Analysis of supply contracts with quantity flexibility

16
Global Optimization Strategy
• What is the best strategy for the entire supply chain?
• Treat both supplier and retailer as one entity
• Transfer of money between the parties is ignored
– Summer season sale price of a swimsuit is $125 per unit.
– Wholesale price paid by retailer to manufacturer is $80 per unit.
– Salvage value after the summer season is $20 per unit
• Optimal order quantity depends on marginal profit and marginal loss but not on the fixed cost.
• Retailer optimal policy is to order 12,000 units for an average profit of $470,700.
• Retailer’s marginal profit for selling a unit during the season, $45, is smaller than the marginal loss, $60, associated with each unit sold at the end of the season to discount stores.
• This order increase leads to increased manufacturer’s profit of $481,375

售电公司电力结算员工作流程及内容1.电力结算员负责处理客户用电数据。

The power settlement clerk is responsible for processing customer electricity usage data.2.根据客户用电数据，计算客户的电力消耗。

Calculate the customer's power consumption based on their electricity usage data.3.审核客户用电数据的准确性和完整性。

Audit the accuracy and completeness of customerelectricity usage data.4.处理客户用电数据的异常情况。

Handle exceptions in customer electricity usage data.5.跟踪客户用电数据的变动情况。

Track changes in customer electricity usage data.6.与其他部门协调，确保客户用电数据的准确性。

Coordinate with other departments to ensure the accuracyof customer electricity usage data.7.制作电力结算报表，用于向客户说明他们的电力消耗情况。

