Multiobjective recommendation for sustainable production systems∗

Abstract

We present a recommendation system to help rebuild sustainable production systems. Our multi-objective system synergizes the public and private actors of a territory. From know-how proximities in the Product Space, we suggest productive jumps for companies in a territory that consider the expectations of companies not only in terms of diversification but also in terms of the expectations of local authorities who are anxious to build sustainable production systems. We formalize a multi-stakeholder recommendation that is applied to the sustainability of a territorial economy and we propose the following new objectives to consider: (i) Economic growth, based on the concept of territorial economic complexity; (ii) Productive resilience, defined rigorously from the theory of dynamic systems; (iii) Food security and more generally basic necessities from an original approach based on Maslow's hierarchy of needs; (iv) The need to develop greener productions that respect the environment.

1 INTRODUCTION

The Covid 19 crisis has shown the fragility of our European production systems. Years of externalizations have damaged our productive capacity. However, a general awareness has emerged following the crisis, and the public and private sector are now ready to collaborate to rebuild a sustainable production system. Financial support programs have been deployed to help companies relocate their production or reinforce their existing activities.

At the same time, companies have understood the importance of securing their supplies through local production units. This ofers new business opportunities to suppliers to develop their production towards new products to overcome shortages. To support this efort, we imagined a recommender system whose goal is to suggest the development of new products to companies to ensure their commercial development, while taking into account territorial policies.

We will start by presenting the area of recommendation. Then, after describing the previous work in relation to the ifeld of industry, we will introduce the public and private stakeholders. We will then detail how our multi-objective recommendation system works and we will present a first experimentation on a French territory. ∗Copyright 2021 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). Presented at the MORS workshop held in conjunction with the 15th ACM Conference on Recommender Systems (RecSys), 2021, in Amsterdam, Netherlands.

PREVIOUS WORKS Recommendation systems are very successful in many areas. There are two types of these systems: content-based and collaborative filtering[ 6, 7 ]. Several recommendation systems are derived from the two main types, and it is usual to combine them before generating the list of recommended objects[ 10 ]. 2.1

Multi-objective recommendation Traditionally, recommendation systems are oriented towards the end-user and seek to optimize a single cost function. However, recommendation methods can be multi-objective when they aim to optimize several objectives. For example, by integrating diversity and novelty in the proposed products[ 4, 46, 48, 55 ]. Other uses concern the consideration of price in recommended products[ 15, 30 ]. Recommendation systems that seek to improve the fairness of results are also multi-objective recommendation systems[ 11, 40, 56 ]. The dificulty is to take into account each objective without significantly degrading the accuracy on the main objective.

Several approaches to this problem exist. The first approach draws its foundations from multi-objective optimization and seeks to optimize all of the objectives at the same time. This approach is based on Pareto concepts and the associated algorithms are of the evolutionary type[ 13, 17, 35, 41, 55, 57 ].

The second approach considers multi-objectives as a hybridization of methods in which the combination of results can be done in cascade[ 31, 36 ]: an objective refines the result of a previous objective (re-ranking), or mixing[ 46 ]. The multi-objective recommendation is then considered as a weighted hybridization of mono-objective functions. 2.2

Multistakeholder recommendation Multistakeholder recommendation systems[ 2, 3, 5, 12 ] are derived from multi-sided platforms[ 16, 47 ] and reciprocal recommendation systems. The latter require us to take each stakeholder into account independently because their strategies, and therefore their objectives, are diferent. 2.3

Recommendation in the field of industry Pachot et al. [ 43 ] have developed a recommendation system to recommend collaborative synergies between companies in the same territory based on the semantic analysis of product nomenclatures to find the productive link that exists (for example) between seed, wheat, flour and bread. A distribution of products in a vector space allows us to make recommendations.

The recommendations can be similar to client-supplier or co-production relationships. To improve the industrial resilience of a territory, it is appropriate to develop distributed manufacturing by encouraging the companies of a territory to work with each other.

The recommendation system integrates an alternative operation when no potential supplier is present on a territory, which suggests that suppliers are able to make "productive jumps" to produce the required goods. These productive jumps are made possible by the productive relationship between the classes of products. This relies on the data of productive proximity from the Product Space[ 27 ].

