精品資料（2021-2022年收藏）具有環(huán)保意識(shí)的供應(yīng)鏈網(wǎng)絡(luò)長(zhǎng)期設(shè)計(jì)規(guī)劃

1、Environmentally conscious long-range planning and design of supply chain networks具有環(huán)保意識(shí)的供應(yīng)鏈網(wǎng)絡(luò)長(zhǎng)期設(shè)計(jì)規(guī)劃AbstractIn this paper, a mathematical programming-based methodology is presented for the explicit inclusion of life cycle assessment (LCA) criteria as part of the strategic investment decisions related

2、 to the design and planning of supply chain networks. By considering the multiple environmental concerns together with the traditional economic criteria, the planning task is formulated as a multi-objective optimization problem. Over a long-range planning horizon, the methodology utilizes mixed inte

3、ger modeling techniques to address strategic decisions involving the selection, allocation and capacity expansion of processing technologies and assignment of transportation links required to satisfy the demands at the markets. At the operational level, optimal production profiles and flows of mater

4、ial between various components within the supply chain are determined. As such, the formulation presented here combines the elements of the classical plant location and capacity expansion problems with the principles of LCA to develop a quantitative decision-support tool for environmentally consciou

5、s strategic investment planning.本文提出一種數(shù)學(xué)規(guī)劃方法，明確納入生命周期評(píng)估準(zhǔn)則作為與設(shè)計(jì)規(guī)劃供應(yīng)鏈網(wǎng)絡(luò)有關(guān)的戰(zhàn)略投資決策的一部分。通過(guò)將多環(huán)境問(wèn)題和傳統(tǒng)經(jīng)濟(jì)標(biāo)準(zhǔn)一起考慮，規(guī)劃任務(wù)是一個(gè)多目標(biāo)優(yōu)化問(wèn)題。在長(zhǎng)期規(guī)劃中，利用混合整數(shù)建模技術(shù)解決戰(zhàn)略決策問(wèn)題，其包括選擇，分配和擴(kuò)容加工技術(shù)，及滿足市場(chǎng)需求的運(yùn)輸。在操作層面上，決定供應(yīng)鏈內(nèi)部各個(gè)組成部分的最優(yōu)生產(chǎn)概況和物質(zhì)流。因此，這里提出的公式結(jié)合工廠定位和LCA原則的能力擴(kuò)展問(wèn)題來(lái)發(fā)展一個(gè)定量決策工具以支持具有環(huán)保意識(shí)的戰(zhàn)略投資規(guī)劃。1. IntroductionIncreasingly there has be

6、en an awareness of the impact that extended chemical production systems have on the environment, resulting in enterprise-wide management strategies such as product stewardship, life cycle assessment (LCA) and industrial ecology. However, despite the consensus about the relevance and benefits of adop

7、ting more sustainable business practices across entire chemical product value chains, the greatest challenge still lies in the practical application of the environmental management strategies in pursuit of technological innovations. Over the years, the process engineering community has recognized th

8、is challenge with the result being a variety of approaches aimed at the plant-level for environmentally conscious chemical process design. In their extensive review of over 180 citations related to the area of environmentally conscious chemical process design, Cano-Ruiz and McRae 1 analyze various m

9、ethodologies that consider avoiding environmental damage as part of the process design objectives. Undoubtedly, the most important conclusion from their review is that by adopting a strategy that considers the environment as a design objective and not merely as a constraint on operations can lead to

