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1、第五章 供应链整合与配送战略Supply Chain Integration,供 应 链 管 理Supply Chain Management,2,本章内容,供应链整合 推一拉式系统 需求驱动战略 互联网对供应链战略的影响 配送策略 集中还是分散控制 中心和地方机构,3,简介,供应链整合的挑战是如何协调供应链的活动,以使企业能够改善营运绩效,包括降低成本、增加服务水平、减少牛鞭效应、有效善用资源,以及能够快速反应市场所带来的变化 这些挑战需要将供应链的前端顾客需求整合到供应链的后端生产与制造,4,供应链整合的机会和挑战,基于推式的供应链、基于拉式的供应链、以及推式拉式供应链等不同策略 产品及产
2、业与供应链战略匹配的框架 需求驱动的供应链战略 因特网对供应链整合的影响 有效的分销策略,5,推式、拉式与推式拉式的系统,供应链网络通常会被归类为推式或拉式的系统,这个起源可能来自于20世纪80年代的制造改革 当时,制造系统被分为这两大类 在最近几年,许多公司开始采用一种混合推式拉式的供应链模式,6,The Old Paradigm: Push Strategies基于推式的供应链(1),生产预测是以长期的预测为基础 通常制造商以从零售商那里收到的订单来预测顾客需求 Production decisions based on long-term forecasts Ordering decis
3、ions based on inventory & forecasts 基于推式的供应链会花较长的时间反应市场的变动 此外,牛鞭效应导致了资源的未充分利用,因为规划及管理变得更加困难 The bullwhip effect: Excessive inventory Excessive production variability Poor service levels,7,The Old Paradigm: Push Strategies基于推式的供应链(2),例如制造商如何决定产能: 如果产能是以颠峰需求为依据,那代表大部份的时间制造商的昂贵资源将被闲置 若产能是以平均需求为依据,那代表在颠
4、峰状态时,制造商将会需要额外且昂贵的产能 在一个基于推式的供应链中,通常可以发现运输成本提高,库存水平上升及或高的制造成本,都是紧急的生产转换(Changeover)所导致的,8,A Newer Paradigm: Pull Strategies基于拉式的供应链(1),生产和分销是以需求为导向,因此生产是以实际顾客需求,而非以预测资料为依据 公司在真正的拉式系统中是不需持有任何库存,并且只要针对特定订单作出响应即可 为达到上述目的,供应链采用快速信息流动机制来传输顾客需求给供应链中的不同成员(如POS资料) Pull Strategies result in: Reduced lead tim
5、es (better anticipation) Decreased inventory levels at retailers and manufacturers Decreased system variability Better response to changing markets,9,A Newer Paradigm: Pull Strategies 基于拉式的供应链(2),在一个基于拉式的供应链中,当与一个对等的基于推式的系统相比,通常可以看到系统库存水平的大幅减少、管理资源能力的增强与系统成本的下降 当提前期很长,以至于响应需求讯息是不切实际时,基于拉式的供应链通常较难达成
6、在基于拉式的供应链中,通常也较难从制造及运输的规模经济中获益,因为系统并不是很早就作规划的,10,推式拉式供应链(1),A shift from a Push System. Production decisions are based on forecast to a Push-Pull System Initial portion of the supply chain is replenished based on long-term forecasts For example, parts inventory may be replenished based on forecasts
7、Final supply chain stages based on actual customer demand. For example, assembly may based on actual orders,11,推式拉式供应链(2),在一个推式拉式供应链战略中,供应链的一些阶段 尤其是前期,是采用推式策略;而其它阶段则采用拉式策略 推式与拉式策略间的界面则称之为推拉边界(Push-Pull Boundary) 在供应链时间线,开端是未经加工的物料采购所耗的时间,末端是响应顾客订单的时间 推拉界线与时间线的交点代表从使用一个策略来管理供应链(通常是推式策略),改成另一个不同的策略来管理
8、供应链(通常是拉式策略),12,Push-Pull Boundary,PUSH STRATEGY,PULL STRATEGY,Low Uncertainty,High Uncertainty,Customers,Suppliers,The Supply Chain Time Line,Supply chain time line,13,Consider Two PC Manufacturers,Build to Stock Forecast demand Buys components Assembles computers Observes demand and meets demand i
9、f possible A traditional push system,Build to Order Forecast demand Buys components Observes demand Assembles computers Meets demand A push-pull system,14,推式拉式供应链:制造商例子,一家个人计算机制造商采用接单生产策略属于一种推式拉式策略 组件库存水平是依据预测数据进行管理,最后再依顾客特定要求进行装配作业 制造商在装配作业前的供应链系统属于推式策略,依顾客实际需求进行装配作业则属于供应链的拉式策略 推拉界线(Push-Pull Bound
10、ary)位于装配作业的开始 戴尔计算机使用此一策略已深具效率,同时也是实施以推式拉式策略影响供应链绩效表现显著的佼佼者,15,推式拉式供应链:延迟策略(1),产品设计的延迟或延迟差异化也是一种推式拉式策略 在延迟策略中,公司延迟产品设计与制造作业的程序,以便尽可能延迟特定产品的制造 制造流程可先由生产中性产品或族系产品开始,之后当需求产生时,再产生差异化的特定终端产品即可 在制造产品差异化之前的供应链作业是基于推式的策略 中性产品是依据长期的预测来进行生产和预测 因为中性产品的需求相当于所有使用这项中性产品的终端产品需求之总合,使得预测更加准确而降低库存水平 供应链实施产品差异化时间点以后的阶
