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Collaborative Lot-Sizing problem for an Industrial Symbiosis ⁎
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Collaborative Lot-Sizing problem for an Collaborative Lot-Sizing problem for an Collaborative Lot-Sizing problem for an Industrial Symbiosis Collaborative Lot-Sizing problem for an Industrial Symbiosis Industrial Symbiosis Symbiosis C´ ecilia Daquin,Industrial Hamid Allaoui, Gilles Goncalves, Tient´ e Hsu
C´ ecilia Daquin, Hamid Allaoui, Gilles Goncalves, Tient´ e Hsu C´ e e C´ ecilia cilia Daquin, Daquin, Hamid Hamid Allaoui, Allaoui, Gilles Gilles Goncalves, Goncalves, Tient´ Tient´ e Hsu Hsu C´ ecilia Daquin, Hamid Allaoui, Gilles Goncalves, Tient´ Univ. Artois, EA 3926, Laboratoire de G´enie Informatique eetHsu Univ. Artois, EA 3926, Laboratoire de G´ enie Informatique et Univ. 3926, de G´ Informatique et d´Automatique de l´Artois (LGI2A) B´ France Univ. Artois, Artois, EA EA 3926, Laboratoire Laboratoire deeethune, G´eenie nie F-62400, Informatique et d´Automatique de l´Artois (LGI2A) B´ thune, F-62400, France Univ. Artois, EA 3926, Laboratoire de G´ e nie Informatique et d´Automatique de l´Artois (LGI2A) B´ e thune, F-62400, France (e-mail: [email protected] (C. Daquin), d´Automatique de l´Artois (LGI2A) B´ethune, F-62400, France (e-mail: [email protected] (C. Daquin), d´Automatique de l´Artois (LGI2A) B´e(G. thune, (e-mail: [email protected] (C. Daquin), [email protected] Goncalves), (e-mail: [email protected] (C.F-62400, Daquin),France [email protected] (G. Goncalves), (e-mail: [email protected] (C. Daquin), [email protected] (G. Goncalves), [email protected] (G. (H. Goncalves), Allaoui), [email protected] [email protected] (H. Allaoui), [email protected] (G. [email protected] (H. Allaoui), [email protected] (T. Hsu) [email protected] (H. Goncalves), Allaoui), [email protected] (T. Hsu) [email protected] (H. Allaoui), [email protected] (T. Hsu) [email protected] (T. Hsu) [email protected] (T. Hsu) Abstract: Abstract: For For decades, decades, the the industry industry is is aa huge huge consumer consumer of of resources, resources, generates generates waste waste and and has has Abstract: For decades, the industry is a huge consumer of resources, generates waste has serious impacts on our planet. In order to preserve the environment, new economic models Abstract: For decades, the industry is a to huge consumer ofenvironment, resources, generates waste and and has serious impacts on our planet. In order preserve the new economic models Abstract: Forincluding decades, the industry is a to huge consumer of resources, generates wastefits and has serious impacts on our planet. In order preserve the environment, new economic models are emerging circular economy. Circular economy is a system that with serious impacts on our planet. In order to preserve the environment, new economic models are emerging including the circular economy. Circular economy is a system that fits with serious impacts onaims our planet. In both order to preserve the economy environment, economic models are including the circular economy. Circular economy iswaste system that fits fits with sustainability and resources consumption and production. Among are emerging emerging including thereduce circular economy. Circular aa new system that with sustainability and aims to to reduce both resources consumption andis waste production. Among are emerging including the circular economy. Circular economy is a system that fits with sustainability and aims to reduce both resources consumption and waste production. Among the components of circular economy, industrial ecology is the collaboration of industries on sustainability and aims to reduce both resourcesecology consumption and waste production. Among the components of aims circular economy, industrial is the collaboration of industries on aa sustainability and to reduce both resources consumption and waste production. Among the components of circular economy, industrial ecology is the collaboration of industries on territory in order to exchange materials, water or energy through industrial symbiosis. Industrial the components of circular economy, industrial ecology is the collaboration of industries on aa territory in orderof to circular exchangeeconomy, materials, water or ecology energy through industrial symbiosis. Industrial the components industrial is theincollaboration of industries on a territory in order to exchange materials, water or energy through industrial symbiosis. Industrial ecology and industrial symbiosis are more and more present the literature. However, most territory in order to exchange materials, water or energy through industrial symbiosis. Industrial ecology and industrial symbiosis are more and present in industrial the literature. However, most territory inin order to exchange materials, water ormore energy through symbiosis. Industrial ecology and industrial symbiosis are more and more present in literature. However, most of articles the literature focused the strategic decision level. this paper, we focus on ecology and industrial symbiosis areon more and more present in the theIn literature. However, most of articles in the literature focused on the strategic decision level. In this paper, we focus on ecology and industrial symbiosis are more and more present in the literature. However, most of articles in the literature focused on the strategic decision level. In this paper, we focus on tactical decisions, and investigate production planning as a lot sizing problem in a collaborative of articles in the literature focused on the strategic decision level. In this paper, we focus on tactical decisions, and investigate production planning as a lot sizing problem in a collaborative of articles in the literature focused on the strategic decision level. In this paper, we focus on tactical decisions, and investigate production planning as aa lot sizing problem in aa collaborative cc 2019 context involving two actors belong an industrial symbiosis. Copyright IFAC tactical decisions, and investigate production planning as lot sizing problem in collaborative context involving two belong an industrial symbiosis. Copyright 2019 tactical decisions, and actors investigate production planning as a lot sizing problem in IFAC a collaborative cc 2019 context involving two actors belong an industrial symbiosis. Copyright IFAC context involving two actors belong anAutomatic industrial symbiosis. Copyright 2019 IFAC © 2019, IFAC (International Federation of Control) Hosting by Elsevier Ltd. AllIFAC rights reserved. c context involving two actors belong an industrial symbiosis. Copyright 2019 Keywords: Keywords: Industrial Industrial Symbiosis, Symbiosis, Collaboration, Collaboration, Optimization, Optimization, Lot-Sizing, Lot-Sizing, Cost Cost Sharing. Sharing. Keywords: Keywords: Industrial Industrial Symbiosis, Symbiosis, Collaboration, Collaboration, Optimization, Optimization, Lot-Sizing, Lot-Sizing, Cost Cost Sharing. Sharing. Keywords: Industrial Symbiosis, Collaboration, Optimization, Cost of Sharing. 1. INTRODUCTION exchanges andLot-Sizing, mutualizations flows, matters or services 1. INTRODUCTION exchanges and mutualizations of flows, matters or services 1. INTRODUCTION exchanges and mutualizations of matters services between involved partners through Industrial Symbioses 1. INTRODUCTION exchangesinvolved and mutualizations of flows, flows, matters or or services between partners through Industrial Symbioses 1. INTRODUCTION exchanges and mutualizations of flows, matters or services between involved partners through through Industrialseparate Symbioses (IS). An IS is ”the engagement of traditionally inSince the beginning of the industrial area, companies deal between involved partners Industrial Symbioses An IS is ”the engagement of traditionally separate inSince the beginning of the industrial area, companies deal (IS). between involved partners through Industrial Symbioses (IS). An IS is ”the engagement of traditionally separate industries in a collective approach to competitive advantage Since the beginning of the industrial area, deal with production systems that are based on acompanies linear scheme: (IS). An IS is ”the engagement of traditionally separate inSince the beginning of the industrial area, companies deal dustries in a collective approach to competitive advantage with production systems that are based on a linear scheme: (IS). An IS is ”the engagement of traditionally separate industries in a collective approach to competitive advantage Since the beginning of the industrial area, companies deal involving physical exchange of materials, energy, water, with production are based on aakind linear scheme: extract, produce,systems use andthat throw out. This of systems dustries in a collective approach to competitive advantage with production systems that are based on linear scheme: involving physical exchange of materials, energy, water, extract, produce, use and throw out. This kind of systems dustries in a collective approach to competitive advantage involving physical exchange of materials, energy, water, with production systems that are based on a linear scheme: and/or by-products. The keys to industrial symbiosis are extract, produce, use and throw out. This kind of systems considers that our planet offers infinite reserves of natural involving physical exchange water, extract, produce, use and offers throw out. This kind of systems and/or by-products. The keysof tomaterials, industrialenergy, symbiosis are considers that ouruse planet reserves of natural physical exchange energy, water, and/or by-products. by-products. The keysofto tomaterials, industrial symbiosis are extract, andoverconsumption throwinfinite out. This kind of collaboration and the synergistic possibilities offered by considers that planet offers infinite reserves of natural resources. Thisour yields an of resources and involving and/or The keys industrial symbiosis are considersproduce, that our planet offers infinite reserves of systems natural collaboration and the synergistic possibilities offered by resources. This yields an overconsumption of resources and by-products. The keys to(2000)). industrial symbiosis are collaboration and the synergistic possibilities offered by considers that our offerswaste infinite reserves ofand natural geographic proximity”(Chertow This area of georesources. This yields an overconsumption of resources and then generates an planet increasing production dis- and/or collaboration and the synergistic possibilities offered by resources. This yields an overconsumption of resources and geographic proximity”(Chertow (2000)). This area of geothen generates an increasing waste production and discollaboration and the synergistic possibilities offered by geographic proximity”(Chertow (2000)). This area of georesources. This yields an overconsumption of resources and graphic proximity is an Eco-Industrial Park (EIP). There then generates an increasing waste production and disrupts ecosystems. Linear economy hasproduction significant footprint geographic proximity”(Chertow (2000)). This area of geothen generates an increasing waste and disgraphic proximity is an Eco-Industrial Park (EIP). There rupts ecosystems. Linear economy has significant footprint geographic proximity”(Chertow (2000)). This area of geographic proximity is an Eco-Industrial Park (EIP). There then generates an increasing waste production and disare two types of industrial symbiosis : rupts ecosystems. Linear economy has significant footprint on the environment (climate change, biodiversity erosion, graphic proximity is an Eco-Industrial (EIP). There rupts ecosystems. Linear economy has significant footprint are two types of industrial symbiosis : Park on theecosystems. environment (climate change, erosion, proximity is an Eco-Industrial are two two types types of industrial industrial symbiosis :: Park (EIP). There rupts Linear economy hasbiodiversity significant footprint on environment (climate change, biodiversity erosion, etc.) and has reached its limits. In order to preserve the en- graphic are of symbiosis on the the environment (climate change, biodiversity erosion, A substitute synergy enables to use waste etc.) and has reached its limits. In order to preserve the enare- two types of industrial on the environment (climate change, biodiversity erosion, A substitute synergy symbiosis enables to: use waste coming coming etc.) and has its In to the vironment, itreached is necessary to change production, distribuetc.) and hasit reached its limits. limits. In order order to preserve preserve the enen-- from A substitute synergy enables use waste coming an industrial process of aato company, called byvironment, is necessary to change production, distribuA substitute synergy enables to use waste coming etc.) and has reached its limits. In order to preserve the enfrom an industrial process of company, called byvironment, it is