10、 the discovery of novel processing alternatives that achieve both improved economic and environmental performance.擴(kuò)大化學(xué)生產(chǎn)系統(tǒng)對(duì)環(huán)境產(chǎn)生影響的意識(shí)已經(jīng)被越來(lái)越多的人注意到，導(dǎo)致了企業(yè)范圍的管理策略如產(chǎn)品管理，生命周期評(píng)估（LCA）和工業(yè)生態(tài)學(xué)。然而，盡管在整個(gè)化學(xué)產(chǎn)品價(jià)值鏈中實(shí)施更多的可持續(xù)商業(yè)慣例的相關(guān)性和效益型已經(jīng)達(dá)成了共識(shí)，最大的挑戰(zhàn)始終是在追求技術(shù)革新時(shí)，環(huán)境管理策略的實(shí)際應(yīng)用。多年來(lái)，過(guò)程工程社區(qū)已經(jīng)認(rèn)識(shí)到這項(xiàng)挑戰(zhàn)，這種挑戰(zhàn)帶有成為許多方法的結(jié)果，這種方法目的在與環(huán)保

11、意識(shí)化工過(guò)程設(shè)計(jì)的工廠水平。在他們的對(duì)180多個(gè)有關(guān)環(huán)保意識(shí)的化學(xué)工藝設(shè)計(jì)領(lǐng)域引文的廣泛回顧后，Cano-Ruiz and McRae 1分析了各種研究方法，考慮將避免環(huán)境破壞作為工藝設(shè)計(jì)目標(biāo)的一部分。毫無(wú)疑問(wèn)，最重要的結(jié)論是通過(guò)采取將環(huán)境作為設(shè)計(jì)目標(biāo)之一而不僅僅是操作限制的策略可以導(dǎo)致新加工方案的發(fā)現(xiàn)，這種方案可以同時(shí)提高經(jīng)濟(jì)業(yè)績(jī)和減小環(huán)境影響。However, formulating the process design problem such that environmental concerns are treated as decision-making objectives in

12、stead of constraints requires (a) quantifying suitable environmental performance measures, and (b) balancing the environmental criteria against the traditional cost incentives. Especially, the selection of appropriate performance indicators has proven to pose a significant obstacle in developing a d

13、esign strategy driven by an environmental objective. Efforts have, therefore, focussed on developing indices that can be used within a quantitative process decisionmaking framework 2,3. In this respect, LCA 4 has also proven to facilitate the environmental impact assessment of a chemical process des

14、ign 5.然而，規(guī)劃工藝設(shè)計(jì)問(wèn)題如環(huán)境問(wèn)題時(shí)，將其作為決策目標(biāo)而不是作為適當(dāng)?shù)沫h(huán)境績(jī)效指標(biāo)量化的限制規(guī)定，并且在環(huán)境標(biāo)準(zhǔn)和傳統(tǒng)的成本激勵(lì)中尋求平衡。特別是，合適的績(jī)效指標(biāo)的選擇證明在環(huán)境目標(biāo)驅(qū)動(dòng)下制定設(shè)計(jì)策略有重大障礙。因此，重點(diǎn)提出定量過(guò)程的決策框架使用的指標(biāo)。在這方面，LCA使化學(xué)工藝設(shè)計(jì)的環(huán)境影響評(píng)估變得方便。Once a suitable impact assessment technique has been applied, the resulting environmental performance measures can be traded-off against the

15、 economic objectives e as well as against each other - to generate and evaluate alternatives. A number of design methodologies aimed at the plant-level have incorporated multiple criteria decision-making (MCDM) techniques as part of the process design task 3,6-11. Multi-objective optimization, being

16、 one particular MCDM approach, tries to identify the set of non-inferior alternative solutions before they are explicitly evaluated 12. As such, the feasible alternatives are not explicitly known in advance and it is acknowledged that an infinite number of solutions potentially exist. In a similar s

17、pirit, the Methodology for Environmental Impact Minimization was developed with the aim of capturing diverse environmental concerns as objectives within a formal quantitative process design and optimization framework 13,14.一旦一個(gè)合適的影響評(píng)估技術(shù)被應(yīng)用，由此產(chǎn)生的環(huán)境性能措施可以在經(jīng)濟(jì)目標(biāo)之間權(quán)衡，也可以在產(chǎn)生和評(píng)估方案中權(quán)衡。許多設(shè)計(jì)方法目的是工廠納入多準(zhǔn)則決策目標(biāo)（M