The modeling of the companies’ productions is based on a statistical analysis of the productions associated with their economic activity code. A first experiment was carried out on French companies.

We also find recommendation systems dedicated to the supply chain, specifically for distribution[ 14, 29 ] or to promote the use of waste in the context of industrial symbiosis[ 54 ].

Manuscript submitted to ACM

To our knowledge, no study has aimed at the construction of a multi-objective recommendation system in the field of industrial production, and in particular with the aim of favoring the construction of sustainable production systems. 3 3.1

DESCRIPTION OF STAKEHOLDERS Companies

Companies produce manufactured goods or raw materials. Their production units are located on a territory and carry out an economic activity. Firms collaborate with each other within a territory, or import goods or raw materials from other territories or countries.

Companies follow a commercial strategy that not only encourages them to develop their commercial portfolio by seeking new customers but also encourages them to diversify their production by favoring the production of goods that give them a better competitive advantage. At the same time, they seek to secure their supplies by diversifying their suppliers and giving preference to local suppliers. For several years, companies have also been encouraged to improve their social and environmental impact. 3.2

Local authorities Building a sustainable ecosystem requires active collaboration between the private and public sectors. We would like to integrate local authorities into our recommendation system, which through their financial aid, taxation or thanks to their teams on the ground have a certain number of levers to help build such ecosystems.

The territorial policy that is associated with local authorities is defined by several objectives related to economic growth, food security, industrial resilience, and environmental aspects. We consider territorial policy as a "configuration" of the recommendation system in which local authorities indicate their priorities on each of the objectives. 4

FORMALIZATION

We design a recommendation system for the companies of a territory, whose object is the recommendation of new products to be developed. These production units have a know-how that ofers them the possibility to make "productive jumps"; that is, to move from the production of one kind of product to another when the "proximity of know-how" between the two products is relatively strong.

There is naturally a propensity for companies to adapt their ofer to seize new commercial opportunities, but we propose to set up a recommendation system that also takes into account territorial policy. As mentioned earlier, the territorial policy consists in weighing the diferent objectives of the referral system. The public authorities thus have the possibility of influencing the functioning of the system by choosing the objectives that are most important to them. Manuscript submitted to ACM Let {1, 2, . . . , } be the list of algorithms associated with each objective. The territorial policy P on the territory is defined as follows:

P ( ) = { 0, 1, . . . , }

We start by listing the achievable production jumps for a production unit that correspond to the first objective for companies: diversifying their production. To do this, we first calculate the current production associated with each production unit. In this task, we rely on a correspondence table that makes the link between the economic activity code of the production unit and the associated production (product codes in the HS nomenclature).

We then directly use the Product Space developed by the Growth Lab of Harvard University[ 24 ] to identify the opportunities for productive jumps for each of the products that the production unit manufactures. The Product Space is a graph of products in which each node corresponds to a product class (from the HS classification) and the weighting of the edges corresponds to the proximity of know-how between two product classes. For a given production unit , we obtain a list of new products A : {0, 1, . . . , }, which are ranked in descending order with respect to the level of productive relatedness. We choose an additional objective for companies that consists in increasing the competitive advantage and four objectives for territorial authorities that make sense with the development of sustainable systems[ 42 ]. They take into account economic aspects, resilience, security of basic goods and environment: (1) (2) • Economic growth: we integrate the objective of developing the economic growth of the territory. This is a wealth creator, and is essential to ensure economic prosperity and job creation. To identify the products that are the most efective in creating economic growth, we will take into account their level of economic complexity, which is a measure that has been shown to be highly correlated. • Productive resilience: we integrate an objective to improve the level of resilience of a territory. Given the fragility of our production systems, which have been damaged by various economic or health crises, we absolutely must build more robust production systems. We are going to integrate a theoretical measure of resilience of a territory. • Securing basic necessities: we also want to give the possibility to favor the basic necessities (e.g., food and pharmaceuticals) over other products. To do so, we have followed an original approach inspired by Maslow’s hierarchy to distinguish "vital" products. • Green production: finally, we take into account the environmental dimension of production, aware of the importance of repositioning production systems towards the production of greener goods. 4.1

Objective 1: Diversify production Our system makes a recommendation of productive jumps, which are repositioning or industrial diversification opportunities for companies. As presented in Pachot et al. [ 43 ], the Product Space developed by Hausmann and Klinger [ 25 ] provides a model to make recommendations.

