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Journal of Cleaner Production 237 (2019) 117785

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Journal of Cleaner Production

journal homepage: www.elsevier.com/locate/jclepro

Sustainable waste and cost reduction strategies in a strategic buyer-supplier relationship

Seung Ho Yoo a, Hosun Rhim b, *, Myung-Sub Park b

a Division of Interdisciplinary Industrial Studies, Hanyang University, 222 Wangsimni-ro, Seongdong-gu, Seoul, 04763, South Korea b Department of Logistics, Service & Operations Management, Korea University Business School, 145 Anam-ro, Seongbuk-gu, Seoul, 02841, South Korea

a r t i c l e i n f o

Article history: Received 17 January 2019 Received in revised form 27 June 2019 Accepted 25 July 2019 Available online 26 July 2019

Keywords: Sustainable operations Cost reduction Benefit sharing Supply chain management Principal-agent paradigm

* Corresponding author. E-mail addresses: [email protected] (S.H

(H. Rhim), [email protected] (M.-S. Park).

https://doi.org/10.1016/j.jclepro.2019.117785 0959-6526/© 2019 Published by Elsevier Ltd.

a b s t r a c t

We investigate incentive schemes for a sustainable waste and cost reduction activity in a dyadic supply chain. The buyer motivates the internal operations department and external supplier to reduce the supply chain's overall production cost by reducing the waste and energy consumption. By incorporating players' risk aversion and opportunity loss as in practice, we construct three benefit-sharing models: two cost target models to maintain unit profit and profit ratio (UP and PR) and one with no target (NT). Then, we reveal that the benefit-sharing scheme yielding superior cost performance varies depending on the market situation and the relationship intensity between players. In a highly strategic buyer-supplier relationship, the NT scheme yields the best result if the supply chain maintains a low profit ratio. The PR scheme is superior with the high original profit ratio. When the buyer maintains a transactional relationship with the supplier, adopting the UP scheme always guarantees superior cost reduction performance.

© 2019 Published by Elsevier Ltd.

1. Introduction

When supply chains compete with each other, collaboration between supply chain members is critical for the sustainability and competitive advantage of a supply chain. The collaborative activ- ities in a supply chain include various joint activities for cost reduction, research and development (R&D), product development, manufacturing, marketing, distribution, and service (Yoshino and Rangan, 1995). These joint activities, depending on the bargaining power, are often led by buyers, including GM and Ford within the U.S. supply chain system, Toyota and Matsushita within the Japa- nese keiretsu system, and Samsung and Hyundai within the Korean chaebol system. These companies have led numerous supply chain innovation projects with their suppliers. Among various collabo- rative activities, joint cost reduction is essential for the sustainable utilization of resources, especially when the market is volatile or weak.

The waste management is essential in the cost reduction, and the waste reduction is a key component of any cost reduction ac- tivity (Murray, 2018). In the waste and cost reduction, one of the

. Yoo), [email protected]

most important concepts would be 3R (reduce, reuse, and recycle). 3R is primarily driven by the cost reduction motivation but also beneficial for the sustainability of a firm. Material recycling and reuse of resource instead of disposing it are critical for cost reduction, while the reduction of waste at the source is the main priority for sustainable cost reduction (Allen, 1994; Fercoq et al., 2016). Porter and van der Linde (1995) also point out the linkage between cost reduction and environmental activities involving material savings, better utilization of by-products, elimination or reduction of activities, lower energy consumption, lower packaging costs, etc. By reducing materials and energy use, it is important to achieve the established target (Yuan et al., 2018). The final objective is the total elimination of waste, and it needs the radical process changes and the efforts of overall supply chain players (Fercoq et al., 2016). In this context, we focus on investigating how the buyer effectively controls a joint waste reduction activity in a buyer- supplier supply chain beyond a single firm's operational environ- ment. We consider that the amount of cost reduction is the direct indicator of waste management performance.

In this study, we explore a joint cost (or waste) reduction activity for the sustainable operations of a supply chain. A buyer motivates both an external supplier and an internal operations department to reduce overall production cost, composed of the supplier's component cost and the buyer's assembly cost. We propose various

S.H. Yoo et al. / Journal of Cleaner Production 237 (2019) 1177852

benefit-sharing incentive schemes with and without cost targets. We examine which benefit-sharing method yields superior per- formance for the different buyer-supplier relationships.

Value analysis (VA) and value engineering (VE) methods are conventional but very effective practices for joint cost reduction within supply chains. Both methods are based on target costing (Nishiguchi, 1994; Wouters et al., 2016). It is since the 1980s that target costing has impacted many supply chains in the U.S. auto- mobile industry, but it still receives the most attention among various methods for cost reduction (Wouters et al., 2016). We also need to note that the supply chain collaboration based on target costing is not limited to the automobile industry. We observe many firms from various industries enhancing their cost performance based on target costing, such as Samsung, Sony and Sharp in the electronics industry (Khan, 2014).

Target costing is different from cost-plus pricing (Li et al., 2012). In target costing, a sales price in a competitive market is set first to attract consumers, and then the target cost at the product level is obtained by subtracting the profit margin. Finally, the cost is allo- cated to component suppliers through value analysis (Nishiguchi, 1994; Gagne and Discenza, 1995; Wouters et al., 2016). To achieve the target cost through the joint efforts of supply chain members, the benefit-sharing rule based on the target cost is set up to encourage suppliers' efforts to reduce the waste and energy con- sumption and improve the process. The sharing rule has changed significantly from traditional practices, in which suppliers' in- centives for improvement efforts were often ignored by the buyers exploiting the supply chain's benefit (Nishiguchi,1994). However, it is noteworthy that the target costing method innately shifts the buyer's external risk of price variation to suppliers, since the target cost originates from the market price. In addition to benefit sharing, the buyer interacts with its supplier through technological, meth- odological, or financial support (Liker, 2004). This again encourages the supplier's involvement and efforts to foster and sustain a collaborative environment.

To understand the benefit-sharing and interaction issues for a sustainable cost reduction activity under contracts between a buyer and a supplier, we adopt the principal-agent paradigm. The principal-agent paradigm has been applied to various supply chain management issues, such as cost sharing in after-sales service (Kim et al., 2007), supply disruption management under asymmetric information and backup production options (Yang et al., 2009), information sharing and a screening contract in a lean production environment (Inderfurth et al., 2013), dynamic business share allocation with two competing suppliers (Li et al., 2013), manufacturer-hired sales agents and demand forecast accuracy (Khanjari et al., 2014), joint pricing of new and refurbished products (Yoo and Kim, 2016), and trade credit contract under asymmetric credit default risk (Wang et al., 2018). Moreover, there are also various studies on collaborative improvement activities among supply chain members, such as joint cost reduction (Yang, 1994; Iyer et al., 2005), joint quality management (Balachandran and Radhakrishnan, 2005; Hung, 2011; Yoo, 2014), lead time or response time improvement (Ahn et al., 2008), inventory coordi- nation (Keren, 2009), service output improvement (Roels et al., 2010), and cooperative advertising and ordering issues (Zhou et al., 2018).

Our paper is different from the previous literature in the following ways. First, three different benefit-sharing schemes are considered based on various target cost schemes for the sustainable waste and cost reduction in a supply chain. Setting a target cost is common in joint cost reduction activities in practice (Wouters et al., 2016), as in the cases of Toyota (Nishiguchi, 1994), Chrysler, Boeing, and Caterpillar (Swenson et al., 2003). However, it is difficult to find literature modeling this issue. There have been many cost

management studies dealing with various issues, such as the integration of quality function deployment and target costing (Hoque et al., 2005), the consideration of cost of capital and the net present value in target costing approach (Kee, 2010), the compar- ison of two different target costing approaches including demand side and supply side (Li et al., 2012), the quality-oriented control approach for value engineering within a target costing concept (Bock and Pütz, 2017), and the incentive mechanism to coordinate suppliers’ cost-reduction effort (Proch et al., 2017). However, they do not focus on investigating the effect of target cost schemes on the sustainable operations in a supply chain. In our study, we introduce two cost targets as references of cost performance: one maintaining a unit profit margin (UP), and the other maintaining the profit-price ratio (PR). In both cases, the cost targets are determined by first considering the market price and then sub- tracting the profit margin, following the target costing convention. We also consider another typical cost reduction method that has no cost target (NT, no target) but measures the improvement of waste management based on the previous cost level. This method is added for comparison with two cost target schemes.

