Environmentally friendly management of dairy supply chain for designing a green products' portfolio

Accepted Manuscript Environmentally friendly management of dairy supply chain for designing a green products' portfolio Elisaveta G. Kirilova, Natasha Gr Vaklieva-Bancheva PII:

S0959-6526(17)31921-2

DOI:

10.1016/j.jclepro.2017.08.188

Reference:

JCLP 10447

To appear in:

Journal of Cleaner Production

Received Date: 19 July 2016 Revised Date:

22 August 2017

Accepted Date: 22 August 2017

Please cite this article as: Kirilova EG, Vaklieva-Bancheva NG, Environmentally friendly management of dairy supply chain for designing a green products' portfolio, Journal of Cleaner Production (2017), doi: 10.1016/j.jclepro.2017.08.188. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Environmentally Friendly Management of Dairy Supply

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Chain for Designing a Green Products’ Portfolio

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Elisaveta G. Kirilova1*, Natasha Gr. Vaklieva-Bancheva1

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Bulgarian Academy of Sciences

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Akad. G. Bontchev, Str., Build. 103, 1113 Sofia, Bulgaria

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Institute of Chemical Engineering,

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E-mails: [email protected], [email protected]

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Abstract

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The study proposes an optimization approach for design of “green” products’

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portfolio of a supply chain for curd production. It includes three interconnected models for

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describing curd production, supply chain and its environmental impact. The latter is assessed

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in terms of wastewater and CO2 emissions associated with the curd production and the

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transportation of raw material and products. The models are included in a broader

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optimization framework whereby the environmental criteria are defined in terms of costs such

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as the best trade-off between total profit and environmental impact to be achieved. The

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proposed approach is applied to a Bulgarian case study for production of two types of curd in

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dairy supply chain involving suppliers, dairies and markets. Two optimization problems for

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“green” products portfolio and profit products’ portfolio design are formulated and solved.

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*

Corresponding author: Address: Institute of Chemical Engineering, Bulgarian Academy of Sciences, Akad. G. Bontchev, Str., Build. 103, 1113 Sofia, Bulgaria; Phone: +35929793481; Fax: +35928707523; E-mail: [email protected]

ACCEPTED MANUSCRIPT The obtained results show that the “green” products portfolio is limited by the environmental

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impact consideration and the optimal profit products’ portfolio is limited by the plants’

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capacities. The successful implementation of the proposed approach opens the prospect of

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expanding not only to the whole range of dairy products but also the entire supply chain that

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includes players which are in a competition with each other.

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Key Words: Green Supply Chain Management; Products’ portfolio design; Environmental impact assessments; Optimization; Curd production.

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1. Introduction

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Production of milk and dairy products takes place in all EU Member States and

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represents a significant proportion of the value of EU agricultural output. For some Member

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States it forms a significant part of the agricultural economy (European Commission, 2016).

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However, dairy production involves considerable amounts of wastewaters and pollutants

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across the whole dairy network. Improving its sustainability requires implementation of so

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called Green Supply Chain Management (GSCM) strategy. The greater part of developed

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GSCM methods has applied the principles of Life Cycle Analysis (LCA) with the aim of

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improving the effectiveness of decision-making process and to facilitate successful

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implementation of the GSCM strategy (Sharma et al, 2015). The LCA appears a suitable tool

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as it allows environmental consideration of the supply chains within larger boundaries, i.e.

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capturing the processes from the dairy farms through dairy production to wastewater

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treatment plants, accounting for all material flows, resources requirements and all pollutants

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which can be expected across the network. For example, Sonesson & Berlin, (2003) have

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implemented LCA to show which actors have the greatest impact on the environment and

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how the environmental impact of the dairy chains is influenced by variation of different

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ACCEPTED MANUSCRIPT social and economic factors such as population size, markets demands etc. across the whole

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network. Djekic et al., (2014) have recognized the key indicators which influence the

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sustainability of the dairy network as the choice of the production/packing portfolio, energy

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fuel profile and water usage. Palmieri, et al., (2016) have extended the environmental

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boundaries of the system aiming to assess the environmental impact of the network in terms

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of animal diets considering the entire life cycle of the cows inside the dairy farms.

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The successful performance of green dairy networks depends not only on the

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environmental impact assessment of the main actors involved but also on the exploration of

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their economic impact on the supply chain sustainability. In this order, Glover et al., (2014)

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have shown the dominant role of supermarkets as the main actor in GSCM, exerting strong

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financial pressure on the smaller organizations across the supply chain to co-operate and

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contribute to energy reduction in order to achieve cost reduction and profit maximization.

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An incorporation of eco-innovations can be used successfully for improvement of

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dairy supply chain sustainability. For that reason it is very important to be identified the

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factors that influence to a great extent the decision-making process of supply-chain members

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and their willingness to make changes and adopt eco-innovations (Mandolesi et al., 2015;

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Mylan et al., 2015).

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The decision-making process in GSCM can also be improved by applying the

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approach for assessment of the risk during the realization of supply chain activities in the

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dairy industry. It can be used for identification of the risk factors that can influence

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sustainability of the supply chain as the risk of non-fulfillment of the demands in terms of

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quality and quantity; the risk of dairy contamination by bacteria and antibiotics; the risk of

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lower dairy production etc. (Septiani et al., 2014).

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One of the most effective ways to improve the supply chain sustainability is to use the

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LCA to optimal supply chain design that allow simultaneous consideration of different

ACCEPTED MANUSCRIPT aspects of supply chain players as the best trade-off between the traditional costs and

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environmental impact to be achieved. For example, distribution of goods consumes fuel and

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makes a significant contribution to global warming. For minimization the location costs,

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traffic congestion and transportation of raw/processed milk and dairy products, Jouzdani et

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al., (2013) have proposed an approach for dynamic location of dairy facility and supply chain

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planning under demand uncertainty. In this sense, Validi et al., (2014) have proposed a green

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multi-objective optimization model for designing the dairy market supply chain in terms of

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the trade-off between transportation costs and CO2 emissions generated during the milk

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transportation.

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As can be seen the developed approaches consider different aspects of GSCM of the

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dairy activities in terms of the environmental impact and economic performance where some

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level of trade-off has been satisfied. On the other hand, the environmental considerations are

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mainly focused on the impact of CO2 emissions produced during transportation of raw

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materials and products, and due to energy consumed in products manufacturing.

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The aim of this study is to propose an optimization approach for “green” products’

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portfolio design of a curd supply chain. It involves a broader objective function including,

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along with environmental impact assessments of CO2 impact associated to the energy

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consumed and generated during transportation and assessments for each production task

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accounting for associated wastewater (including these from the used raw material). The

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optimization criterion is defined in terms of money such as to find the best trade-off between

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the total profit of the dairy complex and the costs incurred for the environmental impact due

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to its operation.

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The rest of the paper is organized as follows: next section provides a detailed

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description of the “green” product portfolio modeling, which involves: problem statement,

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data required, curd production model, supply chain model and modeling the environmental

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impact. The proposed objective function evaluates the trade-off between economic and

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environmental issues in terms of money. Section 3 presents a real case study for supply chain

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for manufacturing of two types of curd and gives the results obtained. Finally, short

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concluding remarks are provided.