necessary to change production, distribution and buying modes. Hence, new production, economic models are vironment, it is necessary to change distribu- A substitute synergy enables use waste coming from an industrial industrial process ofan atocompany, company, called byproduct, as raw materials for industrial process in tion and buying modes. Hence, new economic models are from an process of a called byvironment, it is necessary to change production, distribuproduct, as raw materials for an industrial process in tion and buying modes. Hence, new economic models are emerging including the Circular Economy (CE) (Pearce tion and buying modes. Hence, new economic models are from an company; industrial processfor ofan a company, called byproduct, as raw materials industrial process in another emerging including the Circular Economy (CE) (Pearce product, as raw materials for an industrial process in tion and buying modes. Hence, new economic models are another company; emerging including the Circular Economy (CE) (Pearce and Turner (1991)). emerging including the Circular Economy (CE) (Pearce product, as raw materials for an industrial process in another company; A mutualization synergy makes possible the pooling and Turner (1991)). another company; emerging including the Circular Economy (CE) (Pearce A mutualization synergy makes possible the pooling and (1991)). and Turner Turner (1991)).is a system that reconciles economy company; -- another A mutualization synergy makes possible the pooling of services, equipment and resources between players Circular economy A mutualization synergy possible the pooling and Turner (1991)).is a system that reconciles economy services, equipment andmakes resources between players Circular economy - of A mutualization synergy possible the pooling services, equipment andmakes resources between players of an EIP (e.g. group buy, shared rubbish collection, Circular economy aa system reconciles economy and environmental protection inthat a social approach. This of services, equipment and resources between players Circular economy is isprotection systemin that reconciles economy of an EIP (e.g. group buy, shared rubbish collection, and environmental a social approach. This of services, equipment and resources between players an EIP (e.g. group buy, shared rubbish collection, Circular isprotection a systemin that reconciles economy carpooling or sharing of pallets). and environmental aa social approach. This concept iseconomy part of sustainability and aims to ensure that of an EIP (e.g. group buy, shared rubbish collection, and environmental protection in social approach. This carpooling or sharing of pallets). concept is part of sustainability and aims to ensure that of an EIP (e.g. group buy, shared rubbish collection, carpooling or sharing of pallets). and environmental protection in a social approach. This concept is part of sustainability and aims to ensure that the 9 billion of people being on Earth in 2050 can live carpooling or issharing of pallets). concept is part of sustainability and aims to ensure that Industrial ecology not dream. the 9 of people being on Earth in 2050 can live carpooling or issharing pallets). concept is part of sustainability aims ensure that ecology not an anofutopian utopian dream. The The symbiosis symbiosis the 99 billion billion of people being on Earth in 2050 can live in environmental and social condithesatisfactory billion ofeconomic, people being onand Earth in to 2050 can live Industrial Industrial ecology is not an utopian dream. The of Kalundborg is one of the first experiences of in satisfactory economic, environmental and social condiIndustrial ecology is not an utopian dream. The symbiosis symbiosis the 9 billion of people being on Earth in 2050 can live of Kalundborg is one of the first experiences of indusindusin satisfactory economic, environmental and social conditions. CE is based on the cyclic operation of ecosystems in satisfactory economic, environmental andofsocial condi- trial Industrial ecology is not an utopian dream. The symbiosis of Kalundborg is one of the first experiences of ecology. It was a reference for the development of tions. CE is based on the cyclic operation ecosystems of Kalundborg iswas onea of the firstforexperiences of indusindusin satisfactory economic, environmental and social condiecology. It reference the development of tions. CE is based on the cyclic operation ecosystems by reintroducing matter and products in of the cycle of trial tions. CE is based on the cyclic operation of ecosystems of Kalundborg one the most firstfor experiences of industrial ecology. It iswas was a of reference for the indevelopment development of industrial symbiosis and the cited the literature by reintroducing matter and products in the cycle of trial ecology. It a reference the of tions. CE is based on the cyclic operation of ecosystems industrial symbiosis and the most cited in the literature by reintroducing matter and products in the cycle of production and utilization, as far as possible, in order to by reintroducing matter and products in the cycle to of trial ecology. It Chertow was and a reference the in of industrial symbiosis and the mostfor cited indevelopment the literature (Ehrenfeld and (2002), Ehrenfeld and Gertler production and utilization, as far as possible, in order industrial symbiosis the most cited the literature by reintroducing matter and products in the cycle to of (Ehrenfeld and Chertow (2002), Ehrenfeld and Gertler production and utilization, as as possible, in reduce both resources consumption waste production. production and utilization, as far far asand possible, in order order to industrial symbiosis and the most cited in the literature (Ehrenfeld and Chertow (2002), Ehrenfeld and Gertler (1997), Jacobsen (2006)). This experience is not the only reduce both resources consumption and waste production. and Chertow (2002), Ehrenfeld and the Gertler production utilization, asseveral far asand possible, inincluding order to (Ehrenfeld (1997), Jacobsen (2006)). This experience is not only reduce both resources consumption waste This system revolves around principles, reducesystem bothand resources consumption and waste production. production. (Ehrenfeld and Chertow (2002), Ehrenfeld and Gertler (1997), Jacobsen (2006)). This experience is not the only one. We can also quote the industrial ecology of GrandeThis revolves around several principles, including (1997), Jacobsen (2006)). This experience is not the only reduce both resources consumption and waste production. one. We can also quote the industrial ecology of GrandeThis system revolves around several principles, including Industrial Ecology (IE) (Frosch and Gallopoulos (1989)). 1 2 This system revolves around several principles, including (1997), Jacobsen (2006)). This experience is not the only one. We Weincan can also1quote quote the industrial ecologyinof ofCanada GrandeSynthe France or the one of Saint-Flicien Industrial Ecology (IE) (Frosch and Gallopoulos (1989)). 2. one. also the industrial ecology GrandeThis system revolves around several principles, including Synthe in France or the one of Saint-Flicien in Canada Industrial Ecology (IE) (Frosch and Gallopoulos (1989)). 1quote the industrial ecology of Grande2. Industrial Ecology (IE) (Frosch and Gallopoulos (1989)). one. We can also 1 2 Synthe in France or the one of Saint-Flicien in Canada . Yet the setting-up of industrial symbioses is complicated. IE is a discipline aiming to limit impact of industry on Synthe in France or the one of Saint-Flicien in Canada Industrial Ecology aiming (IE) (Frosch andimpact Gallopoulos (1989)). Yet the setting-up 1 of industrial symbioses is complicated. 2. IE is a discipline to limit of industry on Synthe in France or the one of Saint-Flicien in Canada . Yet the setting-up of industrial symbioses is complicated. Therefore the study of these industrial organizations is a IE aa discipline to of industry the environment. To achieve this impact goal, IE is based on the setting-up symbioses is complicated. IE is isenvironment. discipline aiming aiming to limit limit impact of is industry on Yet Therefore the studyof ofindustrial these industrial organizations is a the To achieve this goal, IE based on Yet the setting-up of industrial symbioses is complicated. Therefore the study of these industrial organizations is a IE is a discipline aiming to limit impact of industry the environment. To achieve this goal, IE is based on the study of these industrial organizations is a the environment. To achieve this goal, IE is based on 1Therefore This research comes from this thegoal, ENCETRE project http://www.ecopal.org/ the study of these industrial organizations is a the environment. To achieve IE is based on 121Therefore research comes from the ENCETRE project http://www.ecopal.org/ This
(https://www.lgi2a.univ-artois.fr/spip/fr/projets/encetre) and This research comes from the ENCETRE project This http://www.ecopal.org/ 1 2 http://www.mamunicipaliteefficace.ca/104-10-tudes-de-casresearch comes from the ENCETRE project http://www.ecopal.org/ (https://www.lgi2a.univ-artois.fr/spip/fr/projets/encetre) and http://www.mamunicipaliteefficace.ca/104-10-tudes-de-cas2 1 receives a financial support from the BPI France and the Hauts de saint-felicien-valorisation-des-rejets-thermiques-de-lunite-de(https://www.lgi2a.univ-artois.fr/spip/fr/projets/encetre) and http://www.mamunicipaliteefficace.ca/104-10-tudes-de-cas2 http://www.ecopal.org/ This research comes from the ENCETRE project (https://www.lgi2a.univ-artois.fr/spip/fr/projets/encetre) http://www.mamunicipaliteefficace.ca/104-10-tudes-de-casreceives a financial support from the BPI France and the Hautsand de saint-felicien-valorisation-des-rejets-thermiques-de-lunite-de2 http://www.mamunicipaliteefficace.ca/104-10-tudes-de-casFrance region. cogeneration.html receives a financial support from the BPI France and the Hauts de saint-felicien-valorisation-des-rejets-thermiques-de-lunite-de(https://www.lgi2a.univ-artois.fr/spip/fr/projets/encetre) and receivesregion. a financial support from the BPI France and the Hauts de saint-felicien-valorisation-des-rejets-thermiques-de-lunite-deFrance cogeneration.html France cogeneration.html receives a financial support from the BPI France and the Hauts de saint-felicien-valorisation-des-rejets-thermiques-de-lunite-deFrance region. region. cogeneration.html France region. cogeneration.html 2405-8963 © IFAC (International Federation of Automatic Control) Copyright © 2019, 2019 IFAC 1342Hosting by Elsevier Ltd. All rights reserved. Copyright ©under 2019 responsibility IFAC 1342Control. Peer review of International Federation of Automatic Copyright © 1342 Copyright © 2019 2019 IFAC IFAC 1342 10.1016/j.ifacol.2019.11.382 Copyright © 2019 IFAC 1342
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Fig. 1. Distribution of articles per publication year from 2000 to 2018 research field aiming to understand their development in order to show their interest and make them easier. The study of EI is more and more present in the literature. The majority of publications focused on strategic decisions like network design. However there are very few works dealing with tactical and operational decisions (see section 2). In this context, we decide to focus on tactical level and more particularly on the production planning of supply chains involved in industrial symbiosis in which collaborators are already identified. The aim of this paper is to optimize the production planning for two actors involved in the IS in order to minimize the total economic cost. We formulate this problem as a collaborative lot-sizing problem for a discrete planning horizon. In the remainder of this paper, a literature review is presented in section 2. Afterwards the problem statement and an ILP model are presented in section 3. The studied problem is illustrated by an example in section 4 and a strategy of cost sharing among the two actors is described is section 5. Finally, a conclusion and some future research directions are discussed in section 6. 2. LITERATURE REVIEW We particularly focussed on modeling and optimization issues related to industrial symbiosis at strategic, tactical and operational decision levels. We used the ScienceDirect database and looked for articles with the words ”industrial ecology” or ”industrial symbiosis” or ”eco-industrial park” and ”optimization” in their abstracts, titles or keywords. In total 107 publications were listed from 2000 to the beginning of 2018. Fig. 1 shows the distribution of these articles per publication year. We notice that this research field aroused strong interest these last years. Then, we identified in these publications mathematical models established within the scope of an industrial symbiosis and analyzed the criteria considered within them. The aim of our work is to show the gaps in this field and then to suggest some relevant perspectives for future works.