Second, the effectiveness of an incentive scheme can differ depending on the characteristics of a supply chain, especially the relationships between supply chain members. Therefore, we consider the strategic relationship intensity between the buyer and supplier utilizing two indicators: relationship length and supply volume. Relationship length is commonly used as an indicator for the strategic importance between partners (Dyer and Chu, 2000; Li et al., 2010). A short-term relationship focuses on economizing transaction cost, and hence it tends to increase opportunism and frustrate collaborative communication. A long-term-oriented rela- tionship promotes collaborative partnerships and stronger rela- tional bonds by helping partners to gain an in-depth understanding of each other (Ghoshal and Moran, 1996; Dyer and Chu, 2000; Paulraj et al., 2008). Contracted supply volume is another indica- tor of interaction intensity. The relationship is more integrated and sustainable when there are fewer suppliers and each supplier is responsible for greater volume, which gives firms the benefits of coordinated replenishment (Shin et al., 2000; Autry and Golicic, 2010). We reveal which benefit-sharing scheme yields superior cost reduction performance for each degree of relationship intensity.

Third, the internal operations department is considered an agent, like an external supplier, as in Porteus and Whang (1991), Yang (1994), and Plambeck and Zenios (2000), since in practice a firm may not perfectly monitor the hidden actions of internal employees. Extended models considering multi-agent problems have been presented (Callen,1988; Porteus and Whang,1991; Yang, 1994; Chalos and Sung, 1998; Wagner and Friedl, 2007; Li et al., 2013). However, cooperation between multiple agents, which is common in supply chain management practice, has not been fully discussed. In this paper, we consider multiple (two) agents, including the operations department (an internal agent) and the supplier (an external agent), where the buyer's operations department supports the supplier to reduce the supplier's component cost.

Finally, we consider the opportunity loss of other beneficial activities due to its internal agent's efforts for a joint cost reduction project, similar to Yang (1994). A buyer with bargaining power usually has a more diversified portfolio of projects than its sup- pliers. Therefore, it always considers the relative efficiency of each project to utilize its limited resources better.

Through the comparison of three benefit-sharing models, NT, UP, and PR, we contribute to the body of knowledge, revealing the effect of target cost in practice and providing important implica- tions. In particular, we provide guidelines for sustainable cost

S.H. Yoo et al. / Journal of Cleaner Production 237 (2019) 117785 3

reduction activities in practical supply chains by answering an important question: Which benefit-sharing scheme induces supe- rior cost reduction performance? We find that it depends mainly on two key factors: the relationship intensity between supply chain members and the market situation, especially the profit-price ratio. When the relationship between players is transactional, the UP scheme involving the cost target to maintain unit profit always induces superior cost reduction performance. However, in a highly strategic buyer-supplier relationship, the result depends on the market situation. When a supply chain is not in a favorable market situation and maintains a low profit-price ratio, the NT scheme, which appraises performance based on the amount of cost and waste reduction without the target, induces superior performance. However, the PR scheme involving the cost target to maintain the profit-price ratio guarantees the best result when a supply chain maintains a high profit ratio. We also reveal that these results are mainly due to the differences in both the effect of the external risk from price variation and the required minimum amount of cost and waste reduction for incentives. They jointly induce different actions by supply chain members with respect to the benefit-sharing schemes. In addition, we provide other important implications by investigating the effect of environmental changes on sustainable cost reduction performance.

2. Model

We investigate a dyadic supply chain consisting of a component supplier and a buyer responsible for assembly and sales. We as- sume that the buyer has bargaining power, as in many traditional supply chains such as those of Samsung, Toyota and GM. The buyer (a principal) delegates a joint innovation activity to two agents, its operations department (an internal agent) and a supplier (an external agent). Those agents need to collaborate with each other to reduce the overall production cost consisting of component and assembly costs. We utilize the principal-agent paradigm frame- works of Callen (1988) and Yang (1994), assuming risk aversion of the principal and multiple agents. This is to address cases in which the risk-averse supply chain members cooperate with each other to create and share the benefit from a joint innovation activity.

In a perfectly competitive market condition, the product price P is exogenously determined. Therefore, the buyer leads a product innovation project to reduce the supply chain's overall production cost C by reducing the waste and energy use and improving the overall processes. Notation for mathematical formulation is sum- marized in Table 1. P is postulated to be normally distributed with mean mp ¼ p and variance sp2. p decreases compared to the original price in the previous period po (p < po), and hence the buyer has a

Table 1 Notation for mathematical formulation.

P product price, P ~ N (mp, sp 2) where mp ¼ p and p < po r1 indicat

po product price in the previous period Si payme whereC production cost, C ~ N (mc, sc

2) where mc ¼ c ¼ c0 e c1a þ c2cs ¼ c0 e c1a þ c2ch e ql$c2 (ch e cl)

cs supplier's component cost, where cs ¼ {ch, cl} with respective probabilities qs ¼ {qh, ql}, where qh þ ql ¼ 1 and ql ¼ ql (b, g)

Bi benefit

co production cost in the previous period h origina ratio, hn contract time-horizon, n � 1

Q production quantity M net present value of market profit, M ¼ l(P � C)Q where l ¼ {[1 e (1/

(1 þ g))n]/[1 e (1/(1 þ g))]} and g is the discount rate ai risk ave

supplie Di disutility, i ¼ d for the operations department and s for the supplier,

Dd ¼ Dd (a, b) and Ds ¼ Ds(g) Vi risk, i ¼

a,b effort levels of the operations department ti margin g effort level of the supplier R buyer's benefit from other activities, R ~ N (mr, sr

2) where mr ¼ r ¼ r0 e r1 (a þ b)

strong incentive to initiate the joint cost reduction activity. On the other hand, C includes the supplier's component cost, the buyer's assembly cost, and the random factor. We assume C is normally distributed with mean mc ¼ c ¼ c0 e c1a þ c2cs and variance sc2. C is positively affected by the supplier's component cost cs, but affected negatively by the operations department's effort a in the assembly line. c1 and c2 are the respective coefficients, and c0 is the average production cost not affected by the agents' efforts. The operations department supports and cooperates with the supplier to reduce the waste and hence supplier's component cost cs down to two levels, cs ¼ {ch, cl} (high and low, where ch > cl), with respective probabilities qs ¼ {qh, ql}, where qh þ ql ¼ 1. The chance of low component cost ql is assumed to be increasing linearly with either the operations department's effort b or the supplier's effort g, i.e. ql ¼ ql(b, g), (ql)b > 0, (ql)g > 0, (ql)bb ¼ (ql)gg ¼ (ql)bg ¼ 0. fx and fxx denote the first- and second-order partial derivatives, respectively, of any function f with respect to any parameter x. Considering the probability of low component cost ql, the average product cost can be rearranged into c ¼ c0 e c1a þ c2ch e ql$c2(ch e cl).

