can be improved by making it resistant to non-linearity such that a more realistic demand curve can be used. Next, one could argue about the fact that the rate of return is now determined only by the retailer. It is reasonable that the retailer has a partial influence by investing in promotional activities, however, it is not unlikely that the consumer also has a card in the game. Also, it is important to make a note on the relation that was derived between the price and the market share. In the light of a monopolistic market it is reasonable that these are positively related. However, it is a point of discussion. On the one hand, one would expect that an increase in the market share will cause the price to drop due to a probable efficiency gain. On the other hand, it can also be that the increase in the market share represents a high presence of environmental awareness among consumers, causing them to willing to pay more for circular goods. On way or another, it is essential to have another look on this relation and its derivation. Another limitation on the model is the fact that it is now assumed that the circular product and the non-circular product are homogeneous. It is arguable if this is a realistic situation since the recycling process can influence the quality of the products. Also it is now assumed that products can be reused for an infinite time. This is doubtful too because some products just simply become worn out after some time. As for the non-circular product, it is important to note that both on the demand as the supply side variables are taken exogenous. For instance, both the price and the demand are exogenous in the model, whereas these are dynamic for the circular product. This
can lead to inconsistent and unrealistic results.
Besides limitations on the derivation of the model, there are also some remarks on the operation of the model. The presence of many parameters makes it complicated to draw conclusions from the outcomes and to make a proper comparison with the original model. Additionally, the absence of data causes problems in setting realistic values for the parameters. To be able generate more useful results, a structural stability analysis is necessary such that the stability and the continuity of the model can be determined.
A final comment on the model is that it is only valid for a monopolistic market and that it only measures the effects of market and behavioral effects, leaving out institutional, organizational and technological barriers.
5.2.2 Suggestions
For future research it is interesting to investigate other ways of expanding the model in order to make it more realistic. In the sequel I list some suggestions for further research. First of all, ways can be investigated to make the model more resistant for non-linearity, such that a more realistic demand curve can be used and game theory can be used to derive optimal values for the variables underlying in the CLSC-model. Secondly, in the current model transport costs are left out in the reverse logistics process. Future research could focus on incorporating this in the model, as well as the fact that products are worn out after it has been used for a certain amount of times. Next, it should be taken into account that there might be a difference in quality between the circular and the non-circular product.
Other ways to improve the model are to take into account the other barriers that influence the complex transition towards a more resource efficient economy. The model used in this paper only focuses on market and behavioral constraints, whereas institu-tional, organizational and technological barriers also play a role. As if it were not complex enough yet, the model could also be improved by making it applicable to the situation of perfect competition instead of considering only a monopolistic market. However, this is extremely complex and, if possible at all, exploring this is on the longer-term research agenda.
to carry out more case studies. Having a clear identification of the parameters, improves the model significantly and sets a positive step in the direction to be able to do draw some useful conclusions from the model.
6
Case study
This section presents a case study to which the model used in this paper applies. A case study illustrates the output of the modelling tools and opens doors to further evaluate and discuss the results and methods developed in this paper. The results and methods are applied to a use case of recycling tires in The Netherlands. First an introduction of the case along with some background information is presented, followed by a description of the method thereafter. The section finishes with an overview of the results.
6.1
Tire industry
As a case study I evaluate the Dutch tires industry and analyze the effect of increased recycling of the material content of tires. By means of a case study it can be quantified how a more resource efficient economy positively effects input and waste flows. This case study is based on the one that was carried out by Moghayer et al. (2015) and for the ease of applicability I will therefore use the same data and assumptions.
From the world rubber consumption, 70% is being used for the tire industry. A relatively small part is already being reused and recycled, but the recycled content of the tires remains low. Moghayer et al. assume that in the Netherlands each year 6 million tires need to be replaced (p.6, 2015). In their case study they focus on increasing the share of recycled material in tires by means of devulcanisation. For a detailed explanation and some more background information on this process I refer to their paper. Increasing the share of recycled material in tires, i.e. increasing so called ’high-value recycling’, reduces both the material input and the waste flows.
6.2
Method
In order to calculate the reduction of material input and waste flows, I use an Envi-ronmentally Extended Input-Output model, an EE-IO model. This model is based on statistics provided by Statistics Netherlands, more specifically it is based on the IO table of the Netherlands of 2013. An IO table represents the interdependencies of sales and purchases between producers and consumers within an economy. In addition to an IO table, an EE-IO table also covers the environmental input and output flows, enabling to measure both the effect in terms of material as environmental impact. To measure the latter, some assumptions are made regarding reduction of input and output flows as a consequence of recycling. For a detailed overview of these assumptions I refer again to Moghayer et al. (p.6, 2015).