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2. “Green” product portfolio modeling

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2.1. Problem statement

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A production complex comprising I dairies for manufacturing of P different types

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of curd (further called products) within predefined time horizon H is considered. The dairies

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are supplied with milk from S suppliers (milk collection centers). Manufactured products

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sell at M markets, see Fig. 1.

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Figure 1. Dairy supply chain.

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Additionally, it is known that each dairy involves equipment of N types with different

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volumes. A single technology (recipe) is used for the manufacturing of each product. The

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production costs are different for the dairies, but invariable within the time horizon.

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Standardized whole milk is used as a raw material. It is skimmed to the same level to produce

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a given type of product in each dairy. Consistent quality of products should be maintained. A

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common mathematical description will be used to model the yield of each product. The

ACCEPTED MANUSCRIPT transportation of milk and products is organized and paid by the dairy complex. The distances

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between milk collection centers, dairies and markets are known. Transportation costs depend

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on the capacity of the vehicles used. Transportation costs and the prices of milk and products

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are also invariable in the time horizon. Capacities of milk collection centers and market

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demands are fixed over the time horizon.

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Assuming that the structure of the supply chain which has to be designed is a constant

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within the time horizon, and accepting that no stocks and milk accumulations are permitted in

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the plants, a deterministic supply chain mathematical model will be developed. Its aim is to

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describe the required total site products’ portfolio and its distribution across the involved plants as amounts of products that have to be produced in each dairy.

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Simultaneously, all emissions generated over the designed supply chain related to the

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operation of the dairy complex should be evaluated. In Figure 2 the boundaries determining

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the environmental framework of the curd supply chain are shown. It is obvious from Figure 2

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that these boundaries cover the emissions generated in the plants during product

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manufacturing, the amounts of CO2 associated with the energy consumed by the processes

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and these which are due to the transportation of both raw milk and products.

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Air

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Suppliers

Fuel combustion

Transport

Energy consumption

Dairies

Fuel combustion

Transport

Waste water

Waste water

Water BOD

BOD

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Figure 2. Environmental impact boundaries of the curd supply chain.

Markets

ACCEPTED MANUSCRIPT Dairy manufacturing is associated with “generation” of a huge amount of wastewater

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that contains considerable amounts of proteins, fat, sugars and other organic residues. The

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main indicator for its assessment is Biochemical Oxygen Demand (BOD) accounted for five

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days. Wastewater produced in the dairies is treated in Wastewater Treatment Plants

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(WWTPs) at a given cost. The expenses associated with the considered products that have to

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be paid to the WWTPs are limited for each dairy. Air Pollution Tax (APT) is also imposed on

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the products manufacturing. It aims to maintain the amount of the emitted CO2 below an

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acceptable level. Exceeding CO2 emissions above this level results in imposition of financial

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penalties. The impact of the pollutants generated along the designed supply chain is evaluated

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in terms of costs which have to be paid.

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From the above it is clear that three interconnected models have to be developed and

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involved in a common optimization framework. They cover manufacturing of products with

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consistent quality, design of the supply chain activities and the environmental impact of the

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emissions of pollutants in air and water produced during manufacturing and transportation of

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raw materials and products. Using the money that have to be paid for the produced wastes

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permits us to apply a “single” objective function in terms of costs instead of a multi-objective

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one looking for the trade-off between economic and environmental issues. The total site

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profit is used as an optimization criterion. It is defined as a cost function represented by the

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income from the market sale of products after the deduction of all expenses incurred such as

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production costs, raw materials costs, transportation costs, and environmental costs.

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2.2. Data required

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In order to develop the mathematical models three groups of data have to be known.

ACCEPTED MANUSCRIPT The raw material and products data are related to the composition of used raw material and

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final products. The supply chain data contain the horizon of interest; summarized data for

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dairy units and processing times; markets’ demands; capacities of the milk suppliers; selling

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prices of milk and products; production costs; distances between milk suppliers, dairies and

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markets; transportation costs; vehicles’ capacities. The environmental data contain data

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required to assess the environmental impact of the pollutants associated with the supply chain

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activities. Some of these pollutants are produced in dairies and the rest during transportation

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of raw material and products (see Figure 2).

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Regarding pollutants produced in dairies, the environmental impact is determined by

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both the “introduced from outside” BOD load, i.e. wastes related to the preparation of used

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raw material like standardization and milk skimming (Stefanis et al., 1997) and BOD

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“generated” within the products manufacturing. Part of the BOD “generated” within the

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processing tasks depends on the composition and amount of the used milk. Moreover, for the

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dairy industry, losses of raw materials, by-products and target products due to spills or

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deposits on the walls of the processing units are significant. Having in mind that these losses

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could not be avoided completely, it assumes them to be regulated within previously defined

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reasonable levels in %, accounted during the calculation of BOD “produced” within the

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corresponding processes. BOD generated from some sources depends on the milk fat content

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and it has to be calculated. For a sake of consistency, all BOD sources will be described in

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detail in the part dedicated to the modeling of the environmental impact of the products

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manufacturing. The costs for BOD removal in the WWTPs and the imposed limiting level on

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the expenses for BOD are also given for each dairy.

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Additionally, dairy production impacts on the air by releasing CO2 emissions

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associated with energy consumption. Pasteurization is the most energy-consuming process.

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The amount of the consumed energy for milk pasteurization depends on the amount of the

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processed skim milk. For assessment of the environmental impact of this process, data about

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the energy required for heating and cooling of 1 kg skim milk; the amount of CO2 associated

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with a kWh of energy; and the costs per 1 kg of CO2 have to be known. During transportation, CO2 emissions are also produced by burning transportation

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fuels. Their environmental impact depends on the vehicle capacities, amount of the

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transported milk/products and respective distances. For its calculation data for mass of CO2

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emitted from a vehicle per 1 km and costs of CO2 due to transportation have to be known.

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Finally, a given value of Air Pollution Tax for manufacturing the products in a dairy complex

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is imposed to limit all CO2 emissions.

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2.3. Curd production modeling

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In the proposed study only curds manufacturing is considered. Curd is low-fat dairy

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product, containing about 80% moisture and 20% solids, mainly casein and other proteins,

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fat, minerals and other elements (Carawan et al., 1979). It is produced by acidification of

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skim milk, as shown in Figure 3, (COWI Consulting Engineers and Planners AS, Denmark,

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2000).

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1 – Pasteurizer 2 – Curd vat 3 - Drainer

Yeast

Skimmed milk

Pasteurized milk

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Curd – raw product

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Figure 3. Curd production tasks.

Whey

Curd-target product

ACCEPTED MANUSCRIPT Curd is manufactured by sequentially conducting three production tasks. Firstly, milk

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pasteurization is carried out. Then, acidification of milk takes place to produce curd – raw

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product. Finaly, draining of residual whey from the curd – raw product to produce curd-target

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product is carried out. Detailed description of the production tasks is listed in Table 1,

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(Stefanis et al., 1997).

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Table 1. Description of the processing tasks in curd production. Task

Processing

In/Out materials

time 0.5 h

Pasteurization

In: Skim milk with fat 1

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Task1

Fractions

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Unit type

Pasteurizer

content x p

Out: Pasteurized milk

1

Task 2

4h

Acidification

In: Pasteurized milk with fat 0.88

Curd vat

content x p

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to produce curd - raw-product

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with fat content x p

Task 3

0.5 h

In: Yeast

0.12

Out: Curd – raw product

YP1( x p )

Out: Whey – by-product

1- YP1( x p )

In: Curd – raw product

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Draining

Out: Curd-target product

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to produce curd

Out: Whey – by-product

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Drainer

- target product 8 9

YP 1( x p ) represents yield of curd – raw product containing residual whey, as a function of milk fat content xp in used raw material.