11、段以拉式为基础,16,推式拉式供应链:延迟策略(2),The push-pull system takes advantage of the rules of forecasting: Forecasts are always wrong The longer the forecast horizon the worst is the forecast Aggregate forecasts are more accurate The Risk Pooling Concept,17,确认合适的供应链战略,确定产品的类型 下图提供一个供应链战略与产品产业相配合的架构,纵轴提供顾客需求不确定性的信
12、息,横轴代表生产或分销作业所需经济规模的重要性 拥有较高需求不确定性会造成供应链倾向实施以实际需求为基础的拉式策略;较低需求不确定性会使供应链倾向实施以长期预测为基础的推式策略,功能性产品与创新性产品,18,19,供应链与产品配合的矩阵式架构,20,确认合适的供应链战略(1),区块(High Uncertainty/ EOS not Important) 代表有高度的需求不确定性,且生产、装配或分销的经济规模较不重要的产业(或者更精确地说是产品),像计算机产业 拥有这些特征的产业或产品适用于基于拉式的供应链战略,熟知的戴尔计算机正是使用此一策略 区块(Low Uncertainty/ EOS
13、Important) 代表有较低的需求不确定性且有较重要规模经济的产品,像食品杂货业中的啤酒、面粉和羹汤等 依据长期预测的管理库存模式将不会增加库存持有成本,通过规模经济来降低分销成本,实施传统的基于推式的零售策略是合适的,21,确认合适的供应链战略(2),区块I和III所代表的是相对容易确认供应链战略的情况,其它两个区块则不适合仅利用不确定性或规模经济的重要性等构面来确定合适的供应链战略 在这些区块中,不确定性构面拉着供应链向一个策略方向发展;而规模经济面又将供应链推向另一个相反的策略方向 区块(Low Uncertainty but Low Value of Economies of Sc
14、ale) 代表低需求不确定性(基于推式的供应链)与低经济规模(基于拉式的供应链)的产品,许多大量的书籍和唱片均属这类商品 需要审慎地分析,因为传统的零售供应链战略和较新的推式拉式策略均可能合适的,不过这得视特定成本和不确定性而定,22,确认合适的供应链战略(3),区块(High Uncertainty and High Value of Economies of Scale) 是指需要藉由经济规模来降低生产或分销成本且高需求不确定性的产品,家具业可谓是此一特征的代表性产业 传统家具零售业提供大量不同形状、颜色或布料的类似商品,结果造成高度的需求不确定性 由于无法依据长期预测来制定生产决策,因此
15、生产策略必须遵循基于拉式的策略 另一方面,分销策略则需利用经济规模来降低运输成本,23,确认合适的供应链战略(4),区块(cont.) 许多不持有任何家具库存的零售商所使用的策略: 当顾客发出订单时,订单就被传送到制造商,接着制造商再去订购物料并生产顾客指定规格的产品 就某方面来说,家具业所使用的供应链战略其实是一个推式拉式策略: 也就是依实际需求进行生产为拉式策略,固定时间进行分销为推式策略的应用,24,Characteristics and Skills,Low Uncertainty Long Lead Times Cost Minimization Resource Allocatio
16、n,High Uncertainty Short Cycle Times Service Level Responsiveness,25,推式与拉式供应链阶段的特性,26,Locating the Push-Pull Boundary(1),The push section: Uncertainty is relatively low Economies of scale important Long lead times Complex supply chain structures Thus Management based on forecasts is appropriate Focu
17、s is on cost minimization Achieved by effective resource utilization supply chain optimization,27,Locating the Push-Pull Boundary(2),The pull section: High uncertainty Simple supply chain structure Short lead times Thus Reacting to realized demand is important Focus on service level Flexible and res
18、ponsive approaches,28,Locating the Push-Pull Boundary(3),The push section requires: Supply chain planning Long term strategies The pull section requires: Order fulfilment processes Customer relationship management Buffer inventory at the boundaries: The output of the tactical planning process The in
19、put to the order fulfilment process,29,Locating the Push-Pull Boundary(4),提前期与推拉系统(1),30,30,提前期与推拉系统(2),A短提前期和高需求不确定性 个人电脑,拉动 B长提前期和需求不确定性低 日用品,推动 C短提前期和较高需求可预测,食品行业中的短生命周期产品 面包和制品,持续补货 D长提前期和需求难以预测 汽车部件,库存配置,安全库存放在区域配送中心,31,32,需求驱动策略(Demand-Driven Strategies),需求信息必须整合到供应链规划程序中,需求信息主要由以下两个程序产生: 需求预测
20、(Demand Forecast):通过历史性的需求数据发展出可计算长期测预的需求程序,也就是所谓的预测 需求调节(Demand Shaping):指公司决定促销、价格折扣、回扣、新产品介绍与产品撤出市场等不同营销计划之影响的程序,33,预测误差,高需求预测误差对供应链绩效表现带来不利的影响,造成销售损失、过时库存,以及无效率的资源利用 利用供应链战略来增加预测准确性并降低预测误差的几种方法: 选择推拉界线使需求能通过下列一个或多个范围来汇总需求:产品 、地理区域 、时间 使用市场分析人口统计学及经济趋势改善预测的准确性 决定各店最佳产品组合以便降低在同一市场竞争的商品种类 将顾客结合到协作计