The buyer enjoys the cost reduction benefit as long as the buyer continues the relationship with the component supplier. However, note that the agents are paid only once, whereas the buyer enjoys the benefit during the contract time-horizon n (n � 1). Therefore, we focus on a one-time benefit-sharing model. This is easily observed in practice, for example, in Toyota, POSCO, and Hyundai Heavy Industries (Ministry of Knowledge Economy, 2015). We as- sume that the production quantity Q is predetermined, and P and C do not change once they are realized. Then, the net present value of

the buyer's market profit over n periods is M ¼ Pi¼ni¼1fðP � CÞQ=ð1 þ gÞi�1g ¼ (P � C)lQ, where g is the discount rate (g > 0) and l ¼ {[1 e (1/(1 þ g))n]/[1 e (1/(1 þ g))]}.

The disutility to the operations department and the supplier, Dd (a, b) and Ds(g), are strictly increasing and convex. That is, (Dd)a > 0, (Dd)b > 0, (Dd)aa > 0, (Dd)bb > 0, (Dd)ab > 0, (Dd)aa(Dd)bb e ((Dd)ab)

2 > 0, (Ds)g > 0, and (Ds)gg > 0. Note that the operations department shares its effort across two activities, the cost reduction in the assembly process with the effort a and the support for the supplier's component cost with the effort b. The marginal disutility of one effort increases the other effort level, i.e. (Dd)ab > 0.

The effort put toward the cost reduction project is unavailable for other productive activities, and hence opportunity loss is incurred. The buyer's benefit from other economic activities R de- creases as the operations department puts more effort into this waste reduction project. R is assumed to be normally distributed with mean mr ¼ r ¼ r0 e r1(a þ b) and variance sr2. r0 is the buyer's return without any effort. r1 is the marginal loss of other beneficial activities incurred owing to the operations department's effort (a þ

or of the relative inefficiency of the joint cost reduction project nt, i ¼ d for the operations department and s for the supplier, Si ¼ Bi(cb e C)Q, cb is the appraisal basis for the cost reduction performance

-sharing ratio, i ¼ d for the operations department and s for the supplier

l cost-price ratio in the previous period, while (1 e h) is the original profit-price ¼ co/po and 1 e h ¼ (po e co)/po

rsion coefficient, i ¼ “” for the buyer, d for the operations department, and s for the r “” for the buyer, d for the operations department, and s for the supplier

al contribution, i ¼ d for the operations department, and s for the supplier

S.H. Yoo et al. / Journal of Cleaner Production 237 (2019) 1177854

b) on the supply chain's joint cost reduction project. Therefore, r1 can be regarded as the indicator of the relative inefficiency of the joint reduction project. We assume that the correlations between three random variables are negligible compared to each respective variance, i.e. the correlations, rpc, rpr and rcr ¼ 0.

Considering the payment scheme from the buyer to the agents, the payment is a function of the realized product cost C, since the buyer cannot observe the effort levels of the agents. The payments are denoted by Sd for the operations department and Ss for the supplier. We assume a linear benefit-sharing scheme, widely accepted owing to its simplicity by many researchers since the work of Holmstrom and Milgrom (1987) (Callen, 1988; Yang, 1994; Sung,1995; Müller,1998; Goetzmann et al., 2003; Stracca, 2006; Lei et al., 2012), and by practitioners such as those at Toyota and many Korean companies, including POSCO and Hyundai Heavy Industries (Ministry of Knowledge Economy, 2015). It includes a fixed fee and a benefit share based on a certain benchmark value. In this study, we focus on benefit shares. Therefore, Sd(C) ¼ Bd(cb e C)Q and Ss(C) ¼ Bs(cb e C)Q, where Bd and Bs are the benefit-sharing ratios, and Q is the production quantity or the contracted supply volume of the component. cb is the appraisal basis for the cost reduction performance which is differently determined depending on the benefit sharing scheme, and C is the realized production cost. Therefore, (cb e C) is the unit cost reduction performance appraised by the buyer. Bd and Bs are less than or equal to l, i.e. Bd, Bs, and (Bd þ Bs) in [0, l]. If Bd þ Bs ¼ l, it means that the buyer offers all the benefit of cost reduction during the period n to agents. Note once again that the agents are paid only once, while the buyer enjoys the benefit as long as it continues the relationship with the supplier as in many practices. By combining all the components, the buyer's problem is obtained based on the principal-agent paradigm as follows.

Maximize B1;B2

U ¼ E " P qh;ql

qsðM þ R � Sd � Ss !#

ðOBJÞ

subject to

Ud ¼ E "X qh;ql

qsðSd � DdÞ # � u d

# ðIRIÞ

Us ¼ E "X qh;ql

qsðSs � DsÞ # � u s

# ðIRSÞ

Maximize a;b

Ud ðICIÞ Maximize

g Us ðICSÞ

where U, Ud, and Us are the expected utilities of the buyer, opera- tions department, and supplier, respectively. E [$] is the expected value. ud and us are the minimum reservation utilities of the op- erations department and supplier. The buyer finds the optimal sharing ratios Bd and Bs by maximizing its expected utility in (OBJ). (IRI) and (IRS) are the individual rationality constraints ensuring the participation of the internal operations department and the supplier in this joint project. (ICI) and (ICS) are the incentive compatibility constraints that incorporate the unobservable effort levels of the internal operations department and the supplier.

We consider three types of appraisal bases cb to motivate effort by sharing the supply chain's benefit, as listed in Table 2. ct is the

Table 2 Three appraisal bases for cost reduction performance.

No Target (NT) Cost Target (ct) to maintain:

Unit Profit (UP) Profit Ratio (PR)

cb c o ct

UP ¼ p e (po e co) ctPR ¼ (co/po)p ¼ hp

cost target established by the buyer, and po and co are the original price and cost levels in the previous period. h is the original cost- price ratio in the previous period, while (1 e h) is the original profit-price ratio, i.e. h ¼ co/po and 1 e h ¼ (po e co)/po. The appraisal basis in the NT scheme is the previous cost level co, so that the agents are appraised by the cost performance itself. On the other hand, we introduce two conservative cost target schemes to ach- ieve by the waste management under the unfavorable market condition where the price falls (p < po). In the first scheme, the buyer maintains the same unit profit margin as in the previous period, i.e. p e ct

UP ¼ po e co (UP scheme). In the second scheme, the buyer aims to sustain the original profit-price ratio, i.e. (p e ct

PR)/p ¼ (po e co)/po (PR scheme). These two cost targets in Table 2 (ct

UP and ct PR) convey the risk from market price changes to the supplier. We assume the utility functions of the buyer, operations

department, and supplier are exponential: that is, we assume constant absolute risk aversion of the principal and agents. The buyer is risk averse. One of the primary reasons for collaborating and sharing benefit with suppliers is to reduce the risk involved with the suppliers’ unobservable action. The operations depart- ment is assumed to be risk averse as risk aversion is often observed in internal employees (Yang, 1994; Chalos and Sung, 1998; Plambeck and Zenios, 2000). We also assume that the supplier, a smaller firm than the buyer, is risk averse. It is well known that the amount of risk aversion increases as the size of a firm decreases, since small firms undertake only a few projects and care about the risk associated with each project (McMillan, 1990). We use a, ad, and as to denote the absolute risk aversion coefficients of the buyer, the operations department, and the supplier, respectively.

Assuming that the supply chain's risk is fully described by the variances of the normally distributed random variables P, C, and R, and combining performance appraisal schemes in Table 2, the buyer's problem above is diversified into three mean-risk models: Programs NT, UP, and PR. When V, Vd and Vs denote the risks of the buyer, operations department and supplier, respectively, for example, the risk of the buyer in Program NT can be described by VNT ¼ Var[Pqs(M þ R e Sd e Ss)] ¼ Var[(P � C)lQ þ R e (co e C) (Bd þ Bs)Q] ¼ l2Q2sp2 þ (l e Bd e Bs)2Q2sc2 þ sr2. Therefore, Programs NT, UP, and PR are as follows.