18、CDM）技術(shù)作為工藝設(shè)計(jì)任務(wù)的一部分3,6-11。作為一個(gè)特定的MCDM方法的多目標(biāo)優(yōu)化，試圖在被明確的評(píng)估之前找出非劣勢(shì)解決方案的解集12。因此，不會(huì)明確地事先知道可行的替代方案，而且一個(gè)無(wú)窮的解決方案是可能存在的。類(lèi)似的，設(shè)計(jì)環(huán)境影響最小化的方法，其目的是在定量工藝設(shè)計(jì)和優(yōu)化框架中將不同的環(huán)境問(wèn)題作為目標(biāo)13,14。While these previous applications have successfully included environmental considerations within a process design context, limited work to

19、date has been conducted on the extension of the same trade-off analysis methodology to assist the strategic planning and design of extended supply chain networks. The opportunity naturally exists to expand the process systems boundary to allow the structure of the supply chain network to be a design

20、 decision within the overall process optimization framework.雖然這些以前的應(yīng)用在工藝設(shè)計(jì)中成功包含環(huán)境因素，迄今為止有限的工作是進(jìn)行權(quán)衡分析方法的擴(kuò)展，以協(xié)助戰(zhàn)略規(guī)劃和供應(yīng)鏈網(wǎng)絡(luò)的設(shè)計(jì)。機(jī)會(huì)自然存在以擴(kuò)大流程系統(tǒng)的邊界，使供應(yīng)鏈網(wǎng)絡(luò)結(jié)構(gòu)在整個(gè)流程優(yōu)化框架中成為一個(gè)設(shè)計(jì)決策。In contrast to the process design task, supply chain management is concerned with activities related to a broader range of business p

21、ractices, such as procurement, processing, marketing, distribution and retail. It adopts a fundamental systems-based approach whereby extended enterprises are seen as an integrated network of cooperating companies instead of isolated hierarchial ones. Decisions generally correspond to four activitie

22、s - scheduling, operational, tactical and strategic 15. Traditionally, the goal of research into supply chain activities has been to achieve greater corporate competitiveness through enterprise efficiency by delivering an increasing number of products, in greater quantities, at the time of product d

23、emand. In order to achieve these goals, quantitative analysis, modelling, optimization and design of the supply chains have been recognized as invaluable tools for supporting the decision-making process 16. Despite the significant advances in the development of supply chain decision-support tools, l

24、imited attention has been given to incorporating quantitative environmental performance modelling 17. This is surprising, especially if one considers the many similarities between emerging environmental management strategies and traditional supply chain research activities 18. For example, total qua

25、lity management, aiming at reducing overall cost across the enterprise, requires just as life cycle assessment and product stewardship knowledge of the entire integrated value chain. Furthermore, many pressures resulting from supply chain dynamics between buyers and suppliers can often initiate envi

26、ronmental change 19.與流程設(shè)計(jì)任務(wù)相比，供應(yīng)鏈管理與更廣泛的商業(yè)行為有關(guān)，比如采購(gòu)、加工、市場(chǎng)配送和零售。它采用了基本系統(tǒng)基礎(chǔ)方法，將企業(yè)擴(kuò)大看做合作公司的綜合網(wǎng)絡(luò)而不是孤立的。決策一般與計(jì)劃、運(yùn)營(yíng)、戰(zhàn)術(shù)和戰(zhàn)略四個(gè)活動(dòng)相對(duì)應(yīng)15。傳統(tǒng)上，供應(yīng)鏈的研究目標(biāo)是，通過(guò)在有需求時(shí)提供越來(lái)越多的產(chǎn)品使企業(yè)具有更大的競(jìng)爭(zhēng)力。為了達(dá)到這個(gè)目標(biāo)，供應(yīng)鏈的定量分析、建模、優(yōu)化和設(shè)計(jì)已經(jīng)被確認(rèn)為寶貴的工具，以支持決策過(guò)程16。盡管供應(yīng)鏈決策支持工具的開(kāi)發(fā)有了很大的進(jìn)展，納入定量環(huán)境績(jī)效模型的的研究很有限17。這是令人驚訝的，尤其如果考慮到新興的環(huán)境管理策略和傳統(tǒng)的供應(yīng)鏈研究活動(dòng)間的許多共同點(diǎn)1