21、划与预测程序中,以便更了解市场需求、促销影响、价格事件与广告,34,因特网对供应链战略的影响(1),因特网与电子商务对经济和商业实务的影响相当大 根据市调公司Forrester Research预测,企业对企业的电子商务将从430亿美元加速成长到2003年的1.3兆美元,将带来便利性和成本的降低 因特网和新兴电子商业模式(e-Business Model)已经让人对这些新科技和商业模式产生可以解决许多供应链问题的期待,35,因特网对供应链战略的影响(2),电子商业策略被视为能降低成本、提高服务水平、增加弹性与利润 为什么在某些个案中,新的商业模式会失败?在其它个案中却又非常成功?如果戴尔和思科
22、能使用因特网发展出这么有效率的商业模式,那么,是什么因素阻碍其它公司采用相似的科技呢? 我们必须针对以因特网为基础的供应链战略进行更深入的探讨,36,电子化企业 vs 电子商务(1),电子化企业(E-Business) E-business is a collection of business models and processes motivated by Internet technology, and focusing on improving the extended enterprise performance 是由因特网科技促成的商业模式与程序的总称,并着重在企业长期绩效的改善
23、 电子商务(E-Commerce) E-commerce is the ability to perform major commerce transactions electronically 是指能够以电子化方式进行主要商业交易的能力,37,电子化企业 vs 电子商务(2),观察: 首先,电子商务只是电子化企业的一部分(e-Commerce is part of e-Business) 其次,因特网科技是企业改造的原动力(Internet technology is the driver of the business change) 最后,电子化企业着重在延伸企业之发展(The focu
24、s is on the extended enterprise),亦即企业内部(Intra-Organisational)、企业对顾客(B2C)以及企业对企业(B2B)间的交易,38,B2C vs B2B,B2C意指可以直接面对顾客的商业模式,尤其是通过因特网的零售活动,包含产品、保险、银行业务等 B2B指企业间通过因特网进行商业交易,包含传统交易方式及以达成共同目标而与供货商协作的方式,39,因特网对供应链战略的影响(1),食品杂货产业 书籍产业 零售产业,40,The Grocery Industry,From Push Systems. Supermarket supply chain
25、.To Pull Systems Peapod, 1989-1999 Picks the products at a nearby supermarket Stock outs 8% to 10% And, finally to Push-Pull Systems Peapod, 1999-Present Dedicated warehouses allow risk pooling Stock outs less than 2%,41,Challenges for On-Line Grocery Stores,Transportation cost Density of customers
26、Very short order cycle times Less than 12 hours Difficult to compete on cost Must provide some added value such as convenience Push system might be a better strategy,42,The Book Selling Industry,From Push Systems. Barnes and Noble .To Pull Systems A, 1996-1999 No inventory, used Ingram to meet most
27、demand And, finally to Push-Pull Systems A, 1999-present 7 warehouses around the country Why the switch? Product margins, service level, etc Volume grew,43,The Retail Industry,Brick-and-mortar companies establish virtual retail stores Wal-Mart, K-Mart, Barnes & Noble, Circuit City An effective appro
28、ach hybrid stocking strategy High volume/fast moving products for local storage Low volume/slow moving products for browsing and purchase on line (Risk Pooling) Danger of channel conflict,44,运输与订单履行的影响,因特网和相关的新兴供应链模式带来订单履行策略的改变: From shipping cases to single items:从整箱与大量的分销变成单品与少量的分销方式 From shipping
29、 to a relatively small number of stores to individual end users:从分销给少数商店变成服务区域性极为分散的顾客 这样的转变也增加了逆向物流的重要性与复杂性,45,传统订单履行 vs 电子化订单履行,46,E-Business Opportunities(1),Reduce Facility Costs Eliminate retail/distributor sites Reduce Inventory Costs Apply the risk-pooling concept Centralized stocking Postpon
30、ement of product differentiation Use Dynamic Pricing Strategies to Improve Supply Chain Performance,47,E-Business Opportunities(2),Supply Chain Visibility Reduction in the Bullwhip Effect Reduction in Inventory Improved service level Better utilization of Resources Improve supply chain performance P