Programs NT; UPandPR Maximize ðp�cÞlQ �ðcb �cÞðBd þBsÞQ þr�ða=2ÞV ðOBJÞ Subject to

ðcb �cÞBdQ �Dd �ðad=2ÞVd ¼ud ðIRIÞ ðcb �cÞBsQ �Ds �ðas=2ÞVd ¼us ðIRSÞ c1BdQ �ðDdÞa ¼0 ðICI�AÞ ðqlÞbc2ðch �clÞBdQ �ðDdÞb ¼0 ðICI�BÞ ðqlÞgc2ðch �clÞBsQ �ðDsÞg ¼0 ðICS�GÞ

For Program NT, cb ¼ co as in Table 2, and the variances of the buyer, operations department and supplier are V ¼ VNT ¼ l2Q2sp2 þ (l e Bd e Bs)

2Q2sc 2 þ sr2, Vd ¼ VdNT ¼ Bd2Q2sc2 and Vs ¼ VsNT ¼ Bs2Q2sc2. For

Program UP, cb ¼ ctUP ¼ p e (po e co) as in Table 2, and VUP ¼ (l e Bd e Bs)

2Q2(sp 2 þ sc2) þ sr2, VdUP ¼ Bd2Q2(sp2 þ sc2) and VsUP ¼ Bs2Q2(sp2 þ sc2).

For Program PR, cb ¼ ctPR ¼ (co/po)p ¼ hp in Tables 2 and V ¼ VPR ¼ (l e h(Bd þ Bs))2Q2sp2 þ (l e Bd e Bs)2Q2sc2 þ sr2, VdPR ¼ Bd2Q2 (h2sp2 þ sc2) and Vs

PR ¼ Bs2Q2(h2sp2 þ sc2).

3. Optimal compensation and effort level

3.1. Benchmark: The first-best solution

Supply chains consist of different entities having different in- terests, and, in most cases, it is practically impossible to perfectly

S.H. Yoo et al. / Journal of Cleaner Production 237 (2019) 117785 5

monitor and control the effort levels of supply chain members. However, as a benchmark, we first investigate an ideal situation in which the whole supply chain behaves like one single company without any moral hazard or opportunistic behavior in the waste reduction activity. Therefore, we do not need the incentive compatibility constraints of agents, constraints (ICI-A), (ICI-B), and (ICS-G), in Programs NT, UP, and PR. Then, substituting (IRI) and (IRS) into (OBJ) in Programs NT, UP, and PR, we obtain the modified maximization problems to determine the first-best effort levels (a, b, and g) and benefit-sharing ratios (Bd and Bs) as follows:

Programs NT, UP and PR: first-best case Maximize (p e c)lQ þ r e (Dd þ Ds) e (ud þ us) e (a/2)V e (ad/2)Vd e (as/2)Vs (OBJ-FB)

Where V ¼ VNT, Vd ¼ VdNT and Vs ¼ VsNT for Program NT, V ¼ VUP, Vd ¼ VdUP and Vs ¼ VsUP for Program UP, V ¼ VPR, Vd ¼ VdPR and Vs ¼ VsPR for Program PR.

By solving the first-order conditions of above problems, the first-best effort levels, a*, b*, and g*, satisfy the following first-order conditions equally in Programs NT, UP, and PR. The superscript * denotes the first-best solution:

c1lQ e r1 e (Dd)a ¼ 0, (FB-A)

(ql)b$c2(ch e cl)lQ e r1 e (Dd)b ¼ 0, (FBeB)

(ql)g$c2(ch e cl)lQ e (Ds)g ¼ 0. (FB-G)

The first-best benefit-sharing ratios, Bd * and Bs

*, in Programs NT, UP, and PR are:

Bd NT* ¼ BdUP* ¼ aasl/(aad þ aas þ adas), (FB-BD-NT), (FB-BD-UP)

Bs NT* ¼ BsUP* ¼ aadl/(aad þ aas þ adas), (FB-BS-NT), (FB-BS-UP)

Bd PR* ¼ aasl(hsp2 þ sc2)/((aad þ aas þ adas)vPR), and (FB-BD-PR)

Bs PR* ¼ aadl(hsp2 þ sc2)/((aad þ aas þ adas)vPR), (FB-BS-PR)

where vPR ¼ h2sp2 þ sc2. To have the interior solutions in each pro- gram, we need a condition below.

Condition FB. In Program PR, a � adasvPR/(h(1 e h)(ad þ as)sp2). Condition FB implies that the buyer is not highly risk averse in

joint activity, as McMillan (1990) argues that a large firm, having a diversified portfolio of projects, is close to risk neutral with respect to a single project. The properties of the first-best solutions are as follows.

Proposition 1. The first-best solutions have the following properties:

(1) the first-best effort levels (a*, b*, and g*) and the benefit-sharing ratios (Bd

* and Bs *) are independent of each other in all programs,

but (2) the benefit-sharing ratios (Bd

* and Bs *) are affected by risk atti-

tudes (a, ad and as), relationship length (n) and/or amount of risks (sp

2 and sc 2 in Program PR).

Proof. Proofs of all propositions are in the Appendix.

As in Proposition 1(1), the benefit-sharing ratios do not affect agents’ effort levels in the ideal first-best scenario, while the effort

levels also do not affect the sharing ratios at all. Rather, the benefit- sharing ratios are determined by the risk attitudes of the buyer and the agents and the relationship intensity as shown in Propositions 1(2). In the next section, the first-best solution above will be used as a benchmark for the solution in a more practical situation.

3.2. The second-best solution

In this section, we consider a practical situation in which agents’ effort levels are not observable, and hence moral hazard occurs. Since the operations department and the supplier determine their effort levels in the waste and cost reduction to maximize their own utilities, the second-best effort levels, a#, b#, and g#, satisfy the incentive compatibility constraints of (ICI-A), (ICIeB), and (ICS-G) equally in Programs NT, UP, and PR. The superscript # denotes the second-best solution. Considering (ICI-A), (ICIeB), and (ICS-G), we obtain the following result.

Proposition 2. In all programs, the second-best effort levels and hence the amount of cost reduction of each agent increase as the respective benefit-sharing ratio (Bd

# or Bs #) or the supply volume (Q)

increases.

In a practical situation, differently from the first-best case, the buyer can motivate the efforts of agents and induce a better waste and cost reduction performance by providing larger benefit shares or guaranteeing agents a larger supply volume. Therefore, we uti- lize the quantity-weighted sharing ratio, Bd

#Q or Bs #Q, as a driver of

the cost reduction performance in this study. Comparing the first-best and second-best effort levels, we

obtain the following proposition.

Proposition 3. To achieve supply chain coordination, i.e. a# ¼ a*, b# ¼ b*, and g# ¼ g*, we need the following conditions:

(1) the operations department’s effort levels are coordinated when Bd ¼ {l e r1/(c1Q)}, c1 ¼ (ql)b·c2(ch e cl), and r1 � c1lQ, while the supplier’s effort is coordinated when Bs ¼ l.

(2) The effort levels of both the operations department and the supplier are coordinated at the same time only when Bd ¼ 0, Bs ¼ l, and r1 ¼ c1lQ ¼ (ql)b·c2(ch e cl)lQ.

To achieve supply chain coordination, the buyer needs to pro- vide all the benefits from cost reduction to the supplier as shown in Proposition 3(2). Therefore, supply chain coordination is practically difficult since the buyer, the supply chain's focal company, does not have any reason to yield all the benefits of waste reduction to the supplier. Therefore, we focus on investigating how to control the agents' behaviors to induce better performance in a practical situ- ation, as well as comparing the different characteristics and per- formances of the three incentive schemes.