27、8。例如，以減少整個(gè)企業(yè)的成本為目標(biāo)的全面質(zhì)量管理，需要整個(gè)價(jià)值鏈集成的生命周期評(píng)估和產(chǎn)品管理知識(shí)。此外，由買(mǎi)方和供應(yīng)商在之間的動(dòng)態(tài)供應(yīng)鏈導(dǎo)致的壓力常來(lái)自環(huán)境的變化19。An industrial application of environmentally conscious supply chain management can be found in Unilever, where an ecometric approach to assess and quantify the overall effect that a business has on the environment h

28、as been developed 20. Application of this ecometric approach has been used to illustrate the relationship between added value and environmental impact along the supply chain of mobile telephones 21. Recently, the industrial ecology concept was extended by modelling macrolevel waste exchange networks

29、 using Geographic Information Systems (GIS) data 22. Operations Research (OR) has also successfully addressed a variety of environmental problems outside the traditional supply chain management area, such as water resource management, solid waste disposal operations and air quality management 23.一種具

30、環(huán)保意識(shí)的供應(yīng)鏈管理的工業(yè)應(yīng)用可以在聯(lián)合利華中找到，一種評(píng)估和量化企業(yè)在環(huán)境方面整體效果的生態(tài)測(cè)量方法已經(jīng)開(kāi)發(fā)20。這種生態(tài)測(cè)量方法的應(yīng)用已經(jīng)被用于證明移動(dòng)電話供應(yīng)鏈的附加價(jià)值和環(huán)境影響之間的關(guān)系21。近來(lái)，工業(yè)生態(tài)學(xué)的概念已經(jīng)被宏觀的廢物交換網(wǎng)絡(luò)建模擴(kuò)展，其利用了地理信息系統(tǒng)數(shù)據(jù)（GIS）。運(yùn)籌學(xué)（OR）已經(jīng)成功解決了傳統(tǒng)供應(yīng)鏈管理區(qū)域以外許多的環(huán)境問(wèn)題，比如水資源管理、固體廢物處理和空氣質(zhì)量管理23Multi-objective optimization models where environmental concerns are included have also been prop

31、osed to determine the optimal structure of the petrochemical industry 24. Trade-off analysis techniques were used to establish the relationship between toxicity and cost of manufacturing chemicals in the strategic design of the optimum industrial structure. Similarly, the method of sum of weighted o

32、bjective functions was used to generate the efficient set of possible configurations for 297 manufacturing processes 25. The inherent assumption in both these examples is that the toxicity of the main product manufactured represents the potential environmental damage of the manufacturing process. A

33、more rigorous analysis would also include the environmental impacts resulting from the discharge of the byproducts, wastes and emissions of both the main manufacturing process as well as its off-site utility and material suppliers.環(huán)境問(wèn)題的多目標(biāo)優(yōu)化模型已經(jīng)被提出，來(lái)確定石化工業(yè)的優(yōu)化結(jié)構(gòu)24。在優(yōu)化工業(yè)結(jié)構(gòu)的戰(zhàn)略性設(shè)計(jì)中，權(quán)衡分析技術(shù)用來(lái)確定制造化學(xué)的的毒性和成本

34、之間的關(guān)系。同樣的，加權(quán)目標(biāo)函數(shù)方法被用于297個(gè)制造流程的可能配置的有效集合的生成25。這兩個(gè)例子固有的假設(shè)是，主要產(chǎn)品的毒性代表制造流程的潛在環(huán)境破壞。一個(gè)更加嚴(yán)格的分析也將包括副產(chǎn)品排出的環(huán)境影響，主要制造流程的廢物和排放及場(chǎng)外工具和材料供應(yīng)商。In this paper, we focus on extending our previously developed Methodology for Environmental Impact Minimization by presenting a generic mathematical programming model for ass