31、rovide key performance measures Identify and alert when violations occur Allow planning based on global supply chain data,Summary,Implementation of push-pull strategies and demand-driven strategies have helped many companies to improve performance, reduce costs, increase service levels. Collapse of
32、many Internet companies shows that e-business has great challenges. Companies need to: Identify the appropriate supply chain strategy for individual products. Case for no physical infrastructure or inventory is tenuous Pushpull strategy advocates holding inventory although it pushes the inventory up
33、stream in the supply chain.,48,Distribution Strategies:Introduction,Focus on the distribution function. Various possible distribution strategies, and the opportunities and challenges associated with these strategies. Two fundamental distribution strategies: Items can be directly shipped from the sup
34、plier or manufacturer to the retail stores or end customer Use intermediate inventory storage points (typically warehouses and/or distribution centers). Issues with warehouses Manufacturing strategy (make-to-stock vs. make-to-order) Number of warehouses Inventory policy Inventory turn over ratio Int
35、ernal warehouses vs. outside distributor Owned by a single firm or by a variety of firms,49,50,分销策略,不同的外向分销策略: 直接分销(Direct Shipment) 在这个策略中,物品直接从供货商仓储据点直接运送到零售商店,而不经过分销中心 转运战略 越库作业(Cross-Docking) 在这个策略中,物品持续不断地从供货商经越库设施分销给顾客。越库设施通常保有库存不超过10至15个小时 仓储(Warehousing) 这是最传统的策略 在此策略中,仓库保管库存,当顾客有需求时,就供应物品给顾
36、客 联合库存 调运,51,直接分销(1),直接分销策略的优点: 零售商可以省下经营分销中心的费用 可以降低提前期 直接分销策略的缺点: 由于没有中央仓库,所以风险共担效应会被消除 供货商或分销商的运输成本增加,因为它必须以卡车运送更多的地点,52,直接分销(2),当零售商需要整车运送货物时,直接分销策略经常被使用 这也表示仓库无法帮助减少分销成本 这种策略通常被强大的零售商使用,或当提前期很重要或紧急情况时采用 直接分销策略在食品杂货产业中相当盛行,因为产品的不可储存性使得提前期显得很重要,53,越库作业,越库作业是因Wal-Mart而出名的一种分销策略 在这个系统中,仓库越库作业是库存统合点
37、而非库存储存点 在典型的越库操作系统中,商品从制造商那里送抵仓库,然后迅速装上卡车运送给零售商 商品在仓库停留的时间很短,通常不超过12小时 这个系统因为减少了仓储时间而降低了库存成本,也减少了提前期,54,越库作业的难题(1),越库操作系统需要相当多的初期投资,而在管理上也非常的困难: 分销系统、零售商及供货商必须以先进的信息系统紧密连结,以确保所有的取货作业及配送在要求的时间窗里完成 越库操作系统的运作需要一个可快速响应的运输系统 预测是很重要的,必要信息的分享也是十分的重要,55,越库作业的难题(2),越库作业策略只有在大型的分销系统中才有效 因为必须要有数量众多的车辆可在任何时间在越库
38、作业设施中配送及取货 在这样的系统中,每天必须要有足够的容量可以整车从供货商那里载运到仓库 因为通常这些系统包含了很多的供货商,需求量相当充足,所以商品在运抵越库作业设施时,可以以满载的数量立即运送到零售点,56,Example: Wal-Mart,Wal-Mart是世界上最大且获利最多的零售商 它利用越库作业技术运送85%的商品,而K-Mart只有50% 为了帮助越库作业的进行,Wal-Mart经营一个私人的卫星通讯系统,可以传送POS数据给它所有的供货商,让他们对所有店的销售情况有一个清楚的了解 此外,Wal-Mart拥有一个2000辆卡车的车队,而且它的分店平均每星期补货两次 越库作业使
39、Wal-Mart能够采购整车而达到经济规模 它降低了安全库存的必要性,与该产业的平均数比较起来,它也减少了3%的销货成本 这是Wal-Mart能够创造高边际收益的主要原因,57,What Accounts for Wal-Marts Remarkable Success,A focus on satisfying customer needs Providing customers access to goods when and where they want them Cost structures that enable competitive pricing Wal-Mart empl
40、oyed a logistics technique known as cross-docking Goods are continuously delivered to warehouses where they are dispatched to stores without ever sitting in inventory. This strategy reduced Wal-Marts cost of sales significantly and made it possible to offer everyday low prices to their customers.,58