We present below the technical details of the measurement of each of these objectives. We perform a weighted hybridization[ 46 ] from the diferent objectives to re-rank the list A.

For each production unit we compute the scores {ˆ1 ( |), ˆ2 ( |), . . . , ˆ ( |)} of each product ∈ A for each algorithm {1, 2, . . . , }. All scores must be normalized. Then we perform a weighted sum of each score to obtain a final score for each product: ˆ ( |) = Õ ˆ ( |) × =1

To make the correspondence between a production unit and the products it manufactures, we use a correspondence table1. The productive proximity between product classes is based on the study of country co-exports. From a largescale analysis of the types of products exported by country, Hidalgo et al. [ 27 ] computed the proximity of productive know-how (called "productive kinship") between each type of product and construct a graph of the productive space.

The measurement of the productive proximity between each product is done by looking for the percentage of times that product 1 is co-exported with product 2:

1,2 = ÍÍ112 ÍÍ122 (3)

We consider that a product is exported by a country when it grants the country a revealed competitive advantage (RCA) according to the formula of Balassa [ 8 ]. Let be the exports of product by country , then the revealed competitive advantage that country has for product can be expressed as a function of exports: Í

RCAcp = Í / Í, We consider that a country exports a product if is greater than 1.

4.2 Objective 2: Increase the competitive advantage

Now we need to consider the commercial interest for each firm. Some products are more advantageous for a production unit than others and we have the RCA formula to allow us to rank the productive opportunities according to the competitive advantage that they would grant to the production unit.

We define a modified version of RCA applied to the products of a sub-national territory. We compare the share of an activity in a territory with the share of that activity on a global scale. This prevents the more developed regions of a country from appearing to have a comparative advantage in each product[ 9, 45 ]:

RCA = / /

We define a function 2 (, ), which for each production unit of a territory will associate a list of products ∈ A and their associated score of RCA.

4.3 Objective 3: Improve economic performance

Several studies have confirmed the strong relationship between a country’s economic complexity and its growth rate: regions specializing in the manufacture of more complex products experience faster economic growth[ 18, 27 ]. Therefore, we choose to use the economic complexity indicator (ECI) as a target to improve the growth of a territory. 1There are several correspondence tables according to the nomenclatures used for the classes of economic activities. For example, for the USA, ISIC-HS (https://unstats.un.org/unsd/classifications/Econ) or NAF-CPF, equivalent to NACE-CPA for Europe (https://www.insee.fr/fr/information/2399243). See Pachot et al. [ 43 ] for details (4) (6) Diversity : ,0 = Í

Ubiquity : ,0 = Í , , = 1,0 Í . , −1 = 1,0 Í . , −1 , = 1,0 Í 1,0 Í′ ′ . ′, −2 = Í′ ′, −2 Í ′,0 ,0

We wish to express , as a function of ,0. To do this, we replace , −1 by 1,0 Í . , −2 and then simplify the equation:

We consider the matrix ∼,′ as a weighted (and normalized) diversification similarity matrix. This matrix reflects the extent to which the types of products exported from two countries are similar[ 38 ]:

The calculation of economic complexity presented by Hausmann et al. [ 24 ] is based on two measures: productive diversity and ubiquity. Diversity illustrates the variety of diferent products exported by a country. Ubiquity is an indication of the number of countries that export the same product. Let be a matrix of products exported by country, such that = 1 if country exports product :

From the measures of diversity ,0 and ubiquity ,0, we can recursively define the variables , and , corresponding to the average ubiquity and diversity of products exported by a country .

