【正文】 能力。其目的是確定車輛，確定總成本最低的路線。如果車輛的數(shù)量是固定的，可能還包括一個(gè)額外的任期，如果路線的數(shù)量不同，那么與車輛數(shù)目成正比。
CVRP 和及其各種形式也曾澤范和拉姆澤 (1959年)中推出了文學(xué)研究。其確切的解決方案是很難確定大規(guī)模的問(wèn)題，這是一個(gè)很難解決的問(wèn)題。專門(mén)的算法能夠始終如一的為高達(dá)50家客戶找到最優(yōu)的解決方案；雖然更大的問(wèn)題已經(jīng)解決，但是在某些情況下，往往最優(yōu)性的代價(jià)就是花費(fèi)相當(dāng)長(zhǎng)的時(shí)間。在實(shí)踐中，其他的變化和附加約束，通常必須考慮到使車輛路徑以及其最優(yōu)性。有許多的解決方案過(guò)程基于啟發(fā)式算法，旨在提供良好可行的解決方案，在可接受的計(jì)算時(shí)間內(nèi)，但不保證最優(yōu)性。有幾本書(shū)和調(diào)查文章來(lái)匯總不同的方法，并且在文章中有所引用（例如，黃金與阿薩德 1988年；托特和維 2001年)，這些在雜志撰寫(xiě)的文章中被大量引用。同時(shí)有很多關(guān)于CVRP的研究工作。對(duì)于此問(wèn)題已定制的確切的幾種方法 （如拉波特和諾貝特； 1987年阿格沃爾等1989 年； 里斯加德2004 年；深澤 等l2006 年）。有人建議用近似方法和啟發(fā)式技術(shù)來(lái)解決復(fù)雜的問(wèn)題和算出合理的時(shí)間（請(qǐng)參見(jiàn) 年；拉波特和塞姆特 2002年；科爾多和拉波特 2004年；科爾多 等2005 年）。大多數(shù)的這些做法基于本地搜索技術(shù)。大多數(shù)論文認(rèn)為車廠和客戶之間行駛費(fèi)用和時(shí)間是已知的，固定的。他們一般就是用表或者圖形或者網(wǎng)絡(luò)計(jì)算最小路徑。然而在實(shí)踐中，時(shí)間和最短路徑可能有所不同，尤其是通過(guò)一天的時(shí)間。5 結(jié)論本白皮書(shū)描述了綠色物流所涉領(lǐng)域，并描述了一些新的問(wèn)題出現(xiàn)時(shí)，所考慮的并不僅僅是經(jīng)濟(jì)，而是更加涉及到環(huán)境和社會(huì)因素。有許多不同類型的模型在處理綠色物流問(wèn)題中，扮演了關(guān)鍵角色，但在本文中，我們都集中在描述用組合優(yōu)化模型解決及設(shè)計(jì)方案。據(jù)預(yù)計(jì)由于環(huán)境因素承擔(dān)的重要性日益增加，組合優(yōu)化模型和技術(shù)將面臨更多的挑戰(zhàn)。在英國(guó)，綠色物流模式有許多對(duì)不同方面有研究的聯(lián)合會(huì)和在綠色物流項(xiàng)目的網(wǎng)站上可以找到詳細(xì)信息 。綠色物流項(xiàng)目包括涵蓋的這項(xiàng)討論了逆向物流和物流配送車輛調(diào)度，綠色物流議程上的政策的影響等有關(guān)主題的幾個(gè)模塊。Abstract:The purpose of this paper is to introduce the area of Green Logistics and to describe some of the problems that arise in this subject which can be formulated as binatorial optimization problems. The paper particularly considers the topics of reverse logistics, waste management and vehicle routing and scheduling.Keywords:Green Logistics, Reverse logistics, Combinatorial optimization, Waste management, Hazardous materials1 IntroductionGreen Logistics is concerned with producing and distributing goods in a sustainable way,taking account of environmental and social factors. Thus the objectives are not only concerned with the economic impact of logistics policies on the organization carrying them out,but also with the wider effects on society, such as the effects of pollution on the environment. Green Logistics activities include measuring the environmental impact of different distribution strategies, reducing the energy usage in logistics activities, reducing waste and managing its treatment. In recent years there has been increasing concern about the environmental effects on the planet of human activity and current logistic practices may not be sustainable in the long organizations and businesses are starting to measure their carbon footprints so that the environmental impact of their activities can be monitored. Governments are considering targets for reduced emissions and other environmental is therefore increasing interest in Green Logistics from panies and logistics models for production and distribution have concentrated on minimizing costs subject to operational constraints. But consideration of the wider objectives and issues connected with Green Logistics leads to new methods of working and new models,some of which pose interesting new applications for operational research models of various types. A survey of all operational research models in this area would require a very long article and so the focus of this paper is to concentrate on some of the new or revised binatorial optimization models that arise in Green Logistics applications. For those working in binatorial optimization it is hoped that these new models will pose interesting new challenges that may have significant effects on the environment when the results are original version of this paper can be found in Sbihi and Eglese (2007). It discusses different areas that relate to the Green Logistics agenda. Section 2 concerns Reverse Logistics models that take account of the full lifecycle of a product and the possibilities of various forms of recycling. Section 3 covers Waste Management that includes models for the transportation of hazardous waste, rollon rolloff containers and the collection of household waste. Section 4 deals with Vehicle Routing models and issues relating to Green Logistics objectives. Section 5 contains the final conclusions.2 Reverse LogisticsThere are various definitions of Reverse Logistics to be found in the literature. For example,Fleischmann et al. (1997) say that reverse logistics is “a process which enpasses the logistics activities all the way from used products no longer required by the user to products again usable in a market”. Dowlatshahi (2000) explains Reverse Logistics as “a process in which a manufacturer systematically accepts previously shipped products or parts from the point for consumption for possible recycling, remanufacturing or disposal”. Later, the European Working Group on Reverse Logistics, REVLOG, Dekker et al. (2004), give this definition: “The process of planning, implementing and controlling backward flows of raw materials, in process inventory, packaging and finished goods, from a manufacturing, distribution or use point, to a point of recovery or point of proper disposal”.In their book, Rogers and TibbenLembke (1999) briefly consider the differences between Reverse Logistics and Green Logistics. In Reverse Logistics there should be some flow of products or goods back from the consumer to an earlier stage of the supply reduction of waste that this implies certainly means that Reverse Logistics should be included within Green Logistics. For example, De Brito and Van Der Laan (2003) examine inventory management issues when product returns must be estimated. However there will be other models of logistics activities involving only forward flows of goods that could not be described as reverse logistics, but if they include environmental considerations, will also be included within Green Logistics. For example,Mondschein and Schilkrut (1997) describe a mixed integer linear programming model to determine the optimal investment policies for the copper industry in Chile. A key part of the model was to control air pollution through emissions in the production process. Legislation within the European Community gives high importance to recycled products and, in some cases, it has established the responsibility for the end of life products to the manufacturers. For example, the Wast