35、isting the strategic long-range planning and design of chemical supply chain networks. Firstly, the problem that the model will address is formally stated. Next, the features and capabilities of the model are summarized. The detailed mathematical formulation then follows, highlighting the use of mix

36、ed integer modelling techniques to capture the various strategic planning decisions. Particular emphasis is placed on the use of a recently developed impact assessment method within the quantitative LCA framework. Another important feature of the model is the explicit modelling of the economies of s

37、cale that dictate capital investment decisions associated with optimal selecting, installing and expanding processing technologies. The model formulation concludes with the multiobjective optimization framework and its solution algorithm. Finally, an illustrative example is presented involving the d

38、esign and long-range capacity planning of a bulk chemicals supply chain.本文中，我們通過(guò)提出通用的數(shù)學(xué)規(guī)劃模型來(lái)擴(kuò)展我們以前提出環(huán)境影響最小化的方法，以協(xié)助長(zhǎng)期戰(zhàn)略決策和化學(xué)供應(yīng)鏈網(wǎng)絡(luò)設(shè)計(jì)。首先，正式聲明模型解決的問(wèn)題。其次，總結(jié)模型的特點(diǎn)和功能。然后是詳細(xì)的數(shù)學(xué)公式，強(qiáng)調(diào)使用混合整數(shù)模型技術(shù)獲得各種戰(zhàn)略決策。特別強(qiáng)調(diào)的是在定量LCA框架中使用最近成熟的影響評(píng)估方法。模型另一個(gè)重要的特點(diǎn)是規(guī)模經(jīng)濟(jì)的詳細(xì)建模，它規(guī)定了與最優(yōu)化選擇、安裝和擴(kuò)展加工技術(shù)有關(guān)的資金投資決策。該模型的結(jié)論是多目標(biāo)優(yōu)化框架和其算法。最后，給出一個(gè)涉及

39、大宗化學(xué)品供應(yīng)鏈的設(shè)計(jì)和長(zhǎng)遠(yuǎn)規(guī)劃能力的案例。2. Problem formulationThe environmentally conscious process selection problem for the long-range planning and design of chemical supply chain networks can be stated as follows.具有環(huán)保意識(shí)的化學(xué)品供應(yīng)鏈長(zhǎng)遠(yuǎn)設(shè)計(jì)和規(guī)劃的問(wèn)題選擇，可歸納如下：Given： a set of markets (distributors or customers) and their demands

40、for a set of chemicals over a given future long-term period (planning horizon),在一個(gè)給定的未來(lái)長(zhǎng)期期間內(nèi)的（規(guī)劃期）的化學(xué)品的市場(chǎng)（分銷(xiāo)商和顧客）及需求。 a set of candidate plants using known technologies to produce the desired products,使用已知技術(shù)制造所需產(chǎn)品的候選工廠。 a set of potential geographical sites for locating the plants, and建廠的潛在地理區(qū)域 the

41、availabilities of the raw material and utility suppliers over the planning horizon,規(guī)劃期內(nèi)原材料和設(shè)備供應(yīng)商的有效性，the task is to任務(wù)是 design the supply chain network of the integrated production facilities that would satisfy the demand over the entire planning horizon,設(shè)計(jì)綜合生產(chǎn)設(shè)施供應(yīng)鏈網(wǎng)絡(luò)，能滿足整個(gè)規(guī)劃期的需求such that both the而使(

42、1) net present value of the capital investment evaluated at the end of the planning horizon, is maximized and the在規(guī)劃期末評(píng)估資金投資的凈現(xiàn)值，使其最大化(2) impact that the entire network has on the environment is minimized整個(gè)網(wǎng)絡(luò)的環(huán)境影響最小化。While this problem statement contains elements of a classical dynamic plant locatio