(see Table 1). The first one is collaboration through water network and is the most usual in the literature. In this problem, water have to be optimally allocated, treated, evacuated or reused between each participants included in EIP. The second kind of collaboration is through energy network. However, few publications tackle this problem and no multiobjective model was developed. A possible explanation is the difficulties to obtain reliable and complete data for this kind of problem. Material exchange is the third kind of collaboration that is examined in the literature. Several types of materials can be considered as waste, by-product, etc. But only few studies mentioned material exchanges by actually optimizing the network. Note that these collaborations mentioned above were optimized independently. Table 1. Types of collaboration in an EIP using optimization methods in the litterature Types of collaboration Water network Energy network Material exchange
Now let us focus on criteria considered within mathematical models to optimize the design or planning of industrial symbiosis (see Table 2). The economic objective is mostly present in the models. Not only it is the easiest to quantify, but also is usually the most relevant for participants of EIP. Indeed, an industry will get involved in an industrial symbiosis if costs are reduced or identical to the situation of not being involved in the IS. Hence, cost minimization is the objective that is mostly used. Another objective formalized in models is the topological aspect. The latter enables the evaluation of network complexity. This aspect is often ignored, yet it represents an investment cost and shows the network feasibility. The environmental aspect is the main motivation of industrial ecology. In order to use resources as optimally as possible and to reduce the environmental impact, the majority of studies seek to minimize the consumption of natural resources. Yet this objective is not enough modeled in the literature. Finally, the social aspect is crucial in the development of an EIP, just like the economic and environmental objectives. However, no work in the literature dealing with the social objective. Indeed, social criterion is hard to quantify since it implied some subjective judgements. Aviso et al. (2011) developed indicators in order to estimate the satisfaction of participants in an EIP but this detail guarantees no social benefit. Table 2. Optimization Objectives for an EIP Criteria Economic
Like in a classical supply chain, the encountered problems are categorized according to three decision levels: strategic, tactical and operational. Most of them focused on strategic level. In particular, they tackled design of symbiosis network and identification of synergies within the EIP. The topics studied in the literature are varied: waste, CO2 emissions, flow of matter, water, life cycle, etc. Three options of collaboration have been studied in the publications
References Nobel and Allen (2000), Chew et al. (2008), Boix et al. (2012) Kim et al. (2010), Gonela et al. (2015), Afshari et al. (2018) Cimren et al. (2011), Vadenbo et al. (2014)
Topological Environmental Social
References Nobel and Allen (2000), Hirata et al. (2004), Jung et al. (2013) Rubio-Castro et al. (2011), Boix et al. (2012) Nobel and Allen (2000), Rubio-Castro et al. (2011), Aviso et al. (2011), Mattila et al. (2012) Aviso et al. (2011), Jung et al. (2013), Leong et al. (2017)
In conclusion, the study of EIP is more and more present in the literature, but many aspects still need to be investigated. We noticed that the tactical and operational
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we propose a new model in order to optimize the production planning for both actor 1 and actor 2. We use the following notations : T t dn,t pn,t fn,t Fig. 2. Industrial symbiosis with two actors decisions were not examined in the literature. The majority of publications focused on the network design of symbiosis. The networks of water, energy and materials exchange are optimized independently, but a perspective would be to interact these different networks in order to increase symbiotic connections. Regarding the criteria of mathematical models, there are few multiobjective models. However, by definition, the design and management of an EIP is a multiobjective problem that involved the satisfaction of economic, environmental and social pillars. Consequently, we decided to focus on tactical decision level in this paper. More particularly, we seek to optimize the production planning of supply chains which collaborate inside an industrial symbiosis. To start, we focus on economic aspect. 3. PROBLEM STATEMENT AND FORMULATION
hn,t CapPn,t CapSn pourcentagen bn,t cn,t CapBn,t storage costDn,t CapSDn
We focus on the optimization of production planning for involved actors who decide to collaborate together in an industrial symbiosis. In other words, we seek to obtain a collaborative production planning formulated as a centralized multi-period lot-sizing problem. In this study, we set the number of actors to 2, as shown in Fig. 2. To produce one unit of product, an actor needs raw materials ordered from a supplier. But in the context of industrial symbiosis, the actor can also use the waste produced by another actor. This waste, called byproducts, can substitute the necessary raw materials. Therefore, the actor has to plan his production for each period and decide how many raw materials he must order from his usual supplier and how many byproducts he must order from the partner actor of the symbiosis. Moreover, instead of paying to bury these byproducts, the upstream actor may recycle them in whole or in part with the downstream participant. Our purpose is to minimize the total cost for both actors 1 and 2 which is the sum of the supply cost, the production cost, the storage cost, the burying cost and the symbiosis cost. To solve this problem, we take into consideration several constraints : the demand satisfaction over T periods, (unauthorized delays), the capacity of storage, production, supply and burying as well as production and delivery times. This problem corresponds to a Lot-Sizing (LS) problem applied to the industrial symbiosis. To model it, we start with a basic LS model, the Capacitated Lot-Sizing problem (CLS), and then we add the hypotheses and constraints necessary for the studied industrial symbiosis. Therefore,
symbiosis cost order costMt nomenclaturen
storage costMn,t CapSMn costMn,t
CapMn,t ltMn laMn
ltD2 laD2
Total number of periods Discrete period of the planning horizon (1 ≤ t ≤ T ) demand of end products for actor n in period t (n ∈ N : n ≤ 2) unit production cost for actor n in period t setup production cost for actor n in period t unit end product storage cost for actor n in period t production capacity for actor n in period t end product storage capacity for actor n (constant at each period) ratio between byproducts and end products generated by actor n unit burying cost of byproduct for actor n in period t setup burying cost for actor n in period t burying capacity for actor n in period t unit byproduct storage cost for actor n in period t byproduct storage capacity for actor n (constant at each period unit symbiosis cost applied to the waste flow (constant at each period) fixed raw matter order cost in period t number of matter units necessary to produce one unit of end product for actor n unit matter cost for actor n in period t byproduct storage capacity for actor n (constant at each period) unit raw matter buying cost for actor n in period t (including matter cost and transport) capacity of available raw matter for actor n in period t = 1, lead time of raw matter for actor n expected delivery of raw matter at the beginning of the planning horizon for actor n (according to the previous planning) = 1, lead time of byproduct for acteur 2 expected delivery of byproduct at the beginning of the planning horizon for actor 2 (according to the previous planning)
The decision variables are as follows :
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xn,t sn,t
yn,t wn,t stockDn,t
αn,t
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Quantity of end product manufactured for actor n in period t End product stock level for actor n at the end of period t 1 if production is started for actor n in period t (yn,t = 1 si xn,t > 0) 0 otherwise Quantity of by-products to bury for the actor n in period t Byproduct stock level for actor n at the end of period t 1 if byproduct is buryed for actor n in period t (αn,t = 1 si wn,t > 0) 0 otherwise
stockMn,t Matter stock level for actor n at the end of period t zMn,t Quantity of raw matter ordered for actor n in period t 1 if raw matter is ordered from supplier for actor t (n,t = 1 si zMn,t > 0) n,t 0 otherwise zD2,t
Quantity of byproduct ordered for actor 2 in period t
So, our model has to decide at each period t : - the quantity of end products to manufacture (x1,t and x2,t ) and to stock (s1,t and s2,T ) for actor 1 and actor 2; - the quantity of raw matter to order (zM1,t and zM2,t ) and to stock (stockM1,t and stockM2,t ) for actor 1 and actor 2; - the quantity of by products to order by actor 2 from actor 1 (zD2,t ) and the quantity to stock (stockM2,t ); - the quantity of byproducts generated by actor 2 to bury (w2,t ) and to stock (stockD2,t ); - the quantity of byproducts generated by actor 1 to supply to actor 2 (zD2,t ), to bury (w1,t ) and to stock (stockD1,t ). The decision variable zD2,t represents the byproduct flow which is characteristic of industrial symbiosis. It is the common element between actor 1 and actor 2. Indeed, the quantity of byproduct to provide by actor 1 satisfies some of the needs of actor 2. In order to minimize the total cost, we propose the following ILP model : Supply Cost =
2 t∈T
n=1
(order costMt × n,t
+ costMn,t × zMn,t ) 2 P roduction Cost = (pn,t xn,t + fn,t yn,t ) Storage Cost =
(1) (2)
t∈T n=1 2
( (hn,t sn,t )
t
n=1
+ (storage costMn,t × stockMn,t ) + (storage costDn,t × stockDn,t ) )
(3)
Burying Cost =
2 t∈T
Symbiosis Cost =
t∈T
(bn,t wn,t + cn,t αn,t )
(4)
symbiosis costt × zD2,t
(5)
n=1
minf = Supply Cost + P roduction Cost+ Storage Cost + Burying Cost + Symbiosis Cost
(6)
Subject to: xn,1 = dn,1 + sn,1 sn,t−1 + xn,t = dn,t + sn,t
(∀n ∈ {1, 2}, ∀t ∈ T \{1})
(7)
laM1 = (nomenclature1 × x1,1 ) + stockM1,1 stockM1,t−1 + zM1,t−1 = (nomenclature1 × x1, t) + stockM1,t (∀t ∈ T \{1})
(8)
laM2 + laD2 = (nomenclature2 × x2,1 ) + stockM2,1 stockM2,t−1 + zM2,t−1 + zD2,t−1 = (nomenclature2 × x2,t ) + stockM2,t (∀t ∈ T \{1})
(9)
pourcentage1 × x1,1 = zD2,1 + w1,1 + stockD1,1 100 pourcentage1 × x1,t = zD2,t + w1,t stockD1,t−1 + 100 + stockD1,t (∀t ∈ T \{1})
(10)
pourcentage2 × x2,1 = w2,1 + stockD2,1 100 pourcentage2 × x2,t = w2,t + stockD2,t stockD2,t−1 + 100 (∀t ∈ T \{1}) (11) xn,t ≤ CapPn,t × yn,t (∀n ∈ {1, 2}, ∀t ∈ T ) (12) (13) sn,t ≤ CapSn (∀n ∈ {1, 2}, ∀t ∈ T ) zMn,t ≤ CapMn,t × n,t (∀n ∈ {1, 2}, ∀t ∈ T ) (14) pourcentage1 zD2,1 ≤ CapP1,1 × 100 pourcentage1 zD2,t ≤ CapSD1 + CapP1,t × 100 (∀t ∈ T \{1}) (15) stockMn,t ≤ CapSM1 (∀n ∈ {1, 2}, ∀t ∈ T ) (16) (17) wn,t ≤ CapBn,t × αn,t (∀n ∈ {1, 2}, ∀t ∈ T ) stockDn,t ≤ CapSDn (∀n ∈ {1, 2}, ∀t ∈ T ) (18) (19) yn,t , αn,t , n,t ∈ {0, 1} (∀n ∈ {1, 2}, ∀t ∈ T ) xn,t , sn,t , wn,t , stockDn,t , stockMn,t , zMn,t , (20) zD2,t ≥ 0 (∀n ∈ {1, 2}, ∀t ∈ T ) In this formulation, the objective function (6) minimizes the sum of several costs for the two actors in an industrial symbiose : the supply costs of raw material (1), the production costs (2), the storage costs for raw material, end products and byproducts (3), the burying costs for byproducts (4) and the symbiosis costs (5) which correspond to
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the recycling costs of byproducts provided by actor 1 to actor 2. Constraints (7), (8), (9), (10) and (11) are equations of balance of stocks or flow conservation constraints for each actor at each period t. Constraints (12) ensure that the number of end product to manufacture by the actors 1 and 2 is lower than their production capacity when production is launched. Moreover, these constraints enable to initialize the decision variables yn,t . Constraints (14) (resp. (15)) ensure that the quantity of raw material to order (resp. the quantity of byproducts to order by actor 2) is lower than the available capacity from the supplier (resp. from the actor 1) when raw material is ordered (resp. byproducts). Moreover, these contraints enable to initialize the decision variables n,t . Constraints (13), (16) and (18) check the storage capacities at each period for each actor. Constraints (17) check the burying capacity for byproducts and enable to initialize the decision variables αn,t . Finally, constraints (20) and (19) stipulate the nature of decision variables.