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Production,Manufacturing and LogisticsDouble marginalization and coordination in the supply chain with uncertain supplyXiang Li a ,Yongjian Li b ,⇑,Xiaoqiang Cai caCollege of Economic and Social Development,Nankai University,Tianjin 300071,PR China bBusiness School,Nankai University,Tianjin 300071,PR China cDepartment of Systems Engineering &Engineering Management,The Chinese University of Hong Kong,Shatin,NT,Hong Konga r t i c l e i n f o Article history:Received 6August 2011Accepted 26October 2012Available online 11November 2012Keywords:Supply chain management Uncertain supply Contract designDouble marginalizationa b s t r a c tThis paper explores a generalized supply chain model subject to supply uncertainty after the supplier chooses the production input level.Decentralized systems under wholesale price contracts are investi-gated,with double marginalization effects shown to lead to supply insufficiencies,in the cases of both deterministic and random demands.We then design coordination contracts for each case and find that an accept-all type of contract is required to coordinate the supply chain with random demand,which is a much more complicated situation than that with deterministic demand.Examples are provided to illustrate the application of our findings to specific industrial domains.Moreover,our coordination mech-anisms are shown to be applicable to the multi-supplier situation,which fills the research gap on assem-bly system coordination with random yield and random demand under a voluntary compliance regime.Ó2012Elsevier B.V.All rights reserved.1.IntroductionSupply uncertainty is a major issue in both the industrial and academic worlds.In traditional manufacturing processes,stochas-tic capacity and random yield are regarded as the main causes of supply uncertainty.In the remanufacturing field,uncertainty with-in the supply channel also stems from used product acquisition.These supply uncertainties pose great challenges to supply chain management,and result in substantial revenue losses.In a decen-tralized system,channel performance could be even worse because of the different,and usually conflicting,objectives that the supply chain members attempt to optimize.Therefore,it has been a signif-icant problem to design coordination schemes to increase supply chain performance and to properly allocate the supply risk be-tween the channel members.This paper explores the underlying double marginalization of a supply chain with supply uncertainty and the related problem of coordination contract design.Specifically,a buyer procures a prod-uct from a supplier,who is confronted with uncertain production quantity (output)after deciding a certain production input level because of random disturbance in the production/delivery/supply process.The supplier’s modeling setting (partially or fully)general-izes many of the uncertain supply models in literature.Examples include (i)random yield,such as the models of Gerchak et al.(1994)and Li and Zheng (2006);(2)random capacity,such as those of Ciarallo et al.(1994)and Hsieh and Wu (2008);(3)random deteriorating loss,such as that of Cai et al.(2010);and (4)random used product acquisition,such as that of Kaya (2010).We explore the supply chain model in such a generalized setting and show that double marginalization effect is translated into a lower production input level from the supplier,which leads to supply insufficiency for the buyer.We also investigate coordination mechanisms for the cases of deterministic and random demand.A simple shortage penalty contract is designed to coordinate the supply chain under conditions of deterministic demand,but the coordination issue becomes more complicated when there is a random demand.Our study thus stands on the interface between supply uncer-tainty and supply chain coordination,both of which have attracted a vast amount of research.Most of the papers considering supply uncertainty focus on the production planning problems of uncer-tain production capacity,random manufacturing yield,or unreli-able supplier,such as those of Gerchak et al.(1988),Parlar and Perry (1996),Gupta and Cooper (2005),Chopra et al.(2007),and Pac et al.(2009),among others.The subject of supply chain coordi-nation has been investigated by Muson and Rosenblatt (2001),Cachon and Lariviere (2005),Li and Wang (2007),Chen and Xiao (2009),and Luo et al.(2010),to name just a few.We also refer the reader to Cachon (2003)for an excellent survey of this field.Other than the aforementioned studies,the works most related to this paper involve the study of a supply chain model under con-ditions of uncertain supply from the supplier,which constitutes a rather limited body of literature.Zimmer (2002)investigates the supply chain coordination issue between a buyer facing determin-istic demand and a supplier facing uncertain capacity equal to the sum of newly built capacity and a random leftover.He and Zhang (2008)consider the risk-sharing problem between a retailer and a0377-2217/$-see front matter Ó2012Elsevier B.V.All rights reserved./10.1016/j.ejor.2012.10.047⇑Corresponding author.Tel.:+862223505341.E-mail addresses:xiangli@ (X.Li),liyongjian@ (Y.Li),xqcai@.hk (X.Cai).supplier subject to random production yield and a more expensive emergency production option,but do not address the supply chain coordination issue.In a subsequent work,He and Zhang(2010)fur-ther explore a supply chain with random yield production and a yield-dependent secondary market in which the product is ac-quired or disposed of.Serel(2008)considers a supply chain in which the retailer orders products from one unreliable supplier and one reliable manufacturer,thereby analyzing the retailer’s ordering problem in conjunction with the manufacturer’s pricing problem.Keren(2009)considers a supply chain in which the dis-tributor faces a known demand and orders from the producer sub-ject to a random production yield,and shows that the distributor mayfind it optimal to order more than the demand due to supply uncertainty under a uniform distribution.Li et al.