Let us rewrite the equation: ∼ Õ ′ ,′ ≡ ,0 ,0 , = Õ ∼,′ . ′, −2 ′ ∼

We note that , = , −2 = 1 satisfies this equation when the eigenvector of ,′ is associated with the largest eigenvalue. Since this eigenvector is a vector composed only of 1, it does not contain any information. Therefore, it is better to look at the eigenvector that is associated with the second largest eigenvalue. This is the eigenvector that captures the most variance in the system and is therefore a relevant measure of economic complexity. We denote ® as the i-th eigenvector of ∼,′ , which is associated with the i-th eigenvalue of ∼,′ , ordered in a decreasing order[ 22 ]: ∼ ,′ . ®2 = 2®2 ∼

The economic complexity index [ 26 ] is obtained by normalizing the eigenvector of ,′ associated with its second largest eigenvalue. < ®2 > corresponds to the mean of ®2 and (®2) to its standard deviation.

ECI = ®2− < ®2 > (13)

(®2)

In the same way, the complexity of a product (PCI) is defined by the following formula, with ® the eigenvector of ∼ ∼ ,′ constructed on the same principle as ,′ , but exchanging the countries with the products: (7) (8) (9) (10) (11) (12) (15) (18) PCI = ®2− < ®2 >

(®2)

We now wish to calculate the economic complexity of a sub-national territory. We must use a modified version of the equation 13, which combines PCIs calculated using international trade data with local data: (14) ECI = 1 Õ PCI Where is calculated in the same way as equation 5 but using RCA instead of RCA : = ( 1 RCA ≥ 1; (16)

0

A pre-calculated table with the complexities associated with each Harmonized System (HS) product class is available in open data2. We choose to retain the values for the latest available year (i.e., 2019).

We define a function 3 (), which for each production unit will associate a list of products ∈ A and their associated score of PCI ranked in decreasing order. 4.4 Objective 4: Improve the resilience of the production system Resilience is defined as the ability to recover quickly after a disruptive shock. For a production system, this corresponds to the ability of a system to quickly recover its production level or a higher level.

To measure the resilience indicator of a territorial production system, we start from an approach derived from the theory of dynamic systems[ 49–51 ]. In particular, the studies of Kharrazi [ 32 ], Kharrazi et al. [ 33, 34 ] focus on the definition of a theoretical resilience indicator built from the analysis of imports, while the exports of a territory are of particular interest to us. The theoretical resilience of a dynamic system is proposed based on two measures: eficiency and redundancy. Kharrazi et al. [ 34 ] have conducted a study on the behavior of the production systems of countries between 1996 and 2012, including the economic crisis of 2009, confirming the relevance of the theoretical indicator of resilience. The measure of a territory’s eficiency (also called ascendancy) can be considered as the degree of articulation or constraint of flows in a production system[ 34 ]. The more specialized a system is, the more optimized its connections are, the more eficient it is, and the less resilient it is. The theoretical measure of eficiency is as follows: Eficiency = Õ log .. (17)

, .. ..

Where is a product export value from country to country , . = Í is the total exports leaving country , . = Í is the total imports entering country and .. = Í is the sum of all exports in the system [ 21 ].

Conversely, a redundant system has many connections, and will therefore be "more flexible in re-rooting its flows and maintaining critical functions"[ 32 ]. Redundancy can be defined as the "degree of freedom or overhead of flows in a network"[ 32 ]. It is measured from the conditional entropy:

Redundancy = − Õ, .. log .2. From the eficiency and redundancy measures of a system, we can then measure the theoretical resilience level: = Eficiency /(Eficiency + Redundancy) (19)

Resilience = − log( )

We seek to recommend new products to be developed to companies in a territory that can help to improve the resilience score. We compute the contribution of a each product to the resilience. We define a function 4 () which for each production unit will associate a list of products ∈ A and their associated score of their contribution to the resilience of the territory. 4.5

Objective 5: Secure the production of essential goods We consider that products can be ordered according to their contribution to the needs of individuals. To do so, we propose an approach based on the hierarchy of needs of Maslow [ 37 ].

Genkova [ 20 ] provides a table of correspondence between the categories of needs of Maslow’s pyramid and the categories of products in the CPC nomenclature. All of the indirect products that are necessary for the production of the goods of each category are also associated.