ACCEPTED MANUSCRIPT Both products yields and BOD generated during curd manufacturing depend on the

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composition of the used skim milk. The aim of curd production modeling is to present the

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products yield as a function of the milk fat content in used skim milk. Also it has to provide

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the connection between respective production tasks by calculating the corresponding size

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factors.

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As already mentioned above, the problem comprises three interconnected models – a

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model for products manufacturing, supply chain model and environmental impact model

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which will be described consecutively below. Milk composition impacts on products yield,

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plants’ productivity and the total environmental impact of the supply chain. Milk composition

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is regulated by its fat content. Having in mind that in both plants of the dairy complex the

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milk is skimmed at the same level for manufacturing the same type of products, a set of

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continuous variables x p [%] to account for the fat content in the milk skimmed for products

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p are introduced. They vary in the predefined boundaries as follows:

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max x min p ≤ xp ≤ xp

∀p, p ∈ P

(1)

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Skimming standardized whole milk is not included in the production recipe.

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Skimming is carried out in separators, and cream is obtained as by-product. From the mass

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balance of skimming 1 kg standardized milk, the following equation to calculate the

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concentrations of proteins, casein and lactose in skim milk are obtained:

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 MF ∗ − x p  , MP( x p ) = MP 1 +  CF − MF ∗    *

 MF ∗ − x p  , MC( x p ) = MC 1 +  CF − MF ∗    *

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 MF ∗ − x p  , ML( x p ) = ML 1 +  CF − MF ∗   

∀p, p ∈ P .

*

(2)

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In eq. (2) MF∗ , MP* , MC and ML* denote concentrations in % of milk fat content,

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proteins, casein and lactose in the used raw material – standardized whole milk. CF [%]

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represents cream fat content. MP ( x p ) , MC ( x p ) and ML ( x p ) are the concentrations of

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proteins, casein and lactose in skim milk for manufacturing product p as a function of milk

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fat content x p , [%].

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To calculate the curds yield Van Slyke’s equation is applied, (Johnson, 2000):

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YP ( x p ) =

[RF ( x

p

]

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*

).x p + RC p .MC ( x p ) .RS p PS p

(3)

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, ∀p, p ∈ P ,

where YP ( x p ) is the yield of product p as a function of milk fat content. PS p [%] is a solids’

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content in corresponding target products, and RC p [%] and RS p [%] are recovery factors for

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casein, and all solids. RF ( x p ) [%] is the milk fat recovery factor. The milk fat recovery

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factor is unknown and it is determined with the help of the relations used to maintain

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consistent product quality.

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Fat in Dry Matter (FDM [%]) is used as an indicator for curd quality (Johnson, 2000).

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In order to maintain a consistent quality of the products, FDM has a value determined by

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the relation between the contents of the fat and solids in the target products:

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FDM p =

PF p PS p

∀p, p ∈ P .

(4)

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where PF p fat content of the product p , [%].

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On the other hand, FDM could be determined by the composition of the raw material, using

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contents of casein and fat in it and corresponding recovery factors:

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FDM p =

RF ( x p ).x p

(RF ( x p ).x p + RC p .MC ( x p )) RS p

,

(5)

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∀p, p ∈ P .

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Using Eqs. (4) and (5) milk fat recovery factor RF ( x p ) is determined so as to maintain the

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required consistent quality of the products. Its value should be maintained in the following

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boundaries.

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0 < RF(xp ) ≤ 1, ∀p, p ∈ P .

(6)

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The size factors represent the “volumes” of material that have to be processed in

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production tasks so as to manufacture a unit mass of target products p, (Mauderli, 1979).

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Following the production recipe for curds manufacturing and using the fractions listed in

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Table 1 and yields of target products obtained in Eq. (3), the size factors SF(x p ) [m3/kg] are

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determined for each processing task as follows:

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 0.88   YF(x )  p    1  SF(x p ) =   , ∀p, p ∈ P YF(x ) p        1.11 

(7)

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Each line of equation (7) represents formula for calculating the size factor for each processing

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task included in curd production as a function of milk fat content. For example, line 1

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represents formula for calculating the size factor for pasteurization, line 2 – for acidification

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and line 3 – for draining.

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2.4. Supply chain model

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2.4.1. Conditions for dairy product portfolio feasibility

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Vaklieva-Bancheva et al., (2006) have proposed the conditions that ensure feasible

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products portfolio for a batch plant from the dairy industry. Their advantages are that no

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schedules have to be created for each current product portfolio obtained during the solution

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process but instead the working frame of the schedules is assessed in regard to the horizon of

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interest. Here a brief description of the proposed framework is provided.

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In order to describe the proposed working frame, it is assumed that p different

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products have to be produced in any dairy i within time horizon H [h]. The quantities

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constituting the current products’ portfolio are QPi , p [kg]. Having in mind that in all plants

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the milk skimmed at the same level is used to manufacture the same products, the size factors

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are also the same for the same tasks SF( x p )n . The processing times are assumed to be

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constant T p , n [h].

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The plant is represented with its "block structure", where all equipment units

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belonging to a given type n are gathered in a common processing “block” having a total

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volume U i ,n [m3] determined as a sum of volumes of the respective units. Also it is assumed

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that manufacturing of each product passes through all processing “blocks”. If some product

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does not use some units of a given type, a fictitious processing task is introduced to connect it

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with the unemployed “block”. The number of processing tasks for each product becomes

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equal to the number of processing “blocks”. For the fictitious processing tasks both the size

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factors and processing times are assumed to be equal to 0. By multiplying the size factors by the products quantities SF( x p )n .QPi , p [m3] the

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volumes of materials to be processed in the tasks are determined. Then, relating them to the

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volumes of the corresponding processing “blocks”

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SF( x p )n .QPi , p

the parts of these

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Ui ,n

volumes, used for QPi , p manufacturing are found. Conditionally, these relations could be

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interpreted as “a number of batches” that have to be performed by each “block” to produce

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the quantity of QPi , p

and could be employed to assess the time TQi , p,n [h] of each

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processing “block” required to produce QPi , p :

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TQi , p ,n = SF ( x p )n .QPi , p

T p ,n U i ,n

, ∀n , n ∈ N ; ∀p , p ∈ P ; ∀i , i ∈ I .

(8)

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Obtained time assessments TQi , p,n are functions of the quantities of products determining

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current products’ portfolio QPi , p [kg]. They are used to define the following constraints,

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whose satisfaction results in a feasible products’ portfolio:

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1. Taking into account that the time resource of each processing “block” is shared

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between all products over the horizon H, the sum of time assessments (8) for all products has

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to be less or equal to the horizon H :

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ACCEPTED MANUSCRIPT P

1

∑

SF( x p )n .QPi , p

p =1

T p ,n U i ,n

≤ H,

∀n , n ∈ N ; ∀i , i ∈ I .

(9)

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2. Having in mind that all processing “blocks” are involved in each product

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manufacturing, the sum of the time assessments over all “blocks” would be less or equal to

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the horizon length:

6 N

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∑

T p ,n U i ,n

≤ H,

∀p , p ∈ P ; ∀i , i ∈ I .