43、n problem for siting production facilities within a supply chain context 26, it also resembles models developed for the chemical processing industry to assist technology selection 27-29 and long-range capacity planning 30-32. Features of multi-site supply chain network models where both operation an

44、d strategic decisions are addressed are also captured within this problem formulation 33,34.雖然問(wèn)題的陳述包括供應(yīng)鏈中傳統(tǒng)的動(dòng)態(tài)工廠選址問(wèn)題26，它類(lèi)似于化學(xué)加工工業(yè)模型，以協(xié)助技術(shù)選擇27-29和長(zhǎng)遠(yuǎn)規(guī)劃30-32。解決操作和戰(zhàn)略決策問(wèn)題的多站點(diǎn)供應(yīng)鏈網(wǎng)絡(luò)模型的的特點(diǎn)在問(wèn)題規(guī)劃中獲得33,34。As illustrated in Fig. 1, the model proposed here to solve the aforementioned problem is based upon a sup

45、ply chain network superstructure consisting of a set of NM existing markets - representing an aggregation of distribution centres and final customers - demanding a set of NI chemical products (notation for the model variables is presented in Table 1). Also given is information regarding the location

46、 and availability of a set of NR chemical feedstock suppliers. At the center of the superstructure is a set of NJ candidate chemical processing technologies (plants) that can perform the conversion of the raw materials into final products. A simplifying assumption is made that raw materials are supp

47、lied only from single sources.如圖一所示，這里提出的解決上述問(wèn)題的模型是基于供應(yīng)鏈網(wǎng)絡(luò)上層建筑的，其包括HM存在市場(chǎng)，即配送中心和最終客戶的集合；化學(xué)產(chǎn)品需求（模型的變量在表1中提供）。同時(shí)，關(guān)于選址和橡膠原材料供應(yīng)量信息也是提供的。在上層建筑的中心是新澤西州候選化學(xué)加工技術(shù)（工廠），可以完成從原材料到最終產(chǎn)品的轉(zhuǎn)換。簡(jiǎn)單的假設(shè)原材料只有唯一的來(lái)源。Strategic decisions included are the selection of the optimum combination of plants from the set of candidate

48、s, as well as the allocation of these selected plants to a set of NS potential geographical sites. In addition, the optimal network of transportation links between the selected sites and existing markets needs to be designed. All these decisions are performed in terms of a finite number of NT time p

49、eriods (typically in units of years) constituting the long-range planning horizon during which prices, demands and availabilities of the chemicals, and fixed investment and operating costs of the plants can vary. At the operational level, optimal plant expansion capacities, production profiles and t

50、he flows of materials between the various components within the supply chain are determined over the entire planning horizon.戰(zhàn)略決策包括候選工廠中選擇最優(yōu)化組合，將所選的工廠分配到潛在的地理位置中去。此外，需要設(shè)計(jì)所選的地點(diǎn)和已存在的市場(chǎng)之間的交通聯(lián)系優(yōu)化網(wǎng)絡(luò)。所有的決策在期間（通常以年為單位）內(nèi)按照限定的數(shù)目完成，決策包括長(zhǎng)期規(guī)劃期內(nèi)的價(jià)格、需求和化學(xué)品的供應(yīng)量、固定資產(chǎn)投資和可變運(yùn)營(yíng)成本。在運(yùn)營(yíng)層面上，優(yōu)化工廠擴(kuò)大能力，生產(chǎn)概況和供應(yīng)鏈不同組成部分間的物質(zhì)流也將在這

51、個(gè)計(jì)劃期內(nèi)決定下來(lái)。Unlike most traditional approaches where only an economic criterion is considered, the model developed here also aims at finding the network configuration and capacity planning strategy that minimize the environmental impact of the entire supply chain. Consequently, the formulation results