We weight each product inversely to its corresponding level in Maslow’s pyramid and we obtain a function 5 (), which for each production unit will associate a list of products ∈ A and their associated score of their contribution to the needs. 4.6

Objective 6: Promote the production of environmental products We want the recommendation system to take the environmental impact of products into account. As a priority, we propose the productive jumps towards products with a lower environmental impact. Several studies have been carried out to integrate this dimension into the Product Space [ 19, 23, 28, 39, 44 ].

Initiatives exist to list green products[ 1, 19 ]. We retain the list provided by APEC3, which is defined as products "that directly and positively contribute to green growth and sustainable development objectives".

Let G be the list of green products, we define a function 5 (), which for each production unit will associate a list of products ∈ A and an associated score such that if ∈ G then = 1 else = 0. 5

EXPERIMENTATION We tested the recommender system using open data on French companies: production units, import and export amounts by French department and by product class. We made available the pre-calculated rankings associated with each objective, as well as a first experimentation on a French department 4. 5.1

Datasets We relied on the SIRENE5 dataset that is available history of French production units since 1973. It provides information for every company, relating them to their connected production unit, their NACE economic sector, their workforce group, and their postal address. We choose the HS nomenclature limited to 4 digits as the reference nomenclature for 3APEC List of Environmental Goods: https://www.apec.org/meeting-papers/leaders-declarations/2012/2012_aelm/2012_aelm_annexc.aspx 4https://github.com/apachot/Multiobjective-recommendation-for-sustainable-production-systems 5https://www.sirene.fr/sirene/public/static/acces-donnees

Manuscript submitted to ACM Turbines; steam and other vapour turbines Industrial or laboratory electric furnaces and ovens (including those functioning by induction or dielectric loss); other industrial or laboratory equipment for the heat treatment of materials by induction or dielectric loss Electric motors and generators; parts suitable for use solely or principally with the machines of heading no. 8501 or 8502 Machinery, plant (not domestic), or laboratory equipment; electrically heated or not, (excluding items in 85.14) for the treatment of materials by a process involving change of temperature; including instantaneous or non electric storage water heaters Furnaces and ovens; industrial or laboratory, including incinerators, non-electric HS)6, we associate each NACE class with HS classes. the products. By resorting to a combination of correspondence tables between activities and products (NACE → CPA→

We use datasets from global trade[ 52 ], as well as local datasets from each French department7. These datasets provide us for a given territory or country, the amount of exports of each product class, for each country or french department. We use the year 2019 and convert the French data (French CPF nomenclature) into the HS nomenclature. 5.2

Recommender System We retrieve the list of production units on a territory. From their activity code, our system is able to determine which product classes are manufactured by this production unit. We then use a proximity table between the product classes to determine which products are the closest in the sense of know-how. These products represent the potential production jumps.

At each productive jump we compute a global score from the weighted average of 6 pre-computed rankings, associated to the 6 objectives of our recommendation system. We then propose a list of 5 classes of products whose productive jump has obtained the highest score. You will find in table 2 an example of recommendation for a production unit located in Haute-Loire in France, that manufactures parts and accessories for motor vehicles. 6

CONCLUSION

The expectations of the diferent actors in a territory often come up against the complexity of the production systems. Stakeholders whose strategies are sometimes opposed can find a solution in a recommendation system that takes their 6We parse the NAF to CPF correspondence document (https://www.insee.fr/fr/statistiques/fichier/2399243/Nomenclatures_NAF_et_CPF_Reedition_2020. pdf) to obtain a NACE 2 to CPF 2.1 CSV file. NACE is obtained from NAF code by removing the last letter. CPF and CPA are identical in version 2.1. Matching between CPA 2.1 and HS 2017 is done using the CPA 2.1 to NC 2017 correspondence table (https://ec.europa.eu/eurostat/ramon/relations/index. cfm?TargetUrl=LST_REL) because HS code equivalent to the sixth first digits of the related NC code. 7https://www.data.gouv.fr/fr/datasets/statistiques-regionales-et-departementales-du-commerce-exterieur/ objectives into account. We explored the fields of recommendation, information theory and economics to find objectives that can be integrated, and we formalized a first version of a multi-objective recommendation system. We will continue our work by validating the system on a territory. We also consider a Pareto-eficient hybridization to guide the local authorities in setting the weights of the system.

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