41、,Characteristics of Cross-Docking,Goods spend at most 48 hours in the warehouse Cross Docking avoids inventory and handling costs Wal-Mart delivers about 85% of its goods through its warehouse system, compared to about 50% for Kmart Stores trigger orders for products,59,System Characteristics(1),Ver
42、y difficult to manage Requires advanced information technology All of Wal-Marts distribution centres, suppliers and stores are electronically linked to guarantee that any order is processed and executed in a matter of hours Wal-Mart operates a private satellite-communications system that sends point
43、-of-sale data to all its vendors allowing them to have a clear vision of sales at the stores,60,System Characteristics(2),Need a fast and responsive transportation system. Wal-Mart has a dedicated fleet of 2000 truck that serve their 19 warehouses This allows them to Ship goods from warehouses to st
44、ores in less than 48 hours Replenish stores twice a week on average,61,集中式与分布式控制(1),在集中化的系统中,决策是由中央供应网络所决定,通常目标是最小化系统总成本。通常集中式的控制可以导致整体最佳化 在一个分布式物流系统中,每一个设施采取对它最有效率的策略,而不会考虑对供应链中其它设施的影响。通常分布式系统会导致局部最佳化,62,集中式与分布式控制(2),理论上,一个集中式的分销网络会比一个分布式的分销网络有效率: 善用信息科技的力量:在一个集中式的系统中,所有的设施可以存取相同的信息 集中式组织允许信息共享,更重要
45、的是,这些信息的利用方式消除了牛鞭效应及改善预测效果 集中化组织允许供应链整体采用协调策略,该策略可减少系统成本也可改善服务水平,63,中央与地方设施:考虑因素(1),安全库存:作业愈集中化,安全库存就愈低 管理成本:相对于运作很多的小型仓库,运作较少数的大型仓库可导致较低的总管理成本 规模经济:在相同的总产能下,运作很多的小型设施,通常比运作几个大型的设施要昂贵许多 提前期:为数众多的仓库位于市场的附近,可以减少到市场的提前期,64,中央与地方设施:考虑因素(2),服务: 集中化的仓储可以利用风险共担的观念,即更多的订单可以以较低的库存水平来满足 然而仓库到零售商的运送时间会变长 运输成本:
46、 仓库数量增加,从生产设施到仓库间的运输成本也会增加,因为运送的总距离变长 然而从仓库到零售商之间的运输成本会下降,因为仓库会设在靠近市场的附近,65,中央与地方设施,在一个有效率的分销策略中,一些商品可能会被存放在中央的设施,而另一些商品会被存放在几个不同的地方设施里 举例来说,单价高但顾客需求低的商品可能会被储存在中央仓库;单价低但顾客需求高的商品就可能被储存在许多的地方仓库中,A Hybrid Decision,Some products use centralized strategy while others use local strategy Not an either or d
47、ecision Varying degrees of centralization and localization due to the varying levels of advantages and disadvantages,66,Inventory Pooling GM Example,1,500 Cadillacs parked at a regional distribution center in Orlando Await delivery to dealers statewide within 24 hours 10% to 11% sales loss because a
48、 car is not available Test program expected to: improve customer service boost sales of Cadillacs by 10%,67,Centralized Pooled Systems Perform Better,For the same inventory level, a centralized system provides: higher service level higher sales Push-pull supply chain Moving from a push supply chain
49、Dealers have to order before demand is realized To a push-pull supply chain Dealers pull from regional distribution centers. Implications: End consumers will see better customer service More cars are available to them.,68,Other Factors,Will GM sell more cars to GM dealers? Total number of cars order
50、ed by dealers will not necessarily increase, even as customer service increases. What about the dealers? Dealers have access to more inventory Potentially can sell more. Levels out the playing field between dealers. Small dealers would favor such a system Competitive advantage of large dealers wiped