52、 in a multi-objective mixed integer linear programming (moMILP) problem, allowing the inherent trade-offs between the conflicting economic and environmental objectives to be explored.不像大部分只考慮經(jīng)濟(jì)標(biāo)準(zhǔn)的傳統(tǒng)方法，這里提出的模型目的在于減小整個(gè)供應(yīng)鏈環(huán)境影響的網(wǎng)絡(luò)配置和能力規(guī)劃策略。結(jié)果，應(yīng)用多目標(biāo)混合整數(shù)線性規(guī)劃問(wèn)題，探討經(jīng)濟(jì)和環(huán)境之間的內(nèi)在權(quán)衡。As a measure of the profitabil

53、ity of the network, the expected net present value (NPV) of the investment required to install, expand and operate the plants is used as the economic objective function. In contrast, the ecological objective function is based upon the environmental impact resulting from the operation of the entire n

54、etwork over the entire planning horizon. This is achieved by adopting the principles of LCA, expanding the network boundaries to incorporate a set of NP life cycle stages and using the Eco-Indicator 99 method 35 to assess the environmental impact of the network. This requires the characterization of

55、 a set of NB environmental burdens into a set of NE impact categories/indicators over the entire horizon.安裝所需的投資的預(yù)計(jì)凈現(xiàn)值（NPV）作為網(wǎng)絡(luò)盈利能力的衡量方法，擴(kuò)展和經(jīng)營(yíng)工廠作為經(jīng)濟(jì)目標(biāo)函數(shù)。相反的，生態(tài)目標(biāo)函數(shù)是根據(jù)整個(gè)規(guī)劃期內(nèi)網(wǎng)絡(luò)的運(yùn)營(yíng)導(dǎo)致的環(huán)境影響來(lái)確定的。這是通過(guò)采用生命周期評(píng)價(jià)的原則和使用環(huán)保指標(biāo)99方法來(lái)實(shí)現(xiàn)的。LCA原則是擴(kuò)大網(wǎng)絡(luò)界限納入NP生命周期階段，而環(huán)保指標(biāo)99方法是用來(lái)評(píng)價(jià)網(wǎng)絡(luò)的環(huán)境影響。這需要將整個(gè)期間內(nèi)的環(huán)境負(fù)擔(dān)設(shè)置成一系列影響類(lèi)別/指標(biāo)。3. Math

56、ematical model3.1. Plant location, capacity expansion and material balances工廠選址，能力擴(kuò)展和物料平衡The problem is formulated such that the variable Fjst represents the total capacity during time interval t of plant j being situated at site s. Existing plant capacities are entered into the model by specifying

57、Fjst at time t = 0. The expansion of plant capacities during time interval t is represented by the variable FEjst. For a plant that has not been installed during previous time intervals (i.e. which has zero capacity at time t=0), the first non-zero value of FEjst during the planning horizon correspo

58、nds to the installation capacity of the plant. As such, no distinction is necessary between capacity location and expansion. FEjst captures both scenarios and, therefore, reflects any form of capacity increase of a particular plant. Throughout the subsequent model description the terms capacity expa

59、nsions and location will be interchanged unless a distinction is explicitly made.Fjst代表位于s的工廠j時(shí)間段t總能力。模型已有的工廠能力是指定時(shí)間t=0時(shí)具體Fjst的值。T階段工廠擴(kuò)展能力用變量FEjst表示。先前時(shí)間階段內(nèi)沒(méi)有安裝的工廠（如在t=0時(shí)能力為0），規(guī)劃期內(nèi)FEjst第一個(gè)非零值與工廠安裝容量有關(guān)。同樣的，沒(méi)必要區(qū)分工廠的位置和能力擴(kuò)展。兩種方案的FEjst捕獲反應(yīng)特定工廠的能力增加。在整個(gè)后續(xù)模型的能力擴(kuò)展和位置描述可以互換，除非明確提出有區(qū)別。Control over the changes in the capacities over the planning horizon is achieved through the binar