【正文】 能力。其目的是確定車輛，確定總成本最低的路線。如果車輛的數量是固定的，可能還包括一個額外的任期，如果路線的數量不同，那么與車輛數目成正比。
CVRP 和及其各種形式也曾澤范和拉姆澤 (1959年)中推出了文學研究。其確切的解決方案是很難確定大規(guī)模的問題，這是一個很難解決的問題。專門的算法能夠始終如一的為高達50家客戶找到最優(yōu)的解決方案；雖然更大的問題已經解決，但是在某些情況下，往往最優(yōu)性的代價就是花費相當長的時間。在實踐中，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，在可接受的計算時間內，但不保證最優(yōu)性。有幾本書和調查文章來匯總不同的方法，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)，這些在雜志撰寫的文章中被大量引用。同時有很多關于CVRP的研究工作。對于此問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)式技術來解決復雜的問題和算出合理的時間（請參見 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）。大多數的這些做法基于本地搜索技術。大多數論文認為車廠和客戶之間行駛費用和時間是已知的，固定的。他們一般就是用表或者圖形或者網絡計算最小路徑。然而在實踐中，時間和最短路徑可能有所不同，尤其是通過一天的時間。5 結論本白皮書描述了綠色物流所涉領域，并描述了一些新的問題出現(xiàn)時，所考慮的并不僅僅是經濟，而是更加涉及到環(huán)境和社會因素。有許多不同類型的模型在處理綠色物流問題中，扮演了關鍵角色，但在本文中，我們都集中在描述用組合優(yōu)化模型解決及設計方案。據預計由于環(huán)境因素承擔的重要性日益增加，組合優(yōu)化模型和技術將面臨更多的挑戰(zhàn)。在英國，綠色物流模式有許多對不同方面有研究的聯(lián)合會和在綠色物流項目的網站上可以找到詳細信息 。綠色物流項目包括涵蓋的這項討論了逆向物流和物流配送車輛調度，綠色物流議程上的政策的影響等有關主題的幾個模塊。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