both actor 1 and actor 2 in industrial symbiosis. Costs mentioned in column ”No symb. A1+A2” are the sum of values in columns ”No symb. A1” and ”No symb. A2” and represent costs for actor 1 and actor 2 without symbiosis. We can notice that the symbiosis enables a saving cost of 100,380 in comparison to scenario of without symbiosis, being around 4%. Let us take a look in the several costs for each actor. Table 4 (resp. table 5) shows costs for actor 1 (resp. actor 2) with solution provided by our centralized model and costs without symbiosis. We note that supply and burying cost with symbiosis are lower than without symbiosis (8,880 for supply cost and 12,000 for burying cost, being 20,880 in total). Indeed, actor1 reduces burying costs by supplying byproducts to actor 2, and actor 2 can reduce supply costs. This obtained saving cost is higher than the symbiosis cost. Consequently, actor 1 and actor 2 are better off collaborating in the symbiosis. Table 4. Costs for Actor 1 with and without symbiosis
4. ILLUSTRATIVE EXAMPLE
Costs Production Supply Storage Burying Symbiosis Obj. function
An example is provided to ease the reader understanding the problem studied. In order to simplify calculation, we make the following assumptions: - Setup and fixed costs are set to 0 (setup production costs fn,t , setup burying costs of byproducts cn,t and fixed raw matter order costs order costMt ); - All storage costs are set to 10 (hn,t = storage costDn,t = storage costMn,t = 10 ∀t ∈ T, ∀n ∈ {1, 2}); - The cost of raw materials and the cost of burying waste are equal and are set to 8 at each period t for both actors (costMn,t = bn,t = 8). The significant data in this problem related to byproducts flow (ie the industrial symbiosis). It’s represented in this paper by the symbiosis cost. As a reminder, this cost is applied to each byproduct unit transferred from actor 1 to actor 2 at each period. It can represent an unit transportation cost or a recycling cost for example and it is supported by actor 1. We choose to set the unit symbiosis cost to 7. We apply our model presented in section 3 to a dataset by taking into consideration the previous hypotheses. We use ILOG CPLEX 12.6.3 to solve it. The obtained results are compared to a production planning model for each actor without symbiosis that we have also developed. The results are summarized in table 3. Table 3. Results of centralized model with symbiosis and without symbiosis Costs Production Supply Storage Burying Symbiosis Obj. function
Symbiosis A1* and A2* 100,000 115,920 0 12,000 10,500 238,420
No symb. A1 50,000 65,600 0 12,000
No symb. A2 50,000 59,200 0 12,000
No symb. A1+A2 100,000 124,800 0 24,000
127,600
121,200
248,800
*A1 (resp A2) denotes Actor 1 (resp. Actor 2)
The values mentioned in column ”Symbiosis A1 and A2” are obtained with the centralized model, ie are costs for
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With Symbiosis Actor 1 50,000 65,600 0 0 10,500 126,100
No Symbiosis Actor 1 50,000 65,600 0 12,000 127,600
Table 5. Costs for Actor 2 with and without symbiosis Costs Production Supply Storage Burying Symbiosis Obj. function
With Symbiosis Actor 2 50,000 50,320 0 12,000 0 112,320
No Symbiosis Actor 2 50,000 59,200 0 12,000 121,200
5. COST SHARING STRATEGY Although the total cost is reduced with the symbiosis, each actor has no guarantee to obtain any advantage in terms of their own cost. In the example presented previously, we note that actor 1 has a gain of 1,500 when actor 2 saves 8,880, being around 6 times more. Indeed, actor 1 takes care of the symbiosis costs and actor 2 has byproducts for free. It would be interested to have a more fair gain distribution between actors. To tackle this issue, a cost sharing strategy is applied in order to find the best division of the symbiosis cost for each actor that guarantees each actor obtains a fair gain. The strategy is based on the Shapley Value (Shapley (1953), Voruganti et al. (2011)). It rests on each participant’s expected marginal contribution to the collaboration. By applying this strategy, actor 1 has to pay 6,810 for the symbiosis costs instead of 10.500, about 35% off. For actor 2, the symbiosis costs go from 0 to 3.690, being around 3% of its total cost. So that meant actor 1 has to pay 122.410 (about 3% off) and 116,010 for actor 2 (about 3% increase) (see table 6). Therefore, each of actors saves 5.190, being around 4% of their cost without symbiosis.
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6. CONCLUSION A huge waste of resources and the deterioration of the environment characterize linear economy, which dominates our planet since the beginning of the industrial age. Nevertheless, circular economy is a concept that is a part of sustainability and aims to reduce the environmental footprint while developing social well-being. Among pillars of circular economy, industrial ecology is a practice meeting the needs of companies to integrate the environment into their strategies. This research field attracted a lot of interest these last years but many aspects still need to be investigated. For example, in mathematical models, tactical decisions are not yet studied in the literature. It is within a sustainability framework that this paper aims to optimize the production planning of supply chains that collaborate within an industrial symbiosis. In this work, we investigated a collaborative lot-sizing problem as a part of an industrial symbiosis. Two actors belonging to different supply chains collaborate to jointly determine the best production plans in order to minimize their total cost. We proposed the first centralized planning model for 2 actors which collaborate within an industrial symbiosis. A perspective to this work would be to extend it to 3, 4, ... or n actors involved in the industrial symbiosis in order to extend the chain. Moreover, the proposed model mades involved actors to reveal all the data of the problem. Nevertheless, actors could share limited informations and negotiate on the flow of byproduct between them.Another perspective would be to formulate environmental and social objective fonctions in order to lead to multi-objective optimization. REFERENCES Afshari, H., Farel, R., and Peng, Q. (2018). Challenges of value creation in Eco-Industrial Parks (EIPs): A stakeholder perspective for optimizing energy exchanges. Resources, Conservation and Recycling, 139, 315–325. Aviso, K.B., Tan, R.R., Culaba, A.B., and Cruz, J.B. (2011). Fuzzy inputoutput model for optimizing ecoindustrial supply chains under water footprint constraints. Journal of Cleaner Production, 19(2-3), 187– 196. Boix, M., Montastruc, L., Pibouleau, L., Azzaro-Pantel, C., and Domenech, S. (2012). Industrial water management by multiobjective optimization: from individual to collective solution through eco-industrial parks. Journal of Cleaner Production, 22(1), 85–97. Chertow, M.R. (2000). INDUSTRIAL SYMBIOSIS: Literature and Taxonomy. Annual Review of Energy and the Environment, 25(1), 313–337. Chew, I.M.L., Tan, R., Ng, D.K.S., Foo, D.C.Y., Majozi, T., and Gouws, J. (2008). Synthesis of Direct and Indirect Interplant Water Network. Industrial & Engineering Chemistry Research, 47(23), 9485–9496. Table 6. Total costs for Actor 1 and Actor 2 with Symbiosis, with cost sharing and without symbiosis
Actor 1 Actor 2
With symbiosis and cost sharing 126,100 112320
With symbiosis
No Symbiosis
122,410 116010
127,600 121,200
Cimren, E., Fiksel, J., Posner, M.E., and Sikdar, K. (2011). Material Flow Optimization in By-product Synergy Networks. Journal of Industrial Ecology, 15(2), 315–332. Ehrenfeld, J. and Gertler, N. (1997). Industrial Ecology in Practice: The Evolution of Interdependence at Kalundborg. Journal of Industrial Ecology, 1(1), 67–79. Ehrenfeld, J.R. and Chertow, M.R. (2002). Industrial symbiosis: the legacy of Kalundborg. A handbook of industrial ecology, 334. Frosch, R.A. and Gallopoulos, N.E. (1989). Strategies for Manufacturing. Scientific American, 261(3), 144–152. Gonela, V., Zhang, J., and Osmani, A. (2015). Stochastic optimization of sustainable industrial symbiosis based hybrid generation bioethanol supply chains. Computers & Industrial Engineering, 87, 40–65. Hirata, K., Sakamoto, H., O’Young, L., Cheung, K.Y., and Hui, C.W. (2004). Multi-site utility integrationan industrial case study. Computers & Chemical Engineering, 28(1-2), 139–148. Jacobsen, N.B. (2006). Industrial Symbiosis in Kalundborg, Denmark: A Quantitative Assessment of Economic and Environmental Aspects. Journal of Industrial Ecology, 10(12), 239–255. Jung, S., Dodbiba, G., Chae, S.H., and Fujita, T. (2013). A novel approach for evaluating the performance of eco-industrial park pilot projects. Journal of Cleaner Production, 39, 50–59. Kim, S.H., Yoon, S.G., Chae, S.H., and Park, S. (2010). Economic and environmental optimization of a multisite utility network for an industrial complex. Journal of Environmental Management, 91(3), 690–705. Leong, Y.T., Lee, J.Y., Tan, R.R., Foo, J.J., and Chew, I.M.L. (2017). Multi-objective optimization for resource network synthesis in eco-industrial parks using an integrated analytic hierarchy process. Journal of Cleaner Production, 143, 1268–1283. Mattila, T., Lehtoranta, S., Sokka, L., Melanen, M., and Nissinen, A. (2012). Methodological Aspects of Applying Life Cycle Assessment to Industrial Symbioses. Journal of Industrial Ecology, 16(1), 51–60. Nobel, C. and Allen, D. (2000). Using Geographic Information Systems (GIS) in Industrial Water Reuse Modelling. Process Safety and Environmental Protection, 78(4), 295–303. Pearce, D.W. and Turner, R.K. (1991). Economics of natural resources and the environment. American Journal of Agricultural Economics, 73(1). Rubio-Castro, E., Ponce-Ortega, J.M., Serna-Gonzlez, M., Jimnez-Gutirrez, A., and El-Halwagi, M.M. (2011). A global optimal formulation for the water integration in eco-industrial parks considering multiple pollutants. Computers & Chemical Engineering, 35(8), 1558–1574. Shapley, L.S. (1953). A value for n-person games. In H.W. Kuhn and A.W. Tucker (eds.), Contributions to the Theory of Games II, 307–317. Princeton University Press, Princeton. Vadenbo, C., Hellweg, S., and Guilln-Goslbez, G. (2014). Multi-objective optimization of waste and resource management in industrial networks Part I: Model description. Resources, Conservation and Recycling, 89, 52–63. Voruganti, A., Unnikrishnan, A., and Waller, S. (2011). Modeling carrier collaboration in freight networks. Transportation Letters, 3(1), 51–61.