In the second-best case, the buyer's problems in Programs NT, UP, and PR are identical to (OBJ-FB). However, we need to additionally consider the agents' effort levels as the functions of benefit-sharing ratios, i.e. a ¼ a(Bd, Bs), b ¼ b(Bd, Bs) and g ¼ g(Bd, Bs). This is because the effort levels and the benefit-sharing ratios are interrelated, as shown in Proposition 2. Then, we obtain the second-best benefit- sharing ratios Bd

# and Bs # in each program from the first-order con-

ditions of (OBJ-FB) by using (ICI-A), (ICI-B), and (ICS-G) and their implicit differentiation results, i.e. [da/dBd] ¼ {(c1(Dd)bb e (ql)b$c2(ch e cl)(Dd)ab)Q/((Dd)aa(Dd)bb e (Dd)ab

2 )}, [db/dBd] ¼ {((ql)b$c2(ch e cl)(Dd)aa e c1(Dd)ab)Q/((Dd)aa(Dd)bb e (Dd)ab

2 )}, [dg/dBd] ¼ 0, [da/ dBs] ¼ 0, [db/dBs] ¼ 0, and [dg/dBs] ¼ {(ql)g$c2(ch e cl)Q/(Ds)gg}.

Bd NT# ¼ [(tdts þ td(a þ as)sc2 þ aas(sc2)2)l e r1e(ts þ (a þ as)sc2)/Q]/

jNT, (SB-BD-NT)

S.H. Yoo et al. / Journal of Cleaner Production 237 (2019) 1177856

Bs NT# ¼ [(tdts þ ts(a þ ad)sc2 þ aad(sc2)2)l þ r1easc2/Q]/jNT,(SB-BS-NT)

Bd UP# ¼ [(tdts þ td(a þ as)(sp2 þ sc2) þ aas(sp2 þ sc2)2)l e r1e(ts þ (a þ

as)(sp 2 þ sc2))/Q]/jUP, (SB-BD-UP)

Bs UP# ¼ [(tdts þ ts(a þ ad)(sp2 þ sc2) þ aad(sp2 þ sc2)2)l þ r1ea(sp2 þ sc2)/

Q]/jUP, (SB-BS-UP)

Bd PR# ¼ [(tdts þ td(a þ as)vPR þ tsah(1 e h)sp2 þ aas(hsp2 þ sc2)2)l e

r1e(ts þ (a þ as)vPR)/Q]/jPR, and (SB-BD-PR)

Bs PR# ¼ [(tdts þ ts(a þ ad)vPR þ tdah(1 e h)sp2 þ aad(hsp2 þ sc2)2)l þ

r1eav PR/Q]/jPR, (SB-BS-PR)

Where jNT ¼ {tdtsþ (td(a þ as)þts(aþ ad))sc2 þ (aadþ aasþ adas)(sc2)2}, jUP ¼ {tdtsþ (td(a þ as) þ ts(a þ ad))(sp2 þ sc2) þ (aadþ aasþ adas)(sp2 þ sc 2)2}, jPR ¼ {tdtsþ (td(a þ as) þ ts(a þ ad))(h2sp2 þ sc2) þ (aadþ aasþ

adas)(h 2sp

2 þ sc2)2}, td ¼ {(x2(Dd)bbþ y2(Dd)aa e 2xy(Dd)ab)/ ((Dd)aa(Dd)bb e(Dd)ab

2 )}, ts ¼ {z2/(Ds)gg}, x ¼ {c1}, y ¼ {(ql)b$c2(ch e cl)}, z ¼ {(ql)g$c2(ch e cl)}, e ¼ {(x(Dd)bbþ y(Dd)aa e (xþ y)(Dd)ab)/ ((Dd)aa(Dd)bb e (Dd)ab

2 )}, and vPR ¼ h2sp2 þ sc2. x, y, and z are the marginal cost reductions by effort levels a, b, and g, respectively. Therefore, td and ts can be regarded as the indicators of marginal contributions of the operations department and the supplier, respectively, considering both cost reduction and disutility induced by effort levels, similarly in Yang (1994). We assume that td and ts are positive (i.e. x(Dd)bb > y(Dd)ab and y(Dd)aa > x(Dd)ab) and sufficiently large so that tdts > (aadþ aasþ adas)(sp2 þ sc2)2. e is the term related to the other activities' opportunity loss. To have the interior point so- lutions in all programs, we need the conditions below.

Conditions SB.

For Program NT, r12 � ðtdts�adasðs2c Þ

2ÞlQ eðtsþass2c Þ

; ðtdtsþtdðaþasÞs2c þaasðs2c Þ

2ÞlQ eðtsþðaþasÞs2c Þ

� .

For Program UP, r12 � ðtdts�adasðs2pþs2c Þ

2ÞlQ eðtsþasðs2pþs2c ÞÞ

;

ðtdtsþtdðaþasÞðs2pþs2c Þþaasðs2pþs2c Þ 2ÞlQ

eðtsþðaþasÞðs2pþs2c ÞÞ

� .

For Program PR, if (1 e h) > {asv PRjPR}/{hasp

2[tdts þ td(a þ as) vPR þ tsa (vPR)2]},

r12

2 4 � tdts þ ðtd þ tsÞahð1 � hÞs2p � adas

� vPR

�2� lQ

e � ts þ asvPR

� ; � tdða þ asÞvPR � tdahð1 � hÞs2p þ asða þ adÞ

� vPR

�2� lQ

eavPR

3 5: Otherwise;

r12

2 4 � tdts þ ðtd þ tsÞahð1 � hÞs2p � adas

� vPR

�2� lQ

e � ts þ asvPR

� ; � tdts þ tdða þ asÞvPR þ tsahð1 � hÞs2p þ aas

� vPR

�2� lQ

e � ts þ ða þ asÞvPR

� 3 5

Conditions SB are all related to r1, the inefficiency of joint cost reduction activity compared to other beneficial activities. These conditions imply that the opportunity loss is unavoidable, but its degree should not be significant.

Supposing the interior solutions satisfy the conditions above, we obtain the following properties of Bd

# and Bs # in Programs NT, UP,

and PR.

Proposition 4. In the second-best case, the agent yielding sufficient contribution is always compensated more than in the first-best case in Programs NT and UP, i.e. Bd

NT# > Bd NT* and Bd

UP# > Bd UP* (Bs

NT# > Bs NT* and

Bs UP# > Bs

UP*) with a sufficiently large td (ts). However, in Program PR, this is true only when the original profit-price ratio (1 e h) is suffi- ciently low, i.e. Bd

PR# > Bd PR* (Bs

PR# > Bs PR*) with a sufficiently large td (ts).

Proposition 4 shows that each benefit-sharing ratio in the second- best case is a function of the marginal contribution of each agent, which is different from the first-best case. Since the agents' effort levels in the waste reduction project are not observable and not contractible, it is reasonable that the relative contribution of each agent tothe outcome isconsidered an alternative tothe agent's effort. At Toyota, John Deere, and Delphi, it is observed that the contribution to the outcome is a basic factor to determine the benefit share (Ministry of Knowledge Economy, 2015). However, we often witness an equal benefit-sharing rule in many practical situations due to the difficulty of measuring the exact contribution of each member (Ministry of Knowledge Economy, 2015). This will not appropriately induce the agents' efforts and subsequent contribution to perfor- mance. Therefore, before initiating a joint activity, a system to pre- cisely measure the performance of each supplychain member should be prepared. On the other hand, when the supply chain originally maintains a low profit (1 e h) (or a high cost h) in an unfavorable environment, Program PR is more effective, requiring higher agent effort levels. The criterion of a low profit ratio (1 e h) in Proposition 4 involves various factors, i.e. (1 e h) < {ad(a þ as)(h2sp2 þ sc2)/(haassp2)} (see Proof of Proposition 4 in the Appendix). For example, if we have the original cost co ¼ 60, the original price po ¼ 100, the cost variance sc 2 ¼ 2000, the price variance sp2 ¼ 12000 and risk aversion co-

efficients a ¼ ad ¼ as ¼ 0.1, then the condition always holds, i.e. (1 e h) (¼ 0.4) < {ad(a þ as)(h2sp2 þ sc2)/(haassp2)} (¼ 1.76). Therefore, in this numerical example, the agent yielding sufficient contribution in the second-best case is always compensated more than in the first-best case also in Program PR, i.e. Bd

PR# > Bd PR* and Bs

PR# > Bs PR*.