(2012)further extends the problem into a generalized distribution of yield ran-domness,and specifies the condition under which ordering more is optimal.Xu(2010)investigates a supply chain model in which the retailer adopts an option contract and the supplier conforms with random yield production and a more expensive emergency production.None of the above papers,except Zimmer(2002),ad-dresses the supply chain coordination issue.In addition,a number of recent papers explore issues of information asymmetry in set-tings of supply uncertainty based on incentive theory,such as Yang et al.(2009)and Chaturvedi and Martinez-de-Albeniz(2011).There is also research on the supply chain coordination of an assembly system with a random yield supply.Gurnani and Gerchak(2007),for example,explore an assembly system with random yield of component production and deterministic demand for thefinal product.They assume the voluntary compliance of the suppliers and propose two coordination contracts,one with a pen-alty only for each undelivered item and the other with an extra penalty for the worst performing supplier.Yan et al.(2010)extend Gurnani and Gerchak’s model to the case of a positive salvage value and asymmetric suppliers,and derive a new coordination scheme that also falls within a voluntary compliance regime.Guler and Bilgic(2009)explore a similar problem under conditions of both random yield and random demand,but their model assumes forced compliance,i.e.,the suppliers have to make the input pro-duction quantities equal to the manufacturer’s ordered quantities.In contrast,the main contributions of our paper can be summa-rized as follows:(1)We prove theoretically that the wholesale price contractundermines the performance of the entire supply chain by lowering the supplier’s production input level,which is shown as the double marginalization effect in the supply chain with uncertain supply.(2)We consider both deterministic and random demands,pro-vide coordination mechanisms for both cases,and point out the essential differences between them.In the case of deterministic demand,a shortage penalty contract could achieve channel coordination and arbitrary profit allocation, as the buyer will not accept more units than the known demand.In the case of random demand,in contrast,coordi-nation contracts require the buyer to accept all yielded units from the supplier in response to the random disturbance on the demand side.(3)Our results are derived in a very generalized setting and arethus applicable to more specific industrial cases,such as ran-dom yield,uncertain capacity,and stochastic used product collection.Moreover,they can easily be extended into a mul-tiple-supplier scenario.In particular,our model covers the problem of a decentralized assembly system with suppliers subject to random component yields,which is related to the aforementioned papers:Gurnani and Gerchak(2007), Guler and Bilgic(2009),and Yan et al.(2010).However,aswe have reviewed,Gurnani and Gerchak(2007)and Yan et al.(2010)only consider the case of deterministic demand, while Guler and Bilgic(2009)explore the case of random demand but assume forced compliance,and thus their derived schemes can be applied only when the manufacturer is substantially pared to them,our coordina-tion contracts are based on voluntary compliance and unify the cases of deterministic and random demands.To the best of our knowledge,this paper is among thefirst to delve into the coordination mechanisms of an assembly system with both random yields and random demand and under a volun-tary compliance regime.Furthermore,our model is analyzed under a more general setup compatible with,e.g.,non-linear production costs and additive production risk,and thus can applied to wider industrial domains.The reminder of the paper is organized as follows.In Section2, we describe the problem.Sections3and4investigate the cases of deterministic demand and random demand,respectively,explore the double marginalization effects,and derive the coordination contracts.Section5provides examples to illustrate applications to specific industrial cases,and Section6further extends the model to the case of multiple suppliers.Section7concludes the paper with directions for future research.2.Problem descriptionConsider a supply chain consisting of a supplier and a buyer. The buyer contracts the supplier to provide a specific product and sells it on the market to meet deterministic demand d or ran-dom demand D.The supplier determines production input level e, which depending on the specific industrial scenario,could repre-sent the product development effort,invested capacity,planned manufacturing quantity,or any other determinants of production.1 Due to the random disturbance