51、 out,69,Example of Inventory Pooling,Two retailers face random demand for a single product. No differences between the retailers Compare two systems centralized pooled system, retailers together operate a joint inventory facility take items out of the pooled inventory to meet demand. decentralized s
52、ystem each retailer individually orders from the manufacturer to meet demand In both systems, inventory is owned by the retailers,70,The Two Systems,FIGURE 7-9: The centralized and decentralized systems,FIGURE 7-10: Probabilistic demand faced by each retailer,71,Other Data,Wholesale price = $80 per
53、unit Selling price = $125 per unit Salvage value = $20 per unit Production cost = $35 per unit,72,Costs and Profits in the Two Systems,Decentralized system Each dealer orders 12,000 units Expected profit per dealer = $470,000, Total = $940,000 Expected sales = 11,340 units, Total = 22,680 units Manu
54、facturer profit = $1,080,000 Centralized system Two dealers together will order 26,000 units Total expected profit = $1,009,392 Joint expected sales = 24,470 units Manufacturer profit = $1,170,000,73,Customer Search,If the customer arrives at a dealer and does not find the item Switches to another d
55、ealer Helps the manufacturer sell more products Which system is better under customer search? No impact on the centralized system,74,Impact on Decentralized System,If a dealer knows that its competitors do not keep enough inventory this dealer should raise the inventory level to satisfy: its own dem
56、and demand of customers who initially approach other dealers with limited inventory. If a dealer knows that its competitors has significant inventory this dealer will reduce the inventory level It is not likely to see customers who switch Dealers strategy depends on its competitors strategy. Dealers
57、 may/may not know their competitor strategy not clear how they decide on their inventory level. not clear about the impact of search on the manufacturer,75,Nash Equilibrium (Game Theory),If two competitors are making decisions, they have reached Nash equilibrium if they have both made a decision Bot
58、h have decided on an amount to order neither can improve their expected profit by changing the order amount if the other dealer doesnt change his order amount.,76,Example, = percentage of customers that search the system Each retailer can determine what their effective demand will be if the other re
59、tailer orders a specific amount. Based on this information, they can calculate how much they should order given any order by their competitors. Best response,77,Best Response with =90%,FIGURE 7-11: Retailers best response,78,Nash Equilibrium of the System,Retailer one orders about 20,000 units, retailer two will respond by ordering about 12,000 units If this is the case, then retailer one should modify its strategy and reduce the order quantity No retailer has an incentive to modify its strategy They order amounts associated with the intersection of the two curves. Optimal or
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