4. Comparison of cost reduction performance

In this section, we examine under which benefit-sharing scheme the supply chain can expect superior performance in waste management based on relationship intensity. As shown in Proposition 2, a larger benefit share and a larger supply volume guarantee better cost reduction performance in the second-best

case by inducing higher effort. Therefore, we compare the sup- plier's quantity-weighted sharing ratio (Bs

#Q) as an indicator of the supplier's cost reduction performance. We use the relationship length (n) and the contracted supply volume (Q) as two indicators

(a) Behavior of Bs#Q in Q

QPR-UP QNT-PR Q

Bs#Q

BsUP#Q

UP PR NT

BsPR#Q

BsNT#Q

(b) Behavior of Bs#Q in n

nPR-UP nNT-PR n

Bs#Q

BsUP#Q

UP PR NT

BsPR#Q BsNT#Q

Fig. 1. Demonstration of Proposition 6 with a low original profit ratio.

S.H. Yoo et al. / Journal of Cleaner Production 237 (2019) 117785 7

of relationship intensity between the buyer and the supplier. Before the comparison, we introduce the effects of n and Q on Bs

#Q.

Proposition 5. The supplier's quantity-weighted sharing ratios (Bs

#Q) in Programs NT, UP, and PR always increase as either the rela- tionship length (n) or the supply volume (Q) increases.

Considering Propositions 2 and 5 together, we can infer that a buyer can expect superior cost reduction performance if it co- operates with a strategic partner in a long-term relationship and responsible for a large supply volume. This result holds regardless of benefit-sharing scheme.

Then, we investigate which incentive scheme induces superior cost reduction performance with the highest quantity-weighted sharing ratio with respect to the relationship intensity. Through the comparison, we obtain Propositions 6 and 7, which show different results depending on the original profit-price ratio (1 e h) (¼ (po e co)/po). The detailed explanation for functions in Propo- sitions 6 and 7 is in the Appendix.

Proposition 6. When the original profit-price ratio is sufficiently low, i.e. (1 e h) < {h[as(a þ ad) (h2sp2 þ sc2) þ hNTtNT-PR/jNT]/(tda)},

(1) Bs UP#Q is the highest when Q < QPR-UP, Bs

PR#Q is the highest when QPR-UP < Q < QNT-PR, and Bs

NT#Q is the highest when Q > QNT-PR, where

QPR�UP ¼ r1eað1 þ hÞt PR�UP�

ð1 þ hÞhUPtPR�UP þ ah

� td þ advPR

� þ asða þ adÞð1 þ hÞvPR

j UP�

l ;

QNT�PR ¼ r1eaht NT�PR�

hhNTtNT�PR þ asða þ adÞhvPR � tdað1 � hÞ

jNT

� l and QPR�UP < QNT�PR

(2) Bs UP#Q is the highest when n < nPR-UP, Bs

PR#Q is the highest when nPR-UP < n < nNT-PR, and Bs

NT#Q is the highest when n > nNT-PR, where

nPR�UP ¼ 1 ln½1=ð1 þ gÞ� ln

" 1 � g

1 þ g r1eað1 þ hÞtPR�UP�

ð1 þ hÞhUPtPR�UP þ h ah

� td þ advPR

� þ asða þ adÞð1 þ hÞvPR

i jUP

o Q

# ;

nNT�PR ¼ 1 ln½1=ð1 þ gÞ� ln

" 1 � g

1 þ g r1eaht

NT�PR� hhNTtNT�PR þ

h asða þ adÞhvPR � tdað1 � hÞ

i jNT

o Q

# ; and nPR�UP < nNT�PR:

Proposition 7. When the original profit-price ratio is sufficiently high, i.e. (1 e h) > {h[as(a þ ad) (h2sp2 þ sc2) þ hNTtNT-PR/jNT]/(tda)},

(1) Bs UP#Q is the highest when Q < QNT-PR, and Bs

PR#Q is the highest when Q > QNT-PR with QNT-PR in Proposition 6(1). Bs

NT#Q is al- ways smaller than either Bs

UP#Q or Bs PR#Q.

(2) Bs UP#Q is the highest when n < nNT-PR, and Bs

PR#Q is the highest when n > nNT-PR with nNT-PR in Proposition 6(2). Bs

NT#Q is al- ways smaller than either Bs

UP#Q or Bs PR#Q.

Figs.1 and 2 demonstrate the results of Propositions 6 and 7. The supplier's quantity-weighted sharing ratios (Bs

#Q) in Programs NT, UP, and PR are concave and increasing in the relationship length (n), and are linear and increasing in the supply volume (Q) from Equations (SB-BS-NT), (SB-BS-UP), and (SB-BS-PR). As shown in

Proposition 7 and Fig. 2, when the original profit ratio is sufficiently high, we do not have to consider Program NT because Bs

NT#Q is al- ways smaller than either Bs

UP#Q or Bs PR#Q.

Combining the results in Propositions 6 and 7 together with Propositions 2 and 5, we can construct Fig. 3 showing which benefit-sharing scheme yields a superior cost reduction perfor- mance. Fig. 3(a) and (b) include two dimensions representing the

(a) When the original profit ratio is low,

relationship length, n

UP

NT

PR

nPR-UP

Larger Reduction

QPR-UP

QNT-PR supply

volume, Q

(b) When the original profit ratio is high,

relationship length, n

UP

PR

nPR-UP

Larger Reduction

QPR-UP

supply volume,

Q

Fig. 3. Regions where each benefit-sharing scheme yields superior waste and cost reduction (a) When the original profit ratio is low, (b) When the original profit ratio is high.

(a) Behavior of Bs#Q in Q

QPR-UP Q

Bs#Q

BsUP#Q

UP PR

BsPR#Q BsNT#Q

(b) Behavior of Bs#Q in n

nPR-UP n

Bs#Q

BsUP#Q

UP PR

BsPR#Q

BsNT#Q

Fig. 2. Graphical presentation of Proposition 7 with a high original profit ratio.

S.H. Yoo et al. / Journal of Cleaner Production 237 (2019) 1177858

relationship intensity between the buyer and the supplier, the relationship length (n), and the contracted supply volume (Q), while nPR-UP and nNT-PR are strictly decreasing and convex with respect to QPR-UP and QNT-PR, respectively, i.e. [vnPR-UP/vQPR-UP] < 0, [v2nPR-UP/v(QPR-UP)2] > 0, [vnNT-PR/vQNT-PR] < 0, and [v2nNT-PR/v(QNT- PR)2] > 0, and vice versa.

To interpret the results in Fig. 3(a) and (b), we need to note three main points below, which explain the characteristics of Programs NT, UP, and PR.

- The required minimum amount of cost reduction for the benefit share, (co e cb), differs depending on the benefit- sharing scheme. We can obtain from Table 2 that (co e cb)

NT < (co e cb) PR < (co e cb)

UP, where co e cb ¼ co e co ¼ 0 in Program NT, co e cb ¼ co e ctUP ¼ po e p in Program UP, and co e cb ¼ co e ctUP ¼ h(po e p) in Program PR with 0 < h < 1. Therefore, the benefit-sharing schemes differently induce the supplier's effort.