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Collaborative Lot-Sizing problem for an Collaborative Lot-Sizing problem for an Collaborative Lot-Sizing problem for an Industrial Symbiosis Collaborative Lot-Sizing problem for an Industrial Symbiosis Industrial Symbiosis Symbiosis C´ ecilia Daquin,Industrial Hamid Allaoui, Gilles Goncalves, Tient´ e Hsu
C´ ecilia Daquin, Hamid Allaoui, Gilles Goncalves, Tient´ e Hsu C´ e e C´ ecilia cilia Daquin, Daquin, Hamid Hamid Allaoui, Allaoui, Gilles Gilles Goncalves, Goncalves, Tient´ Tient´ e Hsu Hsu C´ ecilia Daquin, Hamid Allaoui, Gilles Goncalves, Tient´ Univ. Artois, EA 3926, Laboratoire de G´enie Informatique eetHsu Univ. Artois, EA 3926, Laboratoire de G´ enie Informatique et Univ. 3926, de G´ Informatique et d´Automatique de l´Artois (LGI2A) B´ France Univ. Artois, Artois, EA EA 3926, Laboratoire Laboratoire deeethune, G´eenie nie F-62400, Informatique et d´Automatique de l´Artois (LGI2A) B´ thune, F-62400, France Univ. Artois, EA 3926, Laboratoire de G´ e nie Informatique et d´Automatique de l´Artois (LGI2A) B´ e thune, F-62400, France (e-mail: [email protected] (C. Daquin), d´Automatique de l´Artois (LGI2A) B´ethune, F-62400, France (e-mail: [email protected] (C. Daquin), d´Automatique de l´Artois (LGI2A) B´e(G. thune, (e-mail: [email protected] (C. Daquin), [email protected] Goncalves), (e-mail: [email protected] (C.F-62400, Daquin),France [email protected] (G. Goncalves), (e-mail: [email protected] (C. Daquin), [email protected] (G. Goncalves), [email protected] (G. (H. Goncalves), Allaoui), [email protected] [email protected] (H. Allaoui), [email protected] (G. [email protected] (H. Allaoui), [email protected] (T. Hsu) [email protected] (H. Goncalves), Allaoui), [email protected] (T. Hsu) [email protected] (H. Allaoui), [email protected] (T. Hsu) [email protected] (T. Hsu) [email protected] (T. Hsu) Abstract: Abstract: For For decades, decades, the the industry industry is is aa huge huge consumer consumer of of resources, resources, generates generates waste waste and and has has Abstract: For decades, the industry is a huge consumer of resources, generates waste has serious impacts on our planet. In order to preserve the environment, new economic models Abstract: For decades, the industry is a to huge consumer ofenvironment, resources, generates waste and and has serious impacts on our planet. In order preserve the new economic models Abstract: Forincluding decades, the industry is a to huge consumer of resources, generates wastefits and has serious impacts on our planet. In order preserve the environment, new economic models are emerging circular economy. Circular economy is a system that with serious impacts on our planet. In order to preserve the environment, new economic models are emerging including the circular economy. Circular economy is a system that fits with serious impacts onaims our planet. In both order to preserve the economy environment, economic models are including the circular economy. Circular economy iswaste system that fits fits with sustainability and resources consumption and production. Among are emerging emerging including thereduce circular economy. Circular aa new system that with sustainability and aims to to reduce both resources consumption andis waste production. Among are emerging including the circular economy. Circular economy is a system that fits with sustainability and aims to reduce both resources consumption and waste production. Among the components of circular economy, industrial ecology is the collaboration of industries on sustainability and aims to reduce both resourcesecology consumption and waste production. Among the components of aims circular economy, industrial is the collaboration of industries on aa sustainability and to reduce both resources consumption and waste production. Among the components of circular economy, industrial ecology is the collaboration of industries on territory in order to exchange materials, water or energy through industrial symbiosis. Industrial the components of circular economy, industrial ecology is the collaboration of industries on aa territory in orderof to circular exchangeeconomy, materials, water or ecology energy through industrial symbiosis. Industrial the components industrial is theincollaboration of industries on a territory in order to exchange materials, water or energy through industrial symbiosis. Industrial ecology and industrial symbiosis are more and more present the literature. However, most territory in order to exchange materials, water or energy through industrial symbiosis. Industrial ecology and industrial symbiosis are more and present in industrial the literature. However, most territory inin order to exchange materials, water ormore energy through symbiosis. Industrial ecology and industrial symbiosis are more and more present in literature. However, most of articles the literature focused the strategic decision level. this paper, we focus on ecology and industrial symbiosis areon more and more present in the theIn literature. However, most of articles in the literature focused on the strategic decision level. In this paper, we focus on ecology and industrial symbiosis are more and more present in the literature. However, most of articles in the literature focused on the strategic decision level. In this paper, we focus on tactical decisions, and investigate production planning as a lot sizing problem in a collaborative of articles in the literature focused on the strategic decision level. In this paper, we focus on tactical decisions, and investigate production planning as a lot sizing problem in a collaborative of articles in the literature focused on the strategic decision level. In this paper, we focus on tactical decisions, and investigate production planning as aa lot sizing problem in aa collaborative cc 2019 context involving two actors belong an industrial symbiosis. Copyright IFAC tactical decisions, and investigate production planning as lot sizing problem in collaborative context involving two belong an industrial symbiosis. Copyright 2019 tactical decisions, and actors investigate production planning as a lot sizing problem in IFAC a collaborative cc 2019 context involving two actors belong an industrial symbiosis. Copyright IFAC context involving two actors belong anAutomatic industrial symbiosis. Copyright 2019 IFAC © 2019, IFAC (International Federation of Control) Hosting by Elsevier Ltd. AllIFAC rights reserved. c context involving two actors belong an industrial symbiosis. Copyright 2019 Keywords: Keywords: Industrial Industrial Symbiosis, Symbiosis, Collaboration, Collaboration, Optimization, Optimization, Lot-Sizing, Lot-Sizing, Cost Cost Sharing. Sharing. Keywords: Keywords: Industrial Industrial Symbiosis, Symbiosis, Collaboration, Collaboration, Optimization, Optimization, Lot-Sizing, Lot-Sizing, Cost Cost Sharing. Sharing. Keywords: Industrial Symbiosis, Collaboration, Optimization, Cost of Sharing. 1. INTRODUCTION exchanges andLot-Sizing, mutualizations flows, matters or services 1. INTRODUCTION exchanges and mutualizations of flows, matters or services 1. INTRODUCTION exchanges and mutualizations of matters services between involved partners through Industrial Symbioses 1. INTRODUCTION exchangesinvolved and mutualizations of flows, flows, matters or or services between partners through Industrial Symbioses 1. INTRODUCTION exchanges and mutualizations of flows, matters or services between involved partners through through Industrialseparate Symbioses (IS). An IS is ”the engagement of traditionally inSince the beginning of the industrial area, companies deal between involved partners Industrial Symbioses An IS is ”the engagement of traditionally separate inSince the beginning of the industrial area, companies deal (IS). between involved partners through Industrial Symbioses (IS). An IS is ”the engagement of traditionally separate industries in a collective approach to competitive advantage Since the beginning of the industrial area, deal with production systems that are based on acompanies linear scheme: (IS). An IS is ”the engagement of traditionally separate inSince the beginning of the industrial area, companies deal dustries in a collective approach to competitive advantage with production systems that are based on a linear scheme: (IS). An IS is ”the engagement of traditionally separate industries in a collective approach to competitive advantage Since the beginning of the industrial area, companies deal involving physical exchange of materials, energy, water, with production are based on aakind linear scheme: extract, produce,systems use andthat throw out. This of systems dustries in a collective approach to competitive advantage with production systems that are based on linear scheme: involving physical exchange of materials, energy, water, extract, produce, use and throw out. This kind of systems dustries in a collective approach to competitive advantage involving physical exchange of materials, energy, water, with production systems that are based on a linear scheme: and/or by-products. The keys to industrial symbiosis are extract, produce, use and throw out. This kind of systems considers that our planet offers infinite reserves of natural involving physical exchange water, extract, produce, use and offers throw out. This kind of systems and/or by-products. The keysof tomaterials, industrialenergy, symbiosis are considers that ouruse planet reserves of natural physical exchange energy, water, and/or by-products. by-products. The keysofto tomaterials, industrial symbiosis are extract, andoverconsumption throwinfinite out. This kind of collaboration and the synergistic possibilities offered by considers that planet offers infinite reserves of natural resources. Thisour yields an of resources and involving and/or The keys industrial symbiosis are considersproduce, that our planet offers infinite reserves of systems natural collaboration and the synergistic possibilities offered by resources. This yields an overconsumption of resources and by-products. The keys to(2000)). industrial symbiosis are collaboration and the synergistic possibilities offered by considers that our offerswaste infinite reserves ofand natural geographic proximity”(Chertow This area of georesources. This yields an overconsumption of resources and then generates an planet increasing production dis- and/or collaboration and the synergistic possibilities offered by resources. This yields an overconsumption of resources and geographic proximity”(Chertow (2000)). This area of geothen generates an increasing waste production and discollaboration and the synergistic possibilities offered by geographic proximity”(Chertow (2000)). This area of georesources. This yields an overconsumption of resources and graphic proximity is an Eco-Industrial Park (EIP). There then generates an increasing waste production and disrupts ecosystems. Linear economy hasproduction significant footprint geographic proximity”(Chertow (2000)). This area of geothen generates an increasing waste and disgraphic proximity is an Eco-Industrial Park (EIP). There rupts ecosystems. Linear economy has significant footprint geographic proximity”(Chertow (2000)). This area of geographic proximity is an Eco-Industrial Park (EIP). There then generates an increasing waste production and disare two types of industrial symbiosis : rupts ecosystems. Linear economy has significant footprint on the environment (climate change, biodiversity erosion, graphic proximity is an Eco-Industrial (EIP). There rupts ecosystems. Linear economy has significant footprint are two types of industrial symbiosis : Park on theecosystems. environment (climate change, erosion, proximity is an Eco-Industrial are two two types types of industrial industrial symbiosis :: Park (EIP). There rupts Linear economy hasbiodiversity significant footprint on environment (climate change, biodiversity erosion, etc.) and has reached its limits. In order to preserve the en- graphic are of symbiosis on the the environment (climate change, biodiversity erosion, A substitute synergy enables to use waste etc.) and has reached its limits. In order to preserve the enare- two types of industrial on the environment (climate change, biodiversity erosion, A substitute synergy symbiosis enables to: use waste coming coming etc.) and has its In to the vironment, itreached is necessary to change production, distribuetc.) and hasit reached its limits. limits. In order order to preserve preserve the enen-- from A substitute synergy enables use waste coming an industrial process of aato company, called byvironment, is necessary to change production, distribuA substitute synergy enables to use waste coming etc.) and has reached its limits. In order to preserve the enfrom an industrial process of company, called byvironment, it is necessary to change production, distribution and buying