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2.4.2. SC mathematical description

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To describe the problem for optimal “green” portfolio designing the following two groups of control variables have to be introduced:

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(10)

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n =1

SF ( x p )n .QPi , p

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Binary variables which aim to structure the supply chain. Two sets of binary variables

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are set up. Variables χ are used to structure the supply chain between the dairies and

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markets as follows:

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1 − if dairy i is connected with market m 0 - otherwise

χ m ,i = 

(11)

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and variables γ are introduced to structure the supply chain between the milk supply centers

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and dairies:

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ACCEPTED MANUSCRIPT 1

1 − if dairy i is connected with supply center s . 0 - otherwise

γ s ,i = 

(12)

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Continuous variables which are introduced to follow for the products and raw

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materials transferred over the Supply Chain. The variables X i , p , m [kg] are introduced to

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account for the quantities of products p produced in dairies i and sold at markets m . They

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vary in the following boundaries:

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0 ≤ X i , p , m ≤ MDem m , p ,

∀i, i ∈ I ; ∀p , p ∈ P ; ∀m , m ∈ M ,

(13)

M AN U

8

SC

7

9

where MDem p , m [kg] is the demand of products p in markets m for the horizon H .

11

While the variables Yi , s [kg] are used to account for the quantities of milk bought by dairies i

12

from the supply centers s and vary within the boundaries:

TE D

10

13 14

0 ≤ Yi , s ≤ MSup s , ∀ i , i ∈ I ; ∀ s , s ∈ S .

17 18

where MSup s [kg] is the capacity of the milk supply center s for the horizon H .

AC C

16

EP

15

(14)

It is supposed that all products manufactured in the plants i are immediately

19

transported to the markets. Mass balance equations of the subsystem dairies – markets are

20

introduced to follow up that no stocks accumulation will take place in each dairy:

21

22

QPi , p =

M

∑ X i , p ,m ⋅ χ i ,m ,

m =1

∀p , p ∈ P ; ∀i , i ∈ I .

(15)

ACCEPTED MANUSCRIPT 1 2

Using the products’ yields YP ( x p ) , dairy mass balance equations are used to determine

3

required total amount of whole standartized milk QM i [kg] in dairy i :

RI PT

4 P

5

1 ⋅QPi , p , ∀i, i ∈ I . p =1 YP( x p )

QM i = ∑

6

(16)

The total amount of milk bought by the supply centers have to be immediately processed in

8

the dairies for producing the required products. The mass balance equations of the subsystem

9

dairies – milk supply centers preserve dairies from milk accumulation:

M AN U

SC

7

10 S

11

QM i = ∑ Yi ,s ⋅ γ i ,s , ∀i, i ∈ I . s =1

TE D

12

(17)

The constraints represented below ensure feasibility of the obtained product

14

portfolios. They are built by using already determined size factors Eqs. (7) and applying Eqs.

15

(9)-(10):

P

17

∑

SF( x p )n ⋅ QPi , p ⋅

p =1

18 N

19

T p ,n

U i ,n

T p ,n

≤ H , ∀n , n ∈ N ; ∀i , i ∈ I .

∑ SF ( x p )n ⋅ QPi , p ⋅ U i ,n ≤ H ,

n =1

20

AC C

16

EP

13

∀p , p ∈ P; ∀i , i ∈ I .

(18)

(19)

ACCEPTED MANUSCRIPT 1

Market constraints ensure that the quantities of products p processed in all dairies and sold

2

at markets m are less or equal to the markets’ demands:

3 I

4

∑ X i , p ,m ⋅ χ i ,m ≤ MDemm, p ,

∀m , m ∈ M ; ∀p , p ∈ P.

(20)

RI PT

i =1

5

Milk supply centers constraints guarantee that milk bought by dairies from each supply center

7

s is less or equal to its capacity:

SC

6

I

9

∑ Yi ,s ⋅ γ s ≤ MSup s , p ,

∀s , s ∈ S .

i =1

10 11

M AN U

8

2.5. Modeling the environmental impact

13

2.5.1. Environmental impact of curd production.

TE D

12

(21)

14

For modeling the environmental impact of the wastewater Biochemical Oxygen

16

Demand (BOD) indicator is used. BOD M (x p ) load of 1 kg milk (skimmed or standardized)

17

depends on its composition. Presenting the concentrations of the proteins and the lactose as a

18

function of milk fat content, it is calculated as:

20

21

AC C

19

EP

15

[

]

 kg O2  BODM (x p ) = 0.89.x p + 1.031.MP(x p ) + 0.69.ML(x p ) .10 −2 ,   , ∀p , p ∈ P.  kg milk 

(22)

ACCEPTED MANUSCRIPT Following the production tasks described above five types of wastes associated with

2

BOD load have been identified. They refer to the production of 1 kg target product. BOD

3

sources, the tasks where respective BOD are generated and respective eligible levels of

4

accepted losses are listed in Table 2.

5 6

Table 2. Sources producing BOD, production tasks and eligible levels of losses. BOD

BOD calculation

Measure

of losses of BOD, [%]

BODSM (x p ) = BODM (x p ), ∀p, p ∈ P.

Deposits

 kg O 2  Task 2  kg whey    Task 3

AC C

EP

BOD Wh = 32 .10 − 3 , ∀ p , p ∈ P .

BODCu ( x p ) =

∀p, p ∈ P.

Whole milk

“introduced

wastes

” waste

LSSM=1.2

 kg milk   

walls

Curd

generated

BOD Pa = 1 . 5 .10 −3 , ∀ p , p ∈ P .  kg O 2  Task 1

on units

Whey

 kg O 2  Task 1  kg milk   

TE D

milk

Accepted eligible levels

M AN U

Skim

Place

SC

Sources

7

RI PT

1

Task 2 1 .BODM ( x  kg O 2  YP( x p )  kg curd  Task 3

BODWM (x p ) = BODM (x p ), ∀p, p ∈ P.

 kg O 2  Task 1  kg milk   

LSWh=1.6

LS2Cu=0.3 LS3Cu=0.5

LSWM=0.1

ACCEPTED MANUSCRIPT It can be seen from Table 2 that BODSM (x p ) is the BOD load related spills of skim milk

2

during implementation of Task 1 as a function of milk fat content x p , BOD Pa is the BOD

3

load related to deposits on pasteurizers walls during pasteurization of the skim milk, BOD Wh

4

is the BOD load related to spills of whey produced as by-product during discharging of curd

5

vats and BODCu ( x p ) is the BOD load related to losses of curd as a function of milk fat

6

content x p . While, BODWM (x p ) is the BOD load “introduced from outside” which is

7

artificially associated to Task 1 also as a function of milk fat content x p . Losses of whole

8

standardized milk LSWM represent the losses which take place during milk collection,

9

standardization, and skimming. LS SM represent losses of skim milk in milk pasteurization.

10

LSWh represents losses of whey in acidification and draining of the produced curd, while and

11

LS 2Cu and LS 3 Cu represent losses of curd in Tasks 2 and 3.