6.3
Results
I obtain the results for the ’starting-point’ situation, which corresponds to figure 4. Specif-ically, I use the values of the steady state market shares that result in region II, where the long-term steady state is dependent on the initial state. Using the EE-IO model as described in the previous subsection, I calculate the changes in input and waste flows of both the situation of market failure and market success. The results are presented in figure 11. All changes are measured relative to the input and waste flows in the refer-ence year. In the steady state where the circular product dominates the market and the market share is 79.29%, input materials are reduced by 31%, waste by 1.81% and oil by
0.16%. On the contrary, in the steady state of market failure where the market share is 20.71%, input materials are reduced only by 8.28%, oil by 0.04% and waste by 0.48%.
7
Conclusion
In this paper an attempt has been done to model the transition towards a circular econ-omy, taking account a closed-loop supply chain on the supply side. As a starting point the existing discrete choice model, developed by Moghayer et al. (2015) was taken, which was then extended on the supply side by incorporating a closed-loop supply chain into the model. The question that arose is to what extent the incorporation of a closed-loop supply chain affects the conditions for successful introduction of a circular product in the market. Due to the presence of many parameters and the absence of real data, the out-come of the model cannot be used for recommendations, but it does illustrate the method that I have developed. It gives another insight in the complexity of the transition towards a more resource efficient economy, but also forms a step towards gaining more knowledge on modelling this transition. By enriching the supply side of the initial model, the model becomes more realistic, giving rise to future research.
In the gathering of my results I started off with studying the existing literature. I studied the research of Moghayer et al. (2015), modelling the transition towards a resource efficient economy as a complex adaptive system. Next, the research of Savaskan et al. (2004) gave me insights in the derivation of optimal parameters in closed-loop supply chains using a game-theoretic approach. Model R, where the retailer induces collection, appeared to be the most effective reverse logistics structure. Hence I used the derivations of this structure in the further development of the model.
In order to be able to link the derivations that follow from the CLSC-model to the HAM, some simplifications needed to be done. Different approaches were discussed, but it seemed to be most realistic to replace the demand function for a function that depends on the market share. However, this came at the cost of the game-theoretic derivations of the optimal values of the variables, forcing me to take some of them exogenous.
The results that I obtained are shown by bifurcation diagrams and phase portraits. Similar to the outcomes of the original model, this results in a fold bifurcation with three
different regions; region I and III leading to a unique steady state, and region II leading to one of the two steady states dependent on the initial state. More specifically, region I corresponds to the situation of market failure of the circular product, independent of the initial state. Next, in region II the success of the circular product depends on the initial amount of early adopters. If there is a sufficient amount of early adopters, the system goes to the steady state of dominance of the circular product, whereas if this amount of early adopters is not present, the introduction of the circular product fails. Lastly, region III corresponds to the situation of successful introduction of the circular product.
In the evaluation and analysis of the results that I obtained, I made a comparison with the results of Moghayer et al. (2015). I found that the overall structure of the outcome of the model is similar to Moghayer’s. Dependent on how the parameters are fixed, the bifurcation diagram shifts horizontally ore vertically. Due to the absence of real data it is precarious to draw useful conclusions from the comparison. From the phase diagrams, however, it seems to be that the outcomes of the model used in this paper are less extreme since the market shares of the steady states take on less extreme values.
A further evaluation of the model is done by varying the different variables of the underlying CLSC-model. Considering both the economic perspective as well as the model, some results regarding this seem to make more sense than others. Both an increase of the scaling parameter CL and the payment for the consumer A, cause the bifurcation
diagram to shift downward, causing region I, representing a long term market failure, to shrink. On the other side, increasing either the wholesale price or the collection fee, has a negative effect on the size of region I. For the first this seems intuitively right, for the latter, however, not. Nevertheless, it is in line with the derivations of the model. This contradicting property however gives rise for future research and evaluation of the model and its derivations.
As was stated in the last section, the model used in this paper is a highly simpli-fication of the reality. It is therefore not qualified to use for recommendations, but it gives a good illustration of the method I have developed and the complexity that comes across when modelling the transition towards a circular economy. For the short-term research agenda I suggest to carry out more case studies and to investigate other ways of incorporating the CLSC in the HAM such that the game-theoretic approach is not
harmed. For the longer-term research agenda it is interesting to extend the model with institutional, organizational and technological effects, to get a full grasp of the interacting web of constraints.
In all, the extension of the HAM model to the CLSC/HAM-model is a first step towards developing a more realistic illustration of the complexity of the transition towards a circular economy. It is too early to draw useful conclusions from the outcomes of the model, but it gives rise to future research.
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