modes. Hence, new production, economic models are vironment, it is necessary to change distribu- A substitute synergy enables use waste coming from an industrial industrial process ofan atocompany, company, called byproduct, as raw materials for industrial process in tion and buying modes. Hence, new economic models are from an process of a called byvironment, it is necessary to change production, distribuproduct, as raw materials for an industrial process in tion and buying modes. Hence, new economic models are emerging including the Circular Economy (CE) (Pearce tion and buying modes. Hence, new economic models are from an company; industrial processfor ofan a company, called byproduct, as raw materials industrial process in another emerging including the Circular Economy (CE) (Pearce product, as raw materials for an industrial process in tion and buying modes. Hence, new economic models are another company; emerging including the Circular Economy (CE) (Pearce and Turner (1991)). emerging including the Circular Economy (CE) (Pearce product, as raw materials for an industrial process in another company; A mutualization synergy makes possible the pooling and Turner (1991)). another company; emerging including the Circular Economy (CE) (Pearce A mutualization synergy makes possible the pooling and (1991)). and Turner Turner (1991)).is a system that reconciles economy company; -- another A mutualization synergy makes possible the pooling of services, equipment and resources between players Circular economy A mutualization synergy possible the pooling and Turner (1991)).is a system that reconciles economy services, equipment andmakes resources between players Circular economy - of A mutualization synergy possible the pooling services, equipment andmakes resources between players of an EIP (e.g. group buy, shared rubbish collection, Circular economy aa system reconciles economy and environmental protection inthat a social approach. This of services, equipment and resources between players Circular economy is isprotection systemin that reconciles economy of an EIP (e.g. group buy, shared rubbish collection, and environmental a social approach. This of services, equipment and resources between players an EIP (e.g. group buy, shared rubbish collection, Circular isprotection a systemin that reconciles economy carpooling or sharing of pallets). and environmental aa social approach. This concept iseconomy part of sustainability and aims to ensure that of an EIP (e.g. group buy, shared rubbish collection, and environmental protection in social approach. This carpooling or sharing of pallets). concept is part of sustainability and aims to ensure that of an EIP (e.g. group buy, shared rubbish collection, carpooling or sharing of pallets). and environmental protection in a social approach. This concept is part of sustainability and aims to ensure that the 9 billion of people being on Earth in 2050 can live carpooling or issharing of pallets). concept is part of sustainability and aims to ensure that Industrial ecology not dream. the 9 of people being on Earth in 2050 can live carpooling or issharing pallets). concept is part of sustainability aims ensure that ecology not an anofutopian utopian dream. The The symbiosis symbiosis the 99 billion billion of people being on Earth in 2050 can live in environmental and social condithesatisfactory billion ofeconomic, people being onand Earth in to 2050 can live Industrial Industrial ecology is not an utopian dream. The of Kalundborg is one of the first experiences of in satisfactory economic, environmental and social condiIndustrial ecology is not an utopian dream. The symbiosis symbiosis the 9 billion of people being on Earth in 2050 can live of Kalundborg is one of the first experiences of indusindusin satisfactory economic, environmental and social conditions. CE is based on the cyclic operation of ecosystems in satisfactory economic, environmental andofsocial condi- trial Industrial ecology is not an utopian dream. The symbiosis of Kalundborg is one of the first experiences of ecology. It was a reference for the development of tions. CE is based on the cyclic operation ecosystems of Kalundborg iswas onea of the firstforexperiences of indusindusin satisfactory economic, environmental and social condiecology. It reference the development of tions. CE is based on the cyclic operation ecosystems by reintroducing matter and products in of the cycle of trial tions. CE is based on the cyclic operation of ecosystems of Kalundborg one the most firstfor experiences of industrial ecology. It iswas was a of reference for the indevelopment development of industrial symbiosis and the cited the literature by reintroducing matter and products in the cycle of trial ecology. It a reference the of tions. CE is based on the cyclic operation of ecosystems industrial symbiosis and the most cited in the literature by reintroducing matter and products in the cycle of production and utilization, as far as possible, in order to by reintroducing matter and products in the cycle to of trial ecology. It Chertow was and a reference the in of industrial symbiosis and the mostfor cited indevelopment the literature (Ehrenfeld and (2002), Ehrenfeld and Gertler production and utilization, as far as possible, in order industrial symbiosis the most cited the literature by reintroducing matter and products in the cycle to of (Ehrenfeld and Chertow (2002), Ehrenfeld and Gertler production and utilization, as as possible, in reduce both resources consumption waste production. production and utilization, as far far asand possible, in order order to industrial symbiosis and the most cited in the literature (Ehrenfeld and Chertow (2002), Ehrenfeld and Gertler (1997), Jacobsen (2006)). This experience is not the only reduce both resources consumption and waste production. and Chertow (2002), Ehrenfeld and the Gertler production utilization, asseveral far asand possible, inincluding order to (Ehrenfeld (1997), Jacobsen (2006)). This experience is not only reduce both resources consumption waste This system revolves around principles, reducesystem bothand resources consumption and waste production. production. (Ehrenfeld and Chertow (2002), Ehrenfeld and Gertler (1997), Jacobsen (2006)). This experience is not the only one. We can also quote the industrial ecology of GrandeThis revolves around several principles, including (1997), Jacobsen (2006)). This experience is not the only reduce both resources consumption and waste production. one. We can also quote the industrial ecology of GrandeThis system revolves around several principles, including Industrial Ecology (IE) (Frosch and Gallopoulos (1989)). 1 2 This system revolves around several principles, including (1997), Jacobsen (2006)). This experience is not the only one. We Weincan can also1quote quote the industrial ecologyinof ofCanada GrandeSynthe France or the one of Saint-Flicien Industrial Ecology (IE) (Frosch and Gallopoulos (1989)). 2. one. also the industrial ecology GrandeThis system revolves around several principles, including Synthe in France or the one of Saint-Flicien in Canada Industrial Ecology (IE) (Frosch and Gallopoulos (1989)). 1quote the industrial ecology of Grande2. Industrial Ecology (IE) (Frosch and Gallopoulos (1989)). one. We can also 1 2 Synthe in France or the one of Saint-Flicien in Canada . Yet the setting-up of industrial symbioses is complicated. IE is a discipline aiming to limit impact of industry on Synthe in France or the one of Saint-Flicien in Canada Industrial Ecology aiming (IE) (Frosch andimpact Gallopoulos (1989)). Yet the setting-up 1 of industrial symbioses is complicated. 2. IE is a discipline to limit of industry on Synthe in France or the one of Saint-Flicien in Canada . Yet the setting-up of industrial symbioses is complicated. Therefore the study of these industrial organizations is a IE aa discipline to of industry the environment. To achieve this impact goal, IE is based on the setting-up symbioses is complicated. IE is isenvironment. discipline aiming aiming to limit limit impact of is industry on Yet Therefore the studyof ofindustrial these industrial organizations is a the To achieve this goal, IE based on Yet the setting-up of industrial symbioses is complicated. Therefore the study of these industrial organizations is a IE is a discipline aiming to limit impact of industry the environment. To achieve this goal, IE is based on the study of these industrial organizations is a the environment. To achieve this goal, IE is based on 1Therefore This research comes from this thegoal, ENCETRE project http://www.ecopal.org/ the study of these industrial organizations is a the environment. To achieve IE is based on 121Therefore research comes from the ENCETRE project http://www.ecopal.org/ This
(https://www.lgi2a.univ-artois.fr/spip/fr/projets/encetre) and This research comes from the ENCETRE project This http://www.ecopal.org/ 1 2 http://www.mamunicipaliteefficace.ca/104-10-tudes-de-casresearch comes from the ENCETRE project http://www.ecopal.org/ (https://www.lgi2a.univ-artois.fr/spip/fr/projets/encetre) and http://www.mamunicipaliteefficace.ca/104-10-tudes-de-cas2 1 receives a financial support from the BPI France and the Hauts de saint-felicien-valorisation-des-rejets-thermiques-de-lunite-de(https://www.lgi2a.univ-artois.fr/spip/fr/projets/encetre) and http://www.mamunicipaliteefficace.ca/104-10-tudes-de-cas2 http://www.ecopal.org/ This research comes from the ENCETRE project (https://www.lgi2a.univ-artois.fr/spip/fr/projets/encetre) http://www.mamunicipaliteefficace.ca/104-10-tudes-de-casreceives a financial support from the BPI France and the Hautsand de saint-felicien-valorisation-des-rejets-thermiques-de-lunite-de2 http://www.mamunicipaliteefficace.ca/104-10-tudes-de-casFrance region. cogeneration.html receives a financial support from the BPI France and the Hauts de saint-felicien-valorisation-des-rejets-thermiques-de-lunite-de(https://www.lgi2a.univ-artois.fr/spip/fr/projets/encetre) and receivesregion. a financial support from the BPI France and the Hauts de saint-felicien-valorisation-des-rejets-thermiques-de-lunite-deFrance cogeneration.html France cogeneration.html receives a financial support from the BPI France and the Hauts de saint-felicien-valorisation-des-rejets-thermiques-de-lunite-deFrance region. region. cogeneration.html France region. cogeneration.html 2405-8963 © IFAC (International Federation of Automatic Control) Copyright © 2019, 2019 IFAC 1342Hosting by Elsevier Ltd. All rights reserved. Copyright ©under 2019 responsibility IFAC 1342Control. Peer review of International Federation of Automatic Copyright © 1342 Copyright © 2019 2019 IFAC IFAC 1342 10.1016/j.ifacol.2019.11.382 Copyright © 2019 IFAC 1342
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Fig. 1. Distribution of articles per publication year from 2000 to 2018 research field aiming to understand their development in order to show their interest and make them easier. The study of EI is more and more present in the literature. The majority of publications focused on strategic decisions like network design. However there are very few works dealing with tactical and operational decisions (see section 2). In this context, we decide to focus on tactical level and more particularly on the production planning of supply chains involved in industrial symbiosis in which collaborators are already identified. The aim of this paper is to optimize the production planning for two actors involved in the IS in order to minimize the total economic cost. We formulate this problem as a collaborative lot-sizing problem for a discrete planning horizon. In the remainder of this paper, a literature review is presented in section 2. Afterwards the problem statement and an ILP model are presented in section 3. The studied problem is illustrated by an example in section 4 and a strategy of cost sharing among the two actors is described is section 5. Finally, a conclusion and some future research directions are discussed in section 6. 2. LITERATURE REVIEW We particularly focussed on modeling and optimization issues related to industrial symbiosis at strategic, tactical and operational decision levels. We used the ScienceDirect database and looked for articles with the words ”industrial ecology” or ”industrial symbiosis” or ”eco-industrial park” and ”optimization” in their abstracts, titles or keywords. In total 107 publications were listed from 2000 to the beginning of 2018. Fig. 1 shows the distribution of these articles per publication year. We notice that this research field aroused strong interest these last years. Then, we identified in these publications mathematical models established within the scope of an industrial symbiosis and analyzed the criteria considered within them. The aim of our work is to show the gaps in this field and then to suggest some relevant perspectives for future works.