M AN U

SC

RI PT

1

Environmental impact assessment of curd production is carried out according to the

13

Methodology for Minimum Environmental Impact (Pistikopoulos et al., 1994). Firstly, for

14

each product environmental impact indices m xp

15

calculated. They determine the mass of each type of waste w generated in any production

16

task n related to 1 kg target product. For this purpose In/Out fractions listed in Table 1 are

17

applied to connect different production tasks in a common production line so as to compute

18

the mass of generated wastes. Then, the yield, Eq. (3), is used to scale them referring 1 kg

19

target product and finally by the help of data for accepted levels of eligible losses the

20

corresponding environmental impact indices are obtained as follows:

21

( )

w,n

( ∀w , w ∈W ; ∀n, n ∈ N ) are

AC C

EP

TE D

12

ACCEPTED MANUSCRIPT

2

∀p, p ∈ P

    0     0.111   LS 3Cu %  , 1 100      0      0

M AN U

SC

RI PT

1

0.88 LS SM %  0  YP( x p ) 100   0.88 0  YP( x p )    1  LS %   0 − 1.11 Wh  YP( x )  100  p    m( x p ) =  LS 2Cu % 0 1.11  100    MF % − x p     1 +   CF % − MF %   LSWM %   0.88 0   100  YP( x p )        

3

(23)

The environmental impact assessment PBOD p for production of 1 kg of any type of curd is

5

defined as a function of milk fat content, as follows:

6

7

W

N

w=1

n =1

TE D

4

PBOD p = ∑ BODw ∑ m( x p ) w,n ,

∀p, p ∈ P .

(24)

EP

8

[kg O2 ] ,

The amount of CO2 produced during milk pasteurization is used to model the

10

environmental impact of the CO2 emissions in curd production. It depends on the amount of

11

skim milk and calculates from the mass balance of 1 kg standardized whole milk accounting

12

for the fat content of the skim milk. The impact of CO2 emissions associated with the heating

13

and cooling of the skim milk obtained from 1 kg standardized whole milk are calculated as

14

follows:

15

AC C

9

ACCEPTED MANUSCRIPT 1

(EH + EC ) ⋅ ECO 2

EIMCO 2 p =

 CF − MF     CF − x p   

  kg CO2 ,  ∀p , p ∈ P ,  kg skimmed milk 

2

where EH and EC is the energy required for realization of the processes of heating and

4

cooling in the pasteurization in [kWh/kg skim milk], and ECO 2 is the mass of CO2

5

emissions associated with kWh energy [kg CO2/kWh].

RI PT

3

SC

6

Using the yield the environmental impact of CO2 could be referred to the unit of product p

8

produced from skim milk with fat content x p :

9

EIPCO 2 p =

(EH + EC ) ⋅ ECO 2  CF − MF    ⋅ YP( x p )  CF − x  p  

11 12

17

18

∀p , p ∈ P .

(25)

The amounts of CO2 emitted from the vehicles to transport 1 kg standardized whole

AC C

16

 p 

2.5.2. Environmental impact of the transportation

14 15

 kg CO 2  kg product 

EP

13

,

TE D

10

M AN U

7

milk and 1 kg curd/km are as follows:

TMCO 2 = 2 ⋅

TCO 2  kg CO 2  ,  ; VCm  km . kg milk 

(26)

19

20

TPCO 2 = 2

TCO 2  kg CO 2  ,  . VCp  km . kg curd 

(27)

ACCEPTED MANUSCRIPT 1

where TCO2 is the amount of CO2 emissions produced by fuel combustion, [kg CO2/ km] and

2

VCm [kg] and VCp [kg] are the capacities of used vehicles for transportation of milk and

3

products. Equations (26) and (27) take into account that vehicles travel empty one way (to

4

milk collection centers and from the markets).

RI PT

5

2.5.3. Environmental constraints

6 7

The environmental impact assessments obtained above for water and air referred to 1

9

kg manufactured products p are used to determine respective environmental constraints in

10

terms of costs. Multiplying the obtained PBOD p by the quantities of products manufactured

11

in each dairy and by the cost paid in WWTP, the costs for removal of the generated BOD in

12

WWTPs are determined. For each dairy i it has to be less than or equal to the imposed limit

13

on the expenses for BOD removal in Bulgarian Lev (BGN) is BOD _ Li [BGN]:

14

15

BODcosti ⋅

P

M

TE D

M AN U

SC

8

∑ PBOD ⋅ ∑ X p

m =1

⋅ χi ,m ≤ BOD _ Li

∀i , i ∈ I

(28)

EP

p =1

i , p ,m

16

where BOD cos ti is the cost for BOD removal in WWTP connected with dairy i, [BGN/kg

18

BOD].

19

AC C

17

20

Using the environmental impact assessments (25)-(27) the environmental constraint for CO2

21

emissions in the dairy complex in terms of costs is defined as follows:

22

ACCEPTED MANUSCRIPT

1

P M    ECO2cost ⋅ ∑ EIPCO2 p ⋅ ∑ X i , p ,m ⋅ χ i ,m +  I  p =1 m =1  ⋅  ≤ APT (29) ∑ P M S   i =1  TCO2cost ⋅  TMCO2 ⋅ ∑ Yi ,s ⋅ γ i , s ⋅ SDisi ,s + TPCO2 ⋅ ∑∑ X i , p ,m ⋅ χ i ,m ⋅ MDisi ,m    s =1 p =1 m =1   

RI PT

2

where ECO2 cos t is the cost for CO2, associated with energy consumed by the processes of

4

heating and cooling during the pasteurization of milk [BGN/kg CO2] and TCO2 cost is the

5

cost for CO2 due to the transportation of milk and products, [BGN/kg CO2]. SDis i ,s , and

6

MDisi ,m are the distances between supply centers and dairies, and dairies and markets, [km]

7

APT is the value of Air Pollution Tax, [BGN].

2.6. Objective function

9 10

M AN U

8

SC

3

The profit of dairy complex is used as an objective function. It is determined as a

12

difference between the revenues from the sale of the products at the markets and the

13

manufacturing and the environmental costs. It involves the following terms:

14

- revenue from the sale of the products at the markets:

EP

TE D

11

16

FR =

AC C

15 I

P

M

∑∑∑ X

i , p ,m

⋅ χ i ,m ⋅ PSPm , p , [BGN],

(30)

i =1 p =1 m =1

17

where PSP p,m are the selling prices of the products p at the markets m , [BGN/kg];

18 19 20

- total production costs for the dairy complex:

ACCEPTED MANUSCRIPT I

1

P

M

FP _ Cost = ∑∑∑ X i , p ,m ⋅ χ i ,m ⋅ PMCi , p , [BGN],

(31)

i =1 p =1 m=1

2 3

where PMC i , p are the costs for the products p manufacturing in the dairies i , [BGN/kg];

RI PT

4 5

- total costs incurred by the dairy complex for purchasing the necessary quantities of milk

6

from suppliers for the products manufacturing:

I

8

SC

7 S

FM _ Cost = ∑∑ Yi ,s ⋅ γ i ,s ⋅ MSPs , [BGN],

9

(32)

M AN U

i =1 s =1

where MSP s is the selling price of milk in the supply centers s , [BGN/kg];

10

- total costs for the transportation of the milk and products between milk supply centers,

12

dairies and markets:

TE D

11

13 I

S

I

i =1 s =1

i =1 m =1

15

17 18

where MTC

i ,s

and PTC

AC C

16

M

FT _ Cost = ∑∑ Yi , s ⋅ γ i , s ⋅ MTCi , s ⋅ SDisi , s + ∑∑ X i , p ,m ⋅ χ i ,m ⋅ PTC i ,m ⋅ MDisi ,m , [BGN], (33)