- Since the cost target is derived from the market price, it shifts the external risk of price variation (sp

2) to the supplier. The effect of price variation differs depending on the benefit- sharing scheme, as seen in Equations (SB-BS-NT), (SB-BS- UP), and (SB-BS-PR). Bs

NT#Q is not affected at all, since Pro- gram NT does not incorporate the cost target scheme. However, the external risk is amplified in Programs UP and PR, as the relationship between the buyer and supplier in- tensifies by increasing n or Q.

- Since Program PR incorporates the ratio scheme, i.e. h ¼ co/ po, where 0 < h < 1, the effect of external risk is mitigated by adopting Program PR as seen in Equation (SB-BS-PR). The mitigation of external risk depends on the value of the original profit-cost ratio h (or the original profit-price ratio (1 e h)).

Considering the above, the implications of Fig. 3(a) and (b) are as follows.

- Program UP can induce the supplier's effort better by requiring highest waste reduction performance. However,

this is true only when the buyer maintains a non-strategic but transactional relationship with the supplier (small n or Q) such that the external price variation does not signifi- cantly affect the supply chain, as shown in Fig. 3(a) and (b).

- With a high profit ratio (1 e h) (or a low cost ratio h), as in Fig. 3(b), Program PR reduces the effect of external risk by incorporating the ratio scheme h, and dominates Program NT by inducing a better waste and cost reduction effort from the supplier. Therefore, the buyer needs to consider only the cost target schemes, Programs UP and PR, when the original profit ratio is high (or the original cost level is low).

- On the other hand, with a low profit ratio (1 e h) (or a high cost ratio h) as in Fig. 3(a), the external price variation in Program PR cannot be sufficiently mitigated, as seen in Equation (SB-BS-PR). Therefore, Program NT needs to be considered instead of Program PR when the relationship

Table 3 The results of comparative static analyses when the original profit-price ratio is sufficiently low and the joint cost reduction activity is sufficiently efficient ([: increasing; Y: decreasing; -: not affected).

Increase in: Bd NT#, Bd

UP#, Bd PR# Bs

NT#, Bs UP#, Bs

PR#

Inefficiency r1 Y [

Contribution td [ Y ts Y [

Risk aversion a Y Y ad Y [ as [ Y

Volatility sc 2 Y Y

sp 2 -, Y, Y -, Y, Y

S.H. Yoo et al. / Journal of Cleaner Production 237 (2019) 117785 9

intensity is significant (large n and Q), since Program NT is not affected at all by external risk from price variation.

We need to note that different benefit-sharing schemes need to be considered depending on the relationship intensity between supply chain members and the market condition to obtain better cost reduction performance, as shown in Fig. 3(a) and (b).

5. Comparative static analyses

In Proposition 5, we show the effect of relationship length and supply volume on cost reduction performance. In this section, we investigate the effect of other important environmental changes on the benefit-sharing ratio and subsequent cost reduction perfor- mance. We focus on a sufficiently efficient joint cost reduction ac- tivity (a sufficiently small r1) in a harsh market condition in which the buyer maintains a low original profit-price ratio (1 e h) (or a high cost-price ratio h), i.e. (1 e h) z 0. We obtain the comparative static analysis results summarized in Table 3 through partial dif- ferentiation of the benefit-sharing ratios Bd and Bs in each benefit- sharing program for the respective parameters.

The results in Table 3 can be interpreted as follows.

- If a supply chain's joint waste management project is not efficient relative to other projects (increasing r1), the enthusiastic participation of an internal function only causes significant opportunity losses of other activities. In this sit- uation, a rational buyer needs to encourage the external supplier's participation by offering a high benefit share.

- An agent yielding more contribution in waste and cost reduction (increasing td or ts) is compensated more. In particular, the contribution of the agent (td or ts) can increase as the importance of the component (c2), the marginal probability of attaining a low component cost ((ql)b), or the component cost gap (ch e cl) increases. However, it decreases as the marginal disutility change ((Dd)aa, (Dd)bb, or (Dd)ab for the operations department or (Ds)gg for the supplier) in- creases. Note that the effort of the operations department on two different subjects ((Dd)ab) makes it difficult to contribute much to the joint cost reduction. Thus, the buyer should provide an efficient and reasonable effort-sharing schedule of internal functions to induce strong waste reduction performance.

- When the buyer is risk averse (increasing a), it is reluctant to encourage supply chain members with an uncertain benefit. Similarly, if the agent becomes more risk averse (increasing ad or as), it will be reluctant to exert more effort to the joint

activity. Therefore, it needs to be compensated less than does the less risk-averse agent.

- When various uncertain factors surround a joint waste reduction activity (a high sc

2), it is rational that the risk- averse agents do not exert much effort on the activity, since it is difficult to predict the result. Thus, the buyer needs to remove the various factors increasing the uncertainty of the project before the initiation of a joint waste reduction project. It would be possible through a thorough investiga- tion of the internal cost structure and external cost drivers. The buyer also needs to carefully assess not only the capa- bility but also stability of the supplier's process, which affects the overall result of a joint activity.

- When the buyer uses the cost target as the appraisal basis for the benefit share, the cost reduction performance of each agent depends on the external market situation. This is since the cost target transfers the external market risk (price volatility sp

2) to the supply chain members. In this situation, if the external market condition is highly volatile, risk-averse supply chain members cannot put much effort into the joint activity. Moreover, owing to the high uncertainty of the project goal, it is also difficult for the buyer to guarantee a high benefit share and encourage supply chain members. In this situation, the supply chain needs to consider perfor- mance appraisal based on the original cost level (Program NT) rather than the cost target scheme (Program UP or PR).

6. Concluding remarks

In this study, we examined a collaborative waste and cost reduction activity in a supply chain in which the buyer motivates the internal operations department and the external supplier to reduce the supply chain's overall production cost. We considered various benefit-sharing schemes with and without a cost target. Then, we investigated which benefit-sharing scheme yields better waste and cost reduction performance depending on the relation- ship intensity between the buyer and the supplier.

We found important implications for the waste and cost man- agement for the sustainable operations through the analyses as follows. First, only when the buyer yields all the benefits of joint reduction effort to the supplier, the buyer can coordinate the entire supply chain. Thus, it is difficult to get the first-best agent effort levels in practice.

Second, however, the buyer can affect the hidden actions of the operations department and the supplier through the volume and length of the supply contract. Larger supply volume and a longer- term relationship lead to a higher effort level from each agent in waste reduction and hence better cost performance, regardless of the benefit-sharing scheme.

Third, the benefit sharing needs to be based on the contribution of each supply chain member in order to induce better perfor- mance. Therefore, a system precisely measuring the performance of each supply chain member should be prepared before the initiation of any joint innovation activities.

Fourth, the benefit-sharing scheme producing superior cost reduction performance varies depending on the relationship in- tensity between the buyer and the supplier. When the relationship is weak and not strategic, where a small supply volume and a short relationship length are preferred, the cost target to maintain unit profit margin can generate superior cost reduction performance. However, if the relationship between the buyer and the supplier becomes more strategic and stronger, the cost target scheme maintaining the profit ratio can induce better performance in a favorable situation in which the original profit ratio is significantly

S.H. Yoo et al. / Journal of Cleaner Production 237 (2019) 11778510

high. On the other hand, when a supply chain is not in a favorable situation and the original profit ratio is relatively low, appraising the performance based on the amount of waste and cost reduction itself without the cost target induces superior cost reduction per- formance when there is a strong strategic buyer-supplier relationship.

Finally, when the buyer has a portfolio of projects, the relative efficiency of joint innovation activities always needs to be exam- ined carefully. Inefficient projects can consume valuable resources that could be used for other beneficial projects.