in the production process,the output of production quantity S(e)is stochastic and sensitive to input level e.The production cost for the supplier C(e)satisfies C0(e)>0and C00(e)P0,which implies that the marginal production cost is non-decreasing as the production input level is raised.Such a (non-strictly)concave cost is a commonly used assumption in the production planning literature(see, e.g.,Veinott,1964;Morton, 1978;Smith and Zhang,1998;Yang et al.,2005).In our model,it re-flects the idea that the supplierfirst utilizes his most efficient pat-tern of production.However,as the production volume is asked to increase,it exhausts the most attractive resources that are available to the supplier and he has to pay more in order to acquire additional resources to generate the extra output.We assume that the production quantity can be expressed by (1)S(e)=s(e)+e or(2)S(e)=s(e)Áe,where s(e)is a deterministic function of the production input level and e is an independent ran-dom variable withfinite support,denoting the yield randomness. These are called the additive and multiplicative forms,respec-tively,both of which are widely used in the literature.Let f e(Á), F e(Á)and FÀ1eðÁÞbe the density,distribution and inverse distribution functions of e,respectively.Also suppose that s0(e)>0and s00(e)60, which implies that the marginal expected production quantity is non-increasing as the production input level is raised.Without any loss of generality,we assume linear function s(e)=a+b e, b>0,and normalize the yield randomness into E e=0or E e=1 for the additive or multiplicative form,respectively.In fact,for 1Although in practice the decisions concerning product development,capacity reservation,and manufacturing quantity plan can be made at different time points, and thus have different degrees of forecast accuracy,our model can be applied as long as these decisions are appropriately abstracted and meet the required theoretical assumptions.Please see Section4.3for relevant examples.X.Li et al./European Journal of Operational Research226(2013)228–236229any arbitrary function s (e ),let s =s (e )be the new variable repre-senting the production input level and C (s )the new cost function.We then have C 0(s )>0,C 00(s )P 0,and S (s )=s +e or S (s )=s Áe ,and thus the expected production quantity is a linear function.The de-tails can be found in the Supplementary material of this paper.Other parameters include exogenous selling price p and the hold-ing cost of leftover unit,h ,which can be negative if the leftover unit incurs salvage value.We assume that p >Àh .The interaction between the supply chain members is as fol-lows.As the Stackelberg leader,the buyer first proposes to the sup-plier an incentive contract with payment T ,which is related to the realization of production quantity S (e ).As the follower,the sup-plier accordingly chooses production input level e .After S (e )is realized,the supplier delivers a partial or full quantity of units to the buyer,according to the prescription in the contract.Finally,demand is realized (if it is random),and the buyer meets that de-mand.Note that we assume voluntary compliance in the supplier’s decision,which means the supplier freely chooses the production input level without any contracting obligation.In many industries,it would be very difficult or costly for the buyer to monitor the sup-plier’s production input level,thus the supply chain system should indeed be operated under a voluntary compliance regime.Further-more,we assume that both the supplier and the buyer are risk-neutral and seek to maximize their own expected profits,respectively,with information on the system parameters as com-mon knowledge.3.Deterministic demandIn the case of deterministic demand d ,we first investigate the optimization problem for the centralized supply chain,which serves as a benchmark for the decentralized case.The expected profit of the centralized supply chain isp c ðe Þ¼E f p min ½d ;S ðe Þ Àh ½S ðe ÞÀd þÀC ðe Þg :ð1ÞLemma 1.(1)There is a unique e Ãc that maximizes the expected profitof the centralized supply chain,and (2)e Ãc is increasing with p and decreasing with h .Lemma 1shows the uniqueness of the optimal production input level e Ãc that maximizes the expected profit of the entire supply chain,and it is increasing with the selling price and decreasing with the holding cost.In the following,this maximized supplychain profit is assumed to be positive,i.e.,p c e Ãc ÀÁ>0.We now ex-plore the decentralized supply chain.The simplest scheme,which is also widely adopted in practice,is a wholesale price contract with the buyer prescribing an order quantity q and paying whole-sale price w 2(Àh ,p )for each delivered unit in the order.Hence,the payment to the supplier is T (w ,q )=w min[S (e ),q ],and the sup-plier’s expected profit isp s ðe Þ¼E f w min ½q ;S ðe Þ Àh ½S ðe ÞÀq þÀC ðe Þg :ð2ÞLemma 2.For any order quantity q from the buyer,there is a unique optimal production input level e d (q )for the supplier characterized byðw þh Þ@E min ½q ;S ðe Þ¼b h þC 0ðe Þ:ð3ÞGiven the above optimal response from the supplier,the buyer can strategically choose an order quantity q which is no less than the deterministic demand d .In other words,the buyer anticipates the supplier’s response e d (q )characterized by (3)and determines order quantity q to maximizep b ðq Þ¼pE min ½d ;S ðe d ðq ÞÞ ÀhE ½min ½q ;S ðe d ðq ÞÞ Àd þÀwE min ½q ;S ðe d ðq ÞÞ ¼ðp þh ÞE min ½d ;S ðe d ðq ÞÞ Àðw þh ÞE min ½q ;S ðe d ðq ÞÞ ;ð4Þwhere the second equality is because the order quantity q should be no less than the deterministic demand d .We reformulate the above buyer’s expected profit into the func-tion of the induced production input level e as follows:p b ðe Þ¼ðp þh ÞE min ½d ;S ðe Þ Àðw þh ÞE min ½q d ðe Þ;S ðe Þ ;ð5Þwhere q d (e )is characterized by (3).Let e Ãd be the optimally induced production input level under the wholesale price contract,which maximizes the objective function (5).The following result shows the properties of the optimal production input levels in the decen-tralized case.Proposition 1.We have:(1)e Ãd <e Ãc ;(2)e Ãd is increasing with p .Proposition 1indicates that the optimal production input level in the decentralized supply chain is increasing with the selling price,which is an intuitive result.More importantly,it shows that this input level is lower than that in the centralized case,tending towards a smaller supply quantity.It has been well-known that double marginalization generally refers to the channel barrier that causes a lower transfer/delivery amount of products through the channel.This usually exhibits as a result of a higher selling price set by the retailer or a less order quantity submitted from the retailer (see e.g.,Cachon,2003;Dellarocas,2012).However,in a supply chain with uncertain supply,such a lower transfer/delivery amount may not necessarily occur.For example,under deterministic demand d the retailer may submit an order higher than d (see Li et al.,2012),and thus the ac-tual transfer/delivery amount within the channel can be even lar-ger than that in the centralized system.As we can see,the double marginalization in our model is the lower production input level as shown by Proposition 1and the resulting insufficient supply,as compared to that in the centralized optimum.This effect is differ-ent from the traditional one,although the root for such phenome-non is also the double price distortion that occurs when two successive vertical layers in a supply chain independently stack their price–cost margins under a price-only contract,as the term ‘‘double marginalization’’implies.With an appropriate coordination scheme,the systematically optimal decision can be induced and the maximal profit achieved,even if the supply chain members act in a decentralized way.Specifically,we derive a shortage penalty contract T (w ,b )=w min[S (e ),d ]Àb [d ÀS (e )]+,in which the supplier is not only paid wholesale price w for each delivered unit within the demand d ,but is also charged penalty b for each order shortage for the demand.The following result shows that this contract is an imple-mentable coordination scheme that achieves both optimal system performance and flexible profit allocation.Proposition 2.For any k 2(0,1),letw üp Àk p c e Ãc ÀÁ=db ük pc e ÃcÀÁ=d :8<:ð6ÞThen,we have:(1)w ⁄>0,b ⁄>0;and(2)the shortage penalty contract T (w ⁄,b ⁄)coordinates the sup-ply chain with deterministic demand d ,and the resulting expected profit shares of the buyer and supplier are k and 1Àk ,respectively.230X.Li et al./European Journal of Operational Research 226(2013)228–236We have two remarks on the contracts in Proposition1.First, one should note that our contracts can coordinate the supply chain under voluntary compliance since the monetary transfer is based on the realized delivery from the supplier.That is,the supplier is allowed to freely choose the production input,although in the equilibrium resulted from the contract he will rationally choose the production input level that is systematically optimal.In prac-tice,such contracts are more advantageous than those under forced compliance since in many cases the production inputs are not verifiable,and thus the coordination contracts under forced compliance are not applicable(see,for example,Cachon and Lariviere,2001,the case of unverifiable supplier’s capacity input). More importantly,as Cachon(2003)points out,any contract that coordinates a supply chain with voluntary compliance surely coor-dinates the supply chain with forced compliance,but the reverse is not true.We refer to Cachon(2003)and Bolandifar et al.(2010)for more detailed discussion on the concept of compliance regime.In addition,the contracts in Proposition1not only coordinate the supply chain but also leavesflexibility for profit allocation.In general,the particular profit split depends on thefirms’relative bargaining power.As the buyer’s bargaining position becomes stronger,one would anticipate k to increase.In the extreme case, if the buyer is a completely dominating party in the channel she might leave to the supplier only the profit he earns in the uncoor-dinated case to ensure the supplier’s participation in the coordina-tion contract.In the less extreme cases,cooperative game theories such as Nash-bargainning solutions may be adopted to determine what kind of allocation k is a fair one.We refer to Muthoo(1999) for a more detailed discussion on the issue of profit allocation un-der cooperation.4.Random demand4.1.Double marginalizationWe now turn our attention to the case in which the buyer faces random demand D,which is independent of supply randomness e. Let f D(Á),F D(Á)and FÀ1DðÁÞbe the density,distribution and inverse dis-tribution functions of D,respectively.In this subsection we will show how double marginalization is manifested under the whole-sale price contract.The expected profit of the centralized supply chain ispcðeÞ¼E f p min½D;SðeÞ ÀhÁ½SðeÞÀD þÀCðeÞg:ð7ÞLemma3.