【正文】 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 Waste。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(wǎng)站上可以找到詳細(xì)信息 。有許多不同類型的模型在處理綠色物流問題中，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)計方案。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。大多數(shù)論文認(rèn)為車廠和客戶之間行駛費用和時間是已知的，固定的。有人建議用近似方法和啟發(fā)式技術(shù)來解決復(fù)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）。同時有很多關(guān)于CVRP的研究工作。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(nèi)，但不保證最優(yōu)性。專門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；雖然更大的問題已經(jīng)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(dāng)長的時間。
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。其目的是確定車輛，確定總成本最低的路線。我們在已知位置和要求的中央倉庫設(shè)置車輛流量Q，以滿足從中央倉庫交貨的要求。4 車輛路徑與調(diào)度車輛路徑與調(diào)度問題(VRSP)涉及到確定路線和車隊的時間表以滿足客戶的需求。因此在這些管理領(lǐng)域，特別是對于較發(fā)達(dá)的國家方面取得了重大進(jìn)展。第二個變量是假定制造與再制造費用單獨設(shè)置。這被認(rèn)為是兩種變體。：—— 沒有回報的處理方案；—— 持有成本為服務(wù)成本大于持有成本的回報率 ；—— 變制造與再制造費用不包括在內(nèi)。再制造的例子包括一次性使用的相機和復(fù)印機。有關(guān)此模型的詳細(xì)信息，請參閱由布拉默爾和辛智列維書（1997年），約翰遜和蒙哥馬利（1974年)和銀等(1996年)。動態(tài)調(diào)整很多問題得到了很好的研究，因為它是第一個推出了超過四十年前的方法。該模型假設(shè)成本是按照一個固定順序（所設(shè)置的）來支出的，采購成本為一個單位的線性支出，在單位時間內(nèi)，庫存都是具有線性持有成本的。該項目的設(shè)施場所是根據(jù)供應(yīng)機構(gòu)的訂單來決定的。 動態(tài)批量問題