EP

14

i ,m

are the costs for transportation of milk and products between

the supply centers s , the dairies i and the markets m [BGN per kg/km];

19

- total BOD costs paid for treatment of the wastewater generated during products’

20

manufacturing:

21

22

I

P

M

i =1

p =1

m =1

FBOD _ Cost = ∑ BODcost ⋅ ∑ PBODp ⋅ ∑ X i , p ,m ⋅ χ i ,m , [BGN];

(34)

ACCEPTED MANUSCRIPT 1

- total CO2 emissions costs associated with the energy consumed by pasteurization process:

2

3

FCO2 _E_Cost =

I

P

i =1

p =1

M

∑ ECO2cost ⋅ ∑ EIPCO 2 ⋅ ∑ X p

i , p ,m

⋅ χ i ,m , [BGN];

(35)

m =1

RI PT

4 5

- total CO2 costs associated with emissions of pollutants generated during milk and product

6

transportation:

9

I S P M   FCO2 _ T _ Cost = ∑ TCO2cost ⋅  TMCO2 ⋅ ∑ Yi ,s ⋅ γ i ,s ⋅ SDisi ,s + TPCO2 ⋅ ∑∑ X i , p ,m ⋅ χ i ,m ⋅ MDisi ,m  , [BGN]. i =1 s =1 p =1 m =1  

(36)

10

12

The formulated objective function FProfit , [BGN] representing the profit of dairy complex is defined as follows:

TE D

11

13 14

FProfit = FR − ( FP _ Cost + FM _ Cost + FT _ Cost + FBOD _ Cost + FCO 2 _E_Cost + FCO 2 _ T _ Cost ) .

18

19

Objective function (38) is subjected to maximization

AC C

17

(37)

EP

15 16

M AN U

8

SC

7

MAX ( FPr ofit ).

(38)

20

The formulated optimization problem of the “green” products portfolio design for a

21

dairy complex Eqs. (1)-(38) belongs to the MINLP. It contains both binary and continuous

22

variables, sets of modeling equations and inequality constraints. The problem is solved using

23

GAMS software.

ACCEPTED MANUSCRIPT 1

3. Case Study.

2

The case study under consideration includes two dairies called by us I1 and I2. In

4

each of them two products – curd with a fat content of 0.3% (named P1) and curd with a fat

5

content of 1% (P2) have to be produced over the time horizon of one month – 720 h. The

6

dairies are supplied with whole standartized milk from two supply centers, named S1 and S2.

7

The products have to be sold in two markets, M1 and M2.

9

SC

8

3.1. Data

12

M AN U

10 11

RI PT

3

The whole milk, with 3.6% fat content is used as raw material for products manufacturing. Its composition is presented in Table 3.

13

Table 3. Composition of whole standardized milk used as raw material in two types of

15

curd production.

TE D

14

1. Water

EP

Components

AC C

2. Total solids containing:

Composition, [%] 87 13

Fat

MF*

3.6

Lactose

ML*

5

Casein

MC*

2.85

Other Proteins

MP*

0.4

Other solids

1.15

ACCEPTED MANUSCRIPT 1

Milk is skimmed producing cream with a fat content of CF = 30%. The composition of the

2

target products and the respective recovery factors for casein and of all solids of the milk are

3

shown in Table 4.

4

Table 4. Composition of target products and values of extraction factors. Product

RI PT

5

Composition of target products, [%]

Recovery factors

Casein - RC,

Moisture- Fat - PF

Casein - PC

PM

M AN U

SC

Solids-RS

Product 1 80

0.3

Product 2 81.58

1.009

6

Solids - PS

RC

RS

11.3

20

0.96

1.724

12.28

18.42

0.96

1.386

where PM and PC represents moisture and casein content of the products and RC and RS

8

are factors for the extraction of casein and solids from the products (Johnson, 2000).

9

TE D

7

Market demand and respective selling prices of products are given in Table 5.

11

Capacities of milk supply centers and the milk prices are shown in Table 6. Production costs

12

for manufacturing of the products in the first dairy are: 0.9 BGN/kg for the Product 1 and 1.1

13

BGN/kg for the Product 2. Concerning the second dairy, the production costs for products’

14

manufacturing are: 1.2 BGN/kg for Product 1 and 1.3 BGN/kg – for Product 2.

15 16 17 18

AC C

EP

10

ACCEPTED MANUSCRIPT Table 5. Demands and selling prices of the products at the markets. Demands for the

Prices of products,

products, [kg]

[BGN/kg]

Market 1

Market 2

Market 1

Market 2

Product 1

30,000

20,000

3.8

3.9

Product 2

10,000

40,000

4.2

4.6

2

Capacity,

Price of milk,

[kg]

[BGN/kg]

Supplier 1

355,000

0.6

Supplier 2

177,000

0.45

4

SC

Table 6. Capacity of supply centers and price of the milk.

M AN U

3

RI PT

1

In Table 7, distances between supply centers and dairies, and dairies and markets and

6

the respective transportation costs are presented. Thermo-isolated vehicles with capacity of

7

3.5 t are used in both dairies. The capacity of used milk tank-vehicles is 1.5 t. Transportation

8

costs are calculated making an assumption that the average consumption of the vehicles is 8.2

9

l gasoline per 100 km at average speed of 70 km/h. The price of gasoline is 2.10 BGN/l.

AC C

EP

TE D

5

10 11

Table 7. Distances between suplly centers, dairies and markets and respective

12

transportation costs. Distance, [km]

Transportation costs, [BGN/kg.km]

S1

S2

M1

M2

S1

S2

M1

M2

I1

41

36

226

92

1.722.10-4

1.722.10-4

9.84.10-5

9.84.10-5

I2

31

61

238

89

1.722.10-4

1.722.10-4

9.84.10-5

9.84.10-5

ACCEPTED MANUSCRIPT Both dairies involve equipment units of three types (N=3) divided to three processing

2

“blocks”. Their types and summarized volumes are listed in Table 8 for both dairies. To

3

formulate the portfolio feasibility constraints, the processing times have to also be known.

4

They are given in Table 1.

5

Table 8. Types of processing “blocks” and summarized volumes. Pasteurizers, [m3]

Curd vats, [m3] Drainers [m3]

Dairy 1

800

950

300

Dairy 2

950

1,050

340

M AN U

7

SC

6

RI PT

1

Concerning the curd production the acceptable eligible losses associated with the wastes

9

generated in curd production are provided in section 2.5.1. It is also known that the cost of

10

BOD paid to WWTP from the first dairy is 2.9 BGN/kg, while from the second it is 3.5

11

BGN/kg. The fixed monthly expenses of BOD treatment for each dairy i are 2,000

12

BGN/month and 3,000 BGN/month.

TE D

8

The energy consumed for heating of 1 kg skim milk EH is 0.08333 kWh/kg milk,

14

while the energy EC consumed for cooling is 0.06333 kWh/kg milk, (Maslarski & Tomova,

15

1980). The CO2 emissions associated to both processes ECO 2 is 0.46 kg CO2/kWh,

16

(Covenant of Mayors & Joint Research Centre of the European Commission, 2014). The

17

costs of CO2 ECO2cost are 0.00998 BGN/kg CO2.

AC C

18

EP

13

CO2 emissions generated during the transportation depend on the fuel used. Taking

19

into account that the energy content of 1 liter gasoline is 29.00 MJ/l, the CO2 emissions

20

produced by gasoline burning is 0.249 t CO2/MWh, (Covenant of Mayors & Joint Research

21

Centre of the European Commission, 2014) and the fuel consumption is 8.2 l/100 km at

22

average speed of 70 km/h, it is easy to calculate that the mass of CO2 emitted from vehicle

ACCEPTED MANUSCRIPT 1

per 1 km TCO 2 is 0.0164478 kg CO2/km. The CO2 cost due to transportation TCO 2 cos t is 1

2

BGN/kg CO2.

3 4

The Air Pollution Tax for manufacturing the considered products in dairy complex APT is 15,000 BGN/month.

6

RI PT

5

3.2. Results and Discussions

7

The problem solved comprises 8 binary variables; 14 continuous variables and 82

9

equality and inequality constraints. For its solution GAMS optimization software has been used taking less than 1 s solution time.

M AN U

10

SC

8

Obtained optimal monthly net profit of the dairy complex is 63,972 BGN/month. The

12

total income from the products sold on both markets is 282,936 BGN/month. Respective

13

expenses are as follows: i) for production cost – 73,147 BGN/month; ii) for raw materials –

14

124,769 BGN/month; iii) for transportation – 2,780 BGN/month; iv) for environmental cost –

15

18,266 BGN/month. Corresponding optimal “green” portfolios for both dairies are listed in

16

first two columns of Table 9. The obtained optimal feasible solution doesn’t consider the

17

manufacturing of Product 1 in Dairy 2 (mentioned with a blank space in the table), because it

18

is restricted from the imposed environmental constraints (28) and (29).

EP

AC C

19

TE D

11

For comparison the same problem is solved without consideration of the

20

environmental issues (Eqs. 30-33). In this case the used optimization criterion represents the

21

product portfolio providing maximum profit for the dairy complex:

22

23

24

F *Profit = FR − (FP _ Cost + FM _ Cost + FT _ Cost ) .

(39)

ACCEPTED MANUSCRIPT 1

Obtained optimal net profit is of 82,240 BGN/month. The latter is 22% higher than the

2

“green” portfolio. Its distribution over the dairies and products is listed in the last two

3

columns of Table 9. The difference between both portfolios is obvious.

Table 9. Optimal “green” portfolio and the optimal profit portfolio.

Optimal profit portfolio

63,972 BGN/month

82,240 BGN/month

Product 1, [kg]

Product 2, [kg]

Product 1, [kg]

Product 2, [kg]

Dairy 1 25,509

18,110

37,498

8,617

Dairy 2

21,890

6

SC

Optimal “green” portfolio

M AN U

5

RI PT

4

12,502

36,005

The obtained results for BOD related to production of 1 kg of the both products are: 0.015

8

[kg O2/ kg product] for the first product and 0.017 [kg O2/ kg product] for the second product.

9

The latter can be used for obtaining of the quantities of wastewater associated with the both

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products’ portfolios by multiplying the results listed in Table 9. The results for BOD related

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to the wastewater generated during realization of the optimal “green” portfolio and the

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optimal profit portfolio are shown in Table 10.

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Table 10. BOD related to the wastewater generated during realization of the optimal

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“green” portfolio and the optimal profit portfolio. BOD related to optimal “green” BOD related to optimal profit portfolio

1062.635, [kg O2/wastewater]

1508.574, [kg O2/wastewater]

BOD for

BOD for

BOD for

product 1, [kg

product 2, [kg

product 1, [kg

O2/wastewater]

O2/wastewater]

O2/wastewater]

Dairy 1 382.635

307.87

562.47

Dairy 2

372.13

187.53

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O2/wastewater] 146.489

612.085

The structure of the supply chain leading to the design of the optimal “green” portfolio for the dairy complex is shown in Fig. 4.

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product 2, [kg

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BOD for

One can see that the optimal “green” portfolio is associated with lower amount of BOD.

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portfolio

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Figure 4. Supply chain of dairy complex resulting in optimal “green” products’ portfolio.

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Distributions of milk from the supply centers to the dairies and also the products

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distributions from the plants to the markets are given in Figure 4. Likewise, in this Figure

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only the connections between supply centers, dairies and markets which result in a feasible

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optimal “green” portfolio for both dairies are represented. The above listed results show that the monthly demands of the second market are

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fully satisfied concerning both products while only 18.36% of the demand for the first

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product is delivered to the first market and 0% of the demand of the second product. The

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situation for the supply centers is similar. The monthly capacity of the second supplier is

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totally used by both dairies’ curd production and only 21.08% of the capacity of the first

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supplier is used.

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The obtained “green” portfolio is limited by the Air Pollution Tax, which is common

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for the entire dairy complex. In the APT of 15,000 BGN/month, 14,739 BGN/month are due

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to the energy consumed and only 261 BGN/month is due to the transportation, which is less

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than 2%. The corresponding cost for BOD reduction is 3,266 BGN/month. The fixed monthly

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expenses for BOD removal for each dairy also play a significant role in the portfolio design.

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The imposed limit value of 2,000 BGN/month for the first dairy is reached, while the

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contribution of the second dairy to the total BOD cost is only 1,266 BGN/month. The optimal

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portfolio without environmental considerations presented in Table 9 is limited by the

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portfolio feasibility constraints (18) and (19).

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4. Concluding remarks

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This paper addresses the dairy industry in Bulgaria. In it, for the first time, a new

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approach for designing a “green” products’ portfolio for a dairy sector has been proposed.

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The study takes into consideration three main subjects – products manufacturing, supply

ACCEPTED MANUSCRIPT chain management and supply chain environmental impact, which covers the wastes

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produced not only during manufacturing but also these associated with the transportation of

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raw materials and products. Three interconnected models have been created, for

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manufacturing, for supply chain designing and environmental impact assessments of wastes

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released in the air and the water. The environmental impact of the wastewaters generated in

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different processing tasks and these associated with used raw material – milk, are assessed

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using BOD as a global indicator. The CO2 emissions due to energy consumed in

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pasteurization and these which are the result of fuel combustion during the transportation are

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implemented to assess the impact on the air. The value of the Air Pollution Tax imposed on

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the dairy complex has been used to restrict the total amount of generated CO2, while

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producing of BOD is limited by the level of expenses that have to be paid from each dairy to

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the WWTPs.

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The created models have been involved in a common optimization framework along

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with economic and environmental constraints. It has been shown that the milk fat content is

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the key variable controlling the optimization process. The environmental impacts of the

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wastes generated across the designed supply chain are evaluated in terms of costs. Using

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money as a common measure between the total profit and all costs related to the economic

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and environmental performances of the supply chain provides an opportunity for the resulting

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multi-objective problem to be presented as a “single” objective one, which significantly

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facilitates the solution of such complex optimization problems.

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The proposed approach is proved on a real case study from the Bulgarian dairy

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industry. An optimal “green” portfolio has been designed for curd production to demonstrate

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the role of the environmental issues on its structure. It has been shown that the environmental

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requirements restrict the “green” portfolio. Also, it was shown that CO2 emissions highly

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contribute to the environmental costs, which is a sign for the dairy management to look into

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using alternative “green” energy for manufacture. Additionally, the same problem is solved

2

without the environmental considerations to find the portfolio with maximum profit. This

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solution is restricted by the plants’ capacities trough the feasibility constraints. Finally, the successful application of the proposed approach opens the prospective for

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extending it not only to the full spectrum of dairy products but also over the entire supply

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chain, which involves players which are in a competition with each other. It also can be

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adjusted with additional environmental indicators for assessment such as water and air

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pollutants, as well as by consideration of different types of fuel like diesel, biofuels etc. It can

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be shown how all these factors will influence the design of an optimal product portfolio. The

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latter is a subject of further investigations.

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Nomenclature

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Latin symbols APT - value of Air Pollution Tax, [BGN];

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BOD cos t - costs for BOD removal in WWTP connected with dairy, [BGN/kg BOD];

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BODCu - BOD load related to losses of curd, [kg O2/kg milk];

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BOD _ L - limit value of costs for BOD removal from dairy, [BGN];

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BODM - BOD load related to losses of skimmed or standardized milk, [kg O2/kg milk];

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BOD Pa - BOD load related to deposits on pasteurizers walls during skim milk pasteurization,

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[kg O2/kg pasteurized milk];

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BOD SM - BOD load related to losses of skimmed milk, [kg O2/kg skimmed milk];

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BOD Wh - BOD load related to spills of whey produced as by-product during discharging of

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curd vats, [kg O2/kg whey];

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BODWM - “Introduced from outside” BOD load artificially associated to processing task 1

(milk pasteurization), [kg O2/kg milk]; CF - cream fat content of standardized whole milk, [%];

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EC - energy for cooling skim milk in pasteurization process [kWh/kg skim milk];

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ECO2 - mass of CO2 emissions associated with kWh energy [kg CO2/kWh];

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ECO2 cos t - costs of CO2 emissions associated with energy consumed by heating and

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cooling processes during milk pasteurization, [BGN/kg CO2];

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EH - energy for heating skim milk during pasteurization process [kWh/kg skim milk];

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EIMCO 2 - environmental impact of CO2 emissions associated with skimmed milk produced

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from 1 kg standardized whole milk, [kg CO2/kg skimmed milk]; EIPCO 2 - environmental impact of CO2 emissions associated with manufacturing of 1 kg

ACCEPTED MANUSCRIPT product produced from a skimmed milk, [kg CO2/kg product];

1

FBOD _ Cost - total BOD costs paid for treatment of wastewater generated during product

manufacturing, [BGN];

3 4

FCO2 _E_Cost - total CO2 emissions costs associated with energy needed for realization of

pasteurization process, [BGN];

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FCO 2 _T_Cost - total CO2 costs associated with emissions of pollutants generated during milk and

products transportation, [BGN];

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FM _ Cost - total costs incurred by the dairy complex for purchasing the necessary quantities of

milk from suppliers for the products manufacturing, [BGN];

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FP _ Cost - total production costs for dairy complex, [BGN];

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FProfit - profit of dairy complex obtained after accounting for environmental costs, [BGN];

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F * Profit - profit of dairy complex obtained without taking into account environmental costs,

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[BGN];

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FR - revenue from products sale at markets, [BGN];

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FT _ Cost - total costs for transportation of milk and products between milk supply centers,

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dairies and markets, [BGN];

FDM (Fat in Dry Matter) - quality indicator for product, [%];

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H - time horizon for products manufacturing, [h];

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I - number of dairies;

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LS SM - eligible level of losses of skim milk during milk pasteurization, [%];

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LS Wh - eligible level of losses of whey during acidification and draining of produced curd,

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[%]; LS WM - eligible level of losses of whole standardized milk in pre-processing of milk, [%];

ACCEPTED MANUSCRIPT LS 2 Cu - eligible level of losses of curd during processing task 2 (acidification), [%];

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LS 3Cu - eligible level of losses of curd during processing task 3 (draining), [%];

3

M - number of markets;

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m - environmental impact indices;

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MC * - concentration of casein in standardized whole milk, [%];

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MC - concentration of casein in skim milk, [%];

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MF ∗ - concentration of fat in standardized whole milk, [%];

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MDem

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MDis - distance between dairy and market, [km];

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- product demand in market for the time horizon, [kg];

ML* - concentration of lactose in standardized whole milk, [%];

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ML - concentration of lactose in skim milk, [%];

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MP * - concentration of protein in standardized whole milk, [%];

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MP - concentration of proteins in skimmed milk, [%];

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MSP - selling price of milk in supply center, [BGN/kg];

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MSup - capacity of milk supply center, [kg];

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MTC

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N - number of equipment units;

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P - number of products;

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PBOD - environmental impact assessments for production of 1 kg product, [kg O2];

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PC - casein content of product, [%];

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PF - fat content of product, [%];

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PM - moisture content of product, [%];

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PMC - costs for products manufacturing in dairies, [BGN/kg];

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PS - solids content of product, [%];

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- transportation costs between supply centers and dairies, [BGN per kg/km];

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PSP - selling price of product at market, [BGN/kg];

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PTC

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QM - total quantity of whole standartized milk, used for dairy, [kg];

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QP - quantity of product produced in dairy, [kg];

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RC - casein recovery factor for product, [%];

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RF - milk fat recovery factor for product, [%];

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RS - solids recovery factor for product, [%];

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S - number of suppliers;

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SDis - distance between dairy and supply centers, [km];

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- transportation costs between dairies and markets, [BGN per kg/km];

SF - size factors, [m3/kg];

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T

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TCO2 - mass of CO2 emissions produced by fuel combustion, [kg CO2/ km];

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TCO2 cost - costs of CO2 emissions related to transportation of milk and products,

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TMCO 2 - mass of CO2 emissions produced by fuel combustion during milk transportation,

[kg CO2/km. kg milk];

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- processing time of product manufacturing in equipment type, [h];

[BGN/kg CO2];

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TPCO 2 - mass of CO2 emissions produced by fuel combustion during product transportation,

[kg CO2/km. kg product];

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TQ - time of processing “block” required for product manufacturing in dairy, [h];

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U - summarized volumes for units’ types in dairy, [m ];

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VCm – capacity of vehicle used for milk transportation, [kg];

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VCp - capacity of vehicle used for product transportation, [kg];

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X

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3

- continuous variable accounting quantity of product produced in dairy and sold at market, [kg];

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x - continuous variables accounting fat content of skim milk used for product

manufacturing, [%];

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x max - maximum value of fat content of used skim milk for product manufacturing, [%];

4

x min - minimal value of fat content of used skim milk for product manufacturing, [%];

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Y

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- continuous variable accounting quantity of milk bought by dairy from supply center, [kg].

YP - yield of target product, [kg].

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YP1 - yield of raw product containing residual whey, [kg].

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W - number of wastes.

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Greek Symbols

γ - binary variable structuring supply chain between supply center and dairy;

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χ - binary variable structuring supply chain between dairy and market.

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Indices

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i - for dairies;

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m - for markets;

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n – for equipment units;

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p – for products;

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s - for suppliers (milk collection centers);

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w – for wastes.

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ACCEPTED MANUSCRIPT Acronyms BGN – Bulgarian Lev;

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BOD – biochemical oxygen demand;

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GAMS - General Algebraic Modeling System;

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I1, I2 – dairy 1 and dairy 2;

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M1, M2 – market 1 and market 2;

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MINLP – mixed integer non-linear programming;