(see Table 1). The first one is collaboration through water network and is the most usual in the literature. In this problem, water have to be optimally allocated, treated, evacuated or reused between each participants included in EIP. The second kind of collaboration is through energy network. However, few publications tackle this problem and no multiobjective model was developed. A possible explanation is the difficulties to obtain reliable and complete data for this kind of problem. Material exchange is the third kind of collaboration that is examined in the literature. Several types of materials can be considered as waste, by-product, etc. But only few studies mentioned material exchanges by actually optimizing the network. Note that these collaborations mentioned above were optimized independently. Table 1. Types of collaboration in an EIP using optimization methods in the litterature Types of collaboration Water network Energy network Material exchange
Now let us focus on criteria considered within mathematical models to optimize the design or planning of industrial symbiosis (see Table 2). The economic objective is mostly present in the models. Not only it is the easiest to quantify, but also is usually the most relevant for participants of EIP. Indeed, an industry will get involved in an industrial symbiosis if costs are reduced or identical to the situation of not being involved in the IS. Hence, cost minimization is the objective that is mostly used. Another objective formalized in models is the topological aspect. The latter enables the evaluation of network complexity. This aspect is often ignored, yet it represents an investment cost and shows the network feasibility. The environmental aspect is the main motivation of industrial ecology. In order to use resources as optimally as possible and to reduce the environmental impact, the majority of studies seek to minimize the consumption of natural resources. Yet this objective is not enough modeled in the literature. Finally, the social aspect is crucial in the development of an EIP, just like the economic and environmental objectives. However, no work in the literature dealing with the social objective. Indeed, social criterion is hard to quantify since it implied some subjective judgements. Aviso et al. (2011) developed indicators in order to estimate the satisfaction of participants in an EIP but this detail guarantees no social benefit. Table 2. Optimization Objectives for an EIP Criteria Economic
Like in a classical supply chain, the encountered problems are categorized according to three decision levels: strategic, tactical and operational. Most of them focused on strategic level. In particular, they tackled design of symbiosis network and identification of synergies within the EIP. The topics studied in the literature are varied: waste, CO2 emissions, flow of matter, water, life cycle, etc. Three options of collaboration have been studied in the publications
References Nobel and Allen (2000), Chew et al. (2008), Boix et al. (2012) Kim et al. (2010), Gonela et al. (2015), Afshari et al. (2018) Cimren et al. (2011), Vadenbo et al. (2014)
Topological Environmental Social
References Nobel and Allen (2000), Hirata et al. (2004), Jung et al. (2013) Rubio-Castro et al. (2011), Boix et al. (2012) Nobel and Allen (2000), Rubio-Castro et al. (2011), Aviso et al. (2011), Mattila et al. (2012) Aviso et al. (2011), Jung et al. (2013), Leong et al. (2017)
In conclusion, the study of EIP is more and more present in the literature, but many aspects still need to be investigated. We noticed that the tactical and operational
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we propose a new model in order to optimize the production planning for both actor 1 and actor 2. We use the following notations : T t dn,t pn,t fn,t Fig. 2. Industrial symbiosis with two actors decisions were not examined in the literature. The majority of publications focused on the network design of symbiosis. The networks of water, energy and materials exchange are optimized independently, but a perspective would be to interact these different networks in order to increase symbiotic connections. Regarding the criteria of mathematical models, there are few multiobjective models. However, by definition, the design and management of an EIP is a multiobjective problem that involved the satisfaction of economic, environmental and social pillars. Consequently, we decided to focus on tactical decision level in this paper. More particularly, we seek to optimize the production planning of supply chains which collaborate inside an industrial symbiosis. To start, we focus on economic aspect. 3. PROBLEM STATEMENT AND FORMULATION
hn,t CapPn,t CapSn pourcentagen bn,t cn,t CapBn,t storage costDn,t CapSDn
We focus on the optimization of production planning for involved actors who decide to collaborate together in an industrial symbiosis. In other words, we seek to obtain a collaborative production planning formulated as a centralized multi-period lot-sizing problem. In this study, we set the number of actors to 2, as shown in Fig. 2. To produce one unit of product, an actor needs raw materials ordered from a supplier. But in the context of industrial symbiosis, the actor can also use the waste produced by another actor. This waste, called byproducts, can substitute the necessary raw materials. Therefore, the actor has to plan his production for each period and decide how many raw materials he must order from his usual supplier and how many byproducts he must order from the partner actor of the symbiosis. Moreover, instead of paying to bury these byproducts, the upstream actor may recycle them in whole or in part with the downstream participant. Our purpose is to minimize the total cost for both actors 1 and 2 which is the sum of the supply cost, the production cost, the storage cost, the burying cost and the symbiosis cost. To solve this problem, we take into consideration several constraints : the demand satisfaction over T periods, (unauthorized delays), the capacity of storage, production, supply and burying as well as production and delivery times. This problem corresponds to a Lot-Sizing (LS) problem applied to the industrial symbiosis. To model it, we start with a basic LS model, the Capacitated Lot-Sizing problem (CLS), and then we add the hypotheses and constraints necessary for the studied industrial symbiosis. Therefore,
symbiosis cost order costMt nomenclaturen
storage costMn,t CapSMn costMn,t
CapMn,t ltMn laMn
ltD2 laD2
Total number of periods Discrete period of the planning horizon (1 ≤ t ≤ T ) demand of end products for actor n in period t (n ∈ N : n ≤ 2) unit production cost for actor n in period t setup production cost for actor n in period t unit end product storage cost for actor n in period t production capacity for actor n in period t end product storage capacity for actor n (constant at each period) ratio between byproducts and end products generated by actor n unit burying cost of byproduct for actor n in period t setup burying cost for actor n in period t burying capacity for actor n in period t unit byproduct storage cost for actor n in period t byproduct storage capacity for actor n (constant at each period unit symbiosis cost applied to the waste flow (constant at each period) fixed raw matter order cost in period t number of matter units necessary to produce one unit of end product for actor n unit matter cost for actor n in period t byproduct storage capacity for actor n (constant at each period) unit raw matter buying cost for actor n in period t (including matter cost and transport) capacity of available raw matter for actor n in period t = 1, lead time of raw matter for actor n expected delivery of raw matter at the beginning of the planning horizon for actor n (according to the previous planning) = 1, lead time of byproduct for acteur 2 expected delivery of byproduct at the beginning of the planning horizon for actor 2 (according to the previous planning)
The decision variables are as follows :
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xn,t sn,t
yn,t wn,t stockDn,t
αn,t
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Quantity of end product manufactured for actor n in period t End product stock level for actor n at the end of period t 1 if production is started for actor n in period t (yn,t = 1 si xn,t > 0) 0 otherwise Quantity of by-products to bury for the actor n in period t Byproduct stock level for actor n at the end of period t 1 if byproduct is buryed for actor n in period t (αn,t = 1 si wn,t > 0) 0 otherwise
stockMn,t Matter stock level for actor n at the end of period t zMn,t Quantity of raw matter ordered for actor n in period t 1 if raw matter is ordered from supplier for actor t (n,t = 1 si zMn,t > 0) n,t 0 otherwise zD2,t
Quantity of byproduct ordered for actor 2 in period t
So, our model has to decide at each period t : - the quantity of end products to manufacture (x1,t and x2,t ) and to stock (s1,t and s2,T ) for actor 1 and actor 2; - the quantity of raw matter to order (zM1,t and zM2,t ) and to stock (stockM1,t and stockM2,t ) for actor 1 and actor 2; - the quantity of by products to order by actor 2 from actor 1 (zD2,t ) and the quantity to stock (stockM2,t ); - the quantity of byproducts generated by actor 2 to bury (w2,t ) and to stock (stockD2,t ); - the quantity of byproducts generated by actor 1 to supply to actor 2 (zD2,t ), to bury (w1,t ) and to stock (stockD1,t ). The decision variable zD2,t represents the byproduct flow which is characteristic of industrial symbiosis. It is the common element between actor 1 and actor 2. Indeed, the quantity of byproduct to provide by actor 1 satisfies some of the needs of actor 2. In order to minimize the total cost, we propose the following ILP model : Supply Cost =
2 t∈T
n=1
(order costMt × n,t
+ costMn,t × zMn,t ) 2 P roduction Cost = (pn,t xn,t + fn,t yn,t ) Storage Cost =
(1) (2)
t∈T n=1 2
( (hn,t sn,t )
t
n=1
+ (storage costMn,t × stockMn,t ) + (storage costDn,t × stockDn,t ) )
(3)
Burying Cost =
2 t∈T
Symbiosis Cost =
t∈T
(bn,t wn,t + cn,t αn,t )
(4)
symbiosis costt × zD2,t
(5)
n=1