(1)There is a unique eÃcthat maximizes the expected profitof the centralized supply chain(7);(2)eÃcis increasing with p and decreasing with h.Lemma3shows that the uniqueness of the optimal productioninput level eÃcfor the centralized supply chain under random de-mand,and it is increasing with the selling price and decreasing with the holding cost.The results are similar to the case of deter-ministic demand.In the decentralized case,the wholesale price contract T(w,q)=w min[S(e),q]is adopted.The supplier’s expected profit p s(e)and his optimal production input level e d(q)are expressed by(2)and(3),respectively,for given order quantity q.The buyer’s problem is to choose order quantity q to maximize her expected profitpbðqÞ¼E f p min½D;Sðe dðqÞÞ;q Àh½min½Sðe dðqÞÞ;q;q ÀD þÀw min½q;Sðe dðqÞÞ;q g¼ðpþhÞE min½D;Sðe dðqÞÞ;q ÀðwþhÞE min½q;Sðe dðqÞÞ ;ð8Þwhich can be reformulated into the function of the induced produc-tion input level e as follows:pbðeÞ¼ðpþhÞE min½D;SðeÞ;q dðeÞ ÀðwþhÞE min½q dðeÞ;SðeÞ ;ð9Þwhere q d(e)is characterized by(3).Let qÃdand eÃdbe the optimal or-der quantity and its induced production input level,which maxi-mize(8)and(9),respectively.We have the following result.Proposition3.(1)If p b(q)in(8)is a quasi-concave function,theneÃd<eÃc,and eÃdis increasing with p.(2)When C00(e)=0,p b(q)in(8)is a strictly concave function.Proposition3shows that double marginalization also occurs and manifests at a lower production input level,which is similar to the case of deterministic demand.The condition of quasi-concavity for the buyer’s objective function is to ensure the optimal order quan-tity(and the induced production input level)to be unique.This con-dition holds in the case of linear production cost,as indicated in Proposition3.For other cost functions,we point out that although it is very difficult to theoretically prove that the quasi-concavity holds in general,extensive numerical experiments have shown that it is true for many convex polynomial functions of C(e).Proposition 3also shows that the optimal production input level in decentral-ized case is increasing with the selling price.The above results are valid when an order quantity q<+1is ap-pointed as a decision variable in wholesale price contract T(w,q), while the wholesale price w2(Àh,p)can be any given plausible value.In fact,contract T(w,1)can be adopted when the buyer des-ignates a specific supplier for the product supply,which implies that the buyer will accept as many units as the supplier pro-duces/provides and pays for them at a unified wholesale price w. We call this type of payment scheme with q=1as an accept-all type of wholesale price contract for the buyer,and it can be a prac-tical policy mechanism in some cases.For example,in the reman-ufacturing industry if a remanufacturer outsources the acquisition activity of used product to a specialized collector,then this collec-tor may be required to deliver all acquired units to the remanufac-turer,and the accept-all contract T(w,1)can be used.Similar situation also occurs in agriculture in China,where the government encourages the downstreamfirm to provide the farmers(or the production base)a contract with no order limit on the quantity of agricultural products given a certain price mechanism.Under the accept-all type of wholesale price contract T(w,1), the supplier determines the production input level e to maximize p sðeÞ¼E½wSðeÞÀCðeÞ :ð10ÞThe buyer anticipates the supplier’s optimal response e d(w)and determines the wholesale price w to maximizepbðwÞ¼E f p min½D;Sðe dðwÞÞ Àh½Sðe dðwÞÞÀD þÀwSðe dðwÞÞg;ð11Þwhich can be reformulated into the function of the induced produc-tion input level e as follows:pbðwÞ¼E f p min½D;SðeÞ Àh½SðeÞÀD þÀw dðeÞSðeÞgð12Þwhere w d(e)is the inverse function of e d(w)that maximizes(10).LetwÃdand eÃdbe the optimal wholesale price and its induced induced production input level,which maximize(11)and(12),respectively. We have the following result.Corollary1.Under the accept-all wholesale price contract T(w,1),we have eÃd<eÃcwhen C00(e)>0.Corollary1shows that the double marginalization effect is also manifested as a lower production input level with accept-all wholesale price contract T(w,1),in which case the wholesale price w becomes a decision variable.The required condition C00(e)>0X.Li et al./European Journal of Operational Research226(2013)228–236231。

供货产品出现质量问题的相关处理措施1.我们会立即联系供应商，要求退换货物。

We will immediately contact the supplier to request a return or exchange of the goods.2.对有质量问题的产品进行逐一检查，确认问题的具体原因。

Conduct a detailed inspection of the products withquality issues to identify the specific cause of the problem.3.如果是供应商责任造成的质量问题，我们将要求其承担相应的责任和赔偿。

If the quality problem is caused by the supplier, we will request them to take corresponding responsibility and compensation.4.暂停或暂时调整相关产品的供货计划，以确保不再出现质量问题。

Suspend or temporarily adjust the supply plan of the relevant products to ensure that no more quality issues occur.5.对于已经交付的有质量问题的产品，我们会与客户携手处理问题，确保客户满意。

We will work with the customers to handle the issues ofthe delivered products with quality problems to ensure customer satisfaction.6.加强对供货产品的质量控制，确保不再出现类似的问题。

Strengthen the quality control of the supplied productsto ensure that similar problems do not occur again.7.对于导致质量问题的生产工艺或原材料，我们会与供应商一起寻求解决方案。