Appendix. Proofs of Propositions

Proof of Proposition 1. Propositions 1(1) and 1(2) are straight- forward from Equations (FB-A), (FB-B), (FB-G), (FB-BD-NT), (FB-BS- NT), (FB-BD-UP), (FB-BS-UP), (FB-BD-PR) and (FB-BS-PR). ,

Proof of Proposition 2. In Equations (ICI-A), (ICI-B) and (ICS-G), (Dd)a, (Dd)b and (Ds)g increase in their respective effort levels a, b and g, and both Bd and Bs are defined in [0, l] with positive Q, (ql)b and (ql)g. This establishes Proposition 2. ,

Proof of Proposition 3. By letting (FB-A) ¼ (ICI-A) and (FB-B) ¼ (ICI-B), we get Bd ¼ {l e r1/(c1Q)} and Bd ¼ {l e r1/((ql)b$c2(ch e cl) Q)}. To achieve unique Bd, c1 ¼ (ql)b$c2(ch e cl). Similarly, we get Bs ¼ l by taking (FB-G) ¼ (ICS-G). These establish Proposition 3(1). By summing up Bd and Bs in Proposition 3(1), we obtain Bd þ Bs ¼ {2l e r1/(c1Q)}. To have Bd, Bs and (Bd þ Bs) in [0, l], we need r1 ¼ c1lQ ¼ (ql)b$c2(ch e cl)lQ, and hence Bd ¼ 0 and Bs ¼ l. Therefore, Proposition 3(2) holds. ,

Proof of Proposition 4. In Programs NT and UP, Bd NT# e Bd

NT* > 0 when td > {[tsaas(a þ ad)sc2lQ þ r1e(aadþaasþadas) (ts þ (a þ as) sc 2)]/[ad(a þ as) (ts þ (a þ as)sc2)lQ]},

Bs NT# e Bs

NT* > 0 when ts > {a[tdad(a þ as)lQ e r1e(aadþaasþadas)]sc2/ [as(a þ ad) (tdþ(a þ ad)sc2)lQ]},

Bd UP# e Bd

UP* > 0 when td > {[tsaas(a þ ad) (sp2þsc2) lQþr1e(aadþaasþadas) (tsþ(a þ as) (sp2þsc2))]/[ad(a þ as) (tsþ(a þ as) (sp

2þsc2))lQ]}, and

Bs UP# e Bs

UP* > 0 when ts > {a[tdad(a þ as)lQ e r1e(aadþaasþadas)](sp2þsc2)/[as(a þ ad) (tdþ(a þ ad) (sp2þsc2))lQ]}

In Program PR, Bd PR# e Bd

PR* > 0 when (1 e h) < {ad (a þ as) (h2sp

2þsc2)/(haassp2)} and td > {[tsa (as (a þ ad) (hsp2þsc2) e (aadþaasþadas)h (1 e h)sp2)lQþr1e (aadþaasþadas) (tsþ(a þ as) (h2sp

2þsc2))](h2sp2þsc2)/[(ad (a þ as) (h2sp2þsc2) e aash (1 e h)sp2) (tsþ(a þ as) (h2sp2þsc2))lQ]}, and

Bs PR# e Bs

PR* > 0 when (1 e h) < {as(a þ ad) (h2sp2þsc2)/(haadsp2)} and ts > {[tda(ad(a þ as) (hsp2þsc2) e (aadþaasþadas)h(1 e h)sp2)lQ e r1ea(aadþaasþadas) (h2sp2þsc2)](h2sp2þsc2)/[(as(a þ ad) (h2sp2þsc2) e aadh(1 e h)sp

2) (tdþ(a þ ad) (h2sp2þsc2))lQ]}.

Therefore, Proposition 4 holds. ,

Proof of Proposition 5. It is straightforward that Bs NT#Q, Bs

UP#Q or Bs PR#Q increases in n and Q since [vl/vn] > 0. Thus, Proposition 5

holds. ,

Proof of Proposition 6. By comparing Bs #Q in Programs NT, UP

and PR, we obtain the followings:

(Bs NT# e Bs

UP#)Q ¼ {(sp2/(jNTjUP))[(td(a þ as) (tdts e aad(sp2þsc2)sc2)þ tsas(a þ ad) (tdsc2þ(tdþ(a þ ad)sc2) (sp2þsc2)))lQ e r1eatNT-UP]},

(Bs PR# e Bs

UP#)Q ¼ {((1 e h)sp2/(jPRjUP))[((1þh)hUPtPR- UPþ(ah(tdþad(h2sp2þsc2))þas(a þ ad) (1þh) (h2sp2þsc2))jUP)lQ e r1ea(1þh)tPR-UP]}, and

(Bs NT# e Bs

PR#)Q ¼ {(hsp2/(jNTjPR))[(hhNTtNT-PRþ(as(a þ ad)h(h2sp2þsc2) e tda(1 e h))j

NT)lQ e r1eat NT-PR]}.

Let A ¼ aadþaasþadas. Then, jNT ¼ {tdtsþ(td (a þ as)þts (a þ ad)) sc 2þA (sc2)2}, jUP ¼ {tdtsþ(td (a þ as)þts (a þ ad)) (sp2þsc2)þA

(sp 2þsc2)2}, hNT ¼ {td (a þ as)þas (aþad)sc2}, hUP ¼ {td (a þ as)þas

(aþad) (sp2þsc2)}, hPR ¼ {td (a þ as)þas (aþad) (h2sp2þsc2)}, tNT- UP ¼ {tdts e Asc2 (sp2þsc2)}, tPR-UP ¼ {tdts e A (sp2þsc2) (h2sp2þsc2)}, and tNT-PR ¼ {tdts e Asc2 (h2sp2þsc2)}. tNT-UP, tPR-UP and tNT-PR are all posi- tive under the assumption that td and ts are sufficiently large to

satisfy tdts > A (sp 2þsc2)2.

If we suppose the term (hhNTtNT-PRþ(as (a þ ad)h (h2sp2þsc2) e tda (1 e h))jNT) > 0 in (Bs

NT# e Bs PR#)Q, we obtain the condition of (1 e h)

in Proposition 6. Then, it is straightforward to identify the thresh-

olds which divide the regions of Q where Bs #Q of each Program is

superior to the other. We obtain QPR-UP and QNT-PR in Proposition

6(1), and QNT-UP ¼ {(r1eatNT-UP)/[(hNTtNT-UPþas (a þ ad) (sp2þsc2)jNT) l]} where QPR-UP < QNT-UP < QNT-PR. Bs

NT#Q > Bs UP#Q if Q > QNT-UP.

Otherwise, Bs NT#Q < Bs

UP#Q. Bs PR#Q > Bs

UP#Q if Q > QPR-UP. Otherwise,

Bs PR#Q < Bs

UP#Q. Bs NT#Q > Bs

PR#Q if Q > QNT-PR. Otherwise,

Bs NT#Q < Bs

PR#Q. Combining the results above and using QPR-UP < QNT-

UP < QNT-PR, Proposition 6(1) is established. By following the similar track to the Proof of Proposition 6(1)

and using l ¼ [1 e (1/(1þg))n]/[1 e (1/(1þg))], we obtain Bs NT#Q > Bs

UP#Q if n > nNT-UP, Bs PR#Q > Bs

UP#Q if n > nPR-UP, and

Bs NT#Q > Bs

PR#Q if n > nNT-PR with nNT-UP ¼ {ln [1 e (g/(1þg)) ((r1eatNT- UP)/((hNTtNT-UPþas (a þ ad) (sp2þsc2)jNT)Q))]/ln [1/(1þg)]} and nPR- UP < nNT-UP < nNT-PR. This establishes Proposition 6(2). ,

Proof of Proposition 7. Based on the results in Proposition 6, Bs NT#Q < Bs

PR#Q if (1 e h) follows the condition in Proposition 7. This establishes Proposition 7. ,

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