minf = Supply Cost + P roduction Cost+ Storage Cost + Burying Cost + Symbiosis Cost
(6)
Subject to: xn,1 = dn,1 + sn,1 sn,t−1 + xn,t = dn,t + sn,t
(∀n ∈ {1, 2}, ∀t ∈ T \{1})
(7)
laM1 = (nomenclature1 × x1,1 ) + stockM1,1 stockM1,t−1 + zM1,t−1 = (nomenclature1 × x1, t) + stockM1,t (∀t ∈ T \{1})
(8)
laM2 + laD2 = (nomenclature2 × x2,1 ) + stockM2,1 stockM2,t−1 + zM2,t−1 + zD2,t−1 = (nomenclature2 × x2,t ) + stockM2,t (∀t ∈ T \{1})
(9)
pourcentage1 × x1,1 = zD2,1 + w1,1 + stockD1,1 100 pourcentage1 × x1,t = zD2,t + w1,t stockD1,t−1 + 100 + stockD1,t (∀t ∈ T \{1})
(10)
pourcentage2 × x2,1 = w2,1 + stockD2,1 100 pourcentage2 × x2,t = w2,t + stockD2,t stockD2,t−1 + 100 (∀t ∈ T \{1}) (11) xn,t ≤ CapPn,t × yn,t (∀n ∈ {1, 2}, ∀t ∈ T ) (12) (13) sn,t ≤ CapSn (∀n ∈ {1, 2}, ∀t ∈ T ) zMn,t ≤ CapMn,t × n,t (∀n ∈ {1, 2}, ∀t ∈ T ) (14) pourcentage1 zD2,1 ≤ CapP1,1 × 100 pourcentage1 zD2,t ≤ CapSD1 + CapP1,t × 100 (∀t ∈ T \{1}) (15) stockMn,t ≤ CapSM1 (∀n ∈ {1, 2}, ∀t ∈ T ) (16) (17) wn,t ≤ CapBn,t × αn,t (∀n ∈ {1, 2}, ∀t ∈ T ) stockDn,t ≤ CapSDn (∀n ∈ {1, 2}, ∀t ∈ T ) (18) (19) yn,t , αn,t , n,t ∈ {0, 1} (∀n ∈ {1, 2}, ∀t ∈ T ) xn,t , sn,t , wn,t , stockDn,t , stockMn,t , zMn,t , (20) zD2,t ≥ 0 (∀n ∈ {1, 2}, ∀t ∈ T ) In this formulation, the objective function (6) minimizes the sum of several costs for the two actors in an industrial symbiose : the supply costs of raw material (1), the production costs (2), the storage costs for raw material, end products and byproducts (3), the burying costs for byproducts (4) and the symbiosis costs (5) which correspond to
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the recycling costs of byproducts provided by actor 1 to actor 2. Constraints (7), (8), (9), (10) and (11) are equations of balance of stocks or flow conservation constraints for each actor at each period t. Constraints (12) ensure that the number of end product to manufacture by the actors 1 and 2 is lower than their production capacity when production is launched. Moreover, these constraints enable to initialize the decision variables yn,t . Constraints (14) (resp. (15)) ensure that the quantity of raw material to order (resp. the quantity of byproducts to order by actor 2) is lower than the available capacity from the supplier (resp. from the actor 1) when raw material is ordered (resp. byproducts). Moreover, these contraints enable to initialize the decision variables n,t . Constraints (13), (16) and (18) check the storage capacities at each period for each actor. Constraints (17) check the burying capacity for byproducts and enable to initialize the decision variables αn,t . Finally, constraints (20) and (19) stipulate the nature of decision variables.
both actor 1 and actor 2 in industrial symbiosis. Costs mentioned in column ”No symb. A1+A2” are the sum of values in columns ”No symb. A1” and ”No symb. A2” and represent costs for actor 1 and actor 2 without symbiosis. We can notice that the symbiosis enables a saving cost of 100,380 in comparison to scenario of without symbiosis, being around 4%. Let us take a look in the several costs for each actor. Table 4 (resp. table 5) shows costs for actor 1 (resp. actor 2) with solution provided by our centralized model and costs without symbiosis. We note that supply and burying cost with symbiosis are lower than without symbiosis (8,880 for supply cost and 12,000 for burying cost, being 20,880 in total). Indeed, actor1 reduces burying costs by supplying byproducts to actor 2, and actor 2 can reduce supply costs. This obtained saving cost is higher than the symbiosis cost. Consequently, actor 1 and actor 2 are better off collaborating in the symbiosis. Table 4. Costs for Actor 1 with and without symbiosis
4. ILLUSTRATIVE EXAMPLE
Costs Production Supply Storage Burying Symbiosis Obj. function
An example is provided to ease the reader understanding the problem studied. In order to simplify calculation, we make the following assumptions: - Setup and fixed costs are set to 0 (setup production costs fn,t , setup burying costs of byproducts cn,t and fixed raw matter order costs order costMt ); - All storage costs are set to 10 (hn,t = storage costDn,t = storage costMn,t = 10 ∀t ∈ T, ∀n ∈ {1, 2}); - The cost of raw materials and the cost of burying waste are equal and are set to 8 at each period t for both actors (costMn,t = bn,t = 8). The significant data in this problem related to byproducts flow (ie the industrial symbiosis). It’s represented in this paper by the symbiosis cost. As a reminder, this cost is applied to each byproduct unit transferred from actor 1 to actor 2 at each period. It can represent an unit transportation cost or a recycling cost for example and it is supported by actor 1. We choose to set the unit symbiosis cost to 7. We apply our model presented in section 3 to a dataset by taking into consideration the previous hypotheses. We use ILOG CPLEX 12.6.3 to solve it. The obtained results are compared to a production planning model for each actor without symbiosis that we have also developed. The results are summarized in table 3. Table 3. Results of centralized model with symbiosis and without symbiosis Costs Production Supply Storage Burying Symbiosis Obj. function
Symbiosis A1* and A2* 100,000 115,920 0 12,000 10,500 238,420
No symb. A1 50,000 65,600 0 12,000
No symb. A2 50,000 59,200 0 12,000
No symb. A1+A2 100,000 124,800 0 24,000
127,600
121,200
248,800
*A1 (resp A2) denotes Actor 1 (resp. Actor 2)
The values mentioned in column ”Symbiosis A1 and A2” are obtained with the centralized model, ie are costs for
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With Symbiosis Actor 1 50,000 65,600 0 0 10,500 126,100
No Symbiosis Actor 1 50,000 65,600 0 12,000 127,600
Table 5. Costs for Actor 2 with and without symbiosis Costs Production Supply Storage Burying Symbiosis Obj. function
With Symbiosis Actor 2 50,000 50,320 0 12,000 0 112,320
No Symbiosis Actor 2 50,000 59,200 0 12,000 121,200
5. COST SHARING STRATEGY Although the total cost is reduced with the symbiosis, each actor has no guarantee to obtain any advantage in terms of their own cost. In the example presented previously, we note that actor 1 has a gain of 1,500 when actor 2 saves 8,880, being around 6 times more. Indeed, actor 1 takes care of the symbiosis costs and actor 2 has byproducts for free. It would be interested to have a more fair gain distribution between actors. To tackle this issue, a cost sharing strategy is applied in order to find the best division of the symbiosis cost for each actor that guarantees each actor obtains a fair gain. The strategy is based on the Shapley Value (Shapley (1953), Voruganti et al. (2011)). It rests on each participant’s expected marginal contribution to the collaboration. By applying this strategy, actor 1 has to pay 6,810 for the symbiosis costs instead of 10.500, about 35% off. For actor 2, the symbiosis costs go from 0 to 3.690, being around 3% of its total cost. So that meant actor 1 has to pay 122.410 (about 3% off) and 116,010 for actor 2 (about 3% increase) (see table 6). Therefore, each of actors saves 5.190, being around 4% of their cost without symbiosis.
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6. CONCLUSION A huge waste of resources and the deterioration of the environment characterize linear economy, which dominates our planet since the beginning of the industrial age. Nevertheless, circular economy is a concept that is a part of sustainability and aims to reduce the environmental footprint while developing social well-being. Among pillars of circular economy, industrial ecology is a practice meeting the needs of companies to integrate the environment into their strategies. This research field attracted a lot of interest these last years but many aspects still need to be investigated. For example, in mathematical models, tactical decisions are not yet studied in the literature. It is within a sustainability framework that this paper aims to optimize the production planning of supply chains that collaborate within an industrial symbiosis. In this work, we investigated a collaborative lot-sizing problem as a part of an industrial symbiosis. Two actors belonging to different supply chains collaborate to jointly determine the best production plans in order to minimize their total cost. We proposed the first centralized planning model for 2 actors which collaborate within an industrial symbiosis. A perspective to this work would be to extend it to 3, 4, ... or n actors involved in the industrial symbiosis in order to extend the chain. Moreover, the proposed model mades involved actors to reveal all the data of the problem. Nevertheless, actors could share limited informations and negotiate on the flow of byproduct between them.Another perspective would be to formulate environmental and social objective fonctions in order to lead to multi-objective optimization. REFERENCES Afshari, H., Farel, R., and Peng, Q. (2018). Challenges of value creation in Eco-Industrial Parks (EIPs): A stakeholder perspective for optimizing energy exchanges. Resources, Conservation and Recycling, 139, 315–325. Aviso, K.B., Tan, R.R., Culaba, A.B., and Cruz, J.B. (2011). Fuzzy inputoutput model for optimizing ecoindustrial supply chains under water footprint constraints. Journal of Cleaner Production, 19(2-3), 187– 196. Boix, M., Montastruc, L., Pibouleau, L., Azzaro-Pantel, C., and Domenech, S. (2012). Industrial water management by multiobjective optimization: from individual to collective solution through eco-industrial parks. Journal of Cleaner Production, 22(1), 85–97. Chertow, M.R. (2000). INDUSTRIAL SYMBIOSIS: Literature and Taxonomy. Annual Review of Energy and the Environment, 25(1), 313–337. Chew, I.M.L., Tan, R., Ng, D.K.S., Foo, D.C.Y., Majozi, T., and Gouws, J. (2008). Synthesis of Direct and Indirect Interplant Water Network. Industrial & Engineering Chemistry Research, 47(23), 9485–9496. Table 6. Total costs for Actor 1 and Actor 2 with Symbiosis, with cost sharing and without symbiosis
Actor 1 Actor 2
With symbiosis and cost sharing 126,100 112320
With symbiosis
No Symbiosis
122,410 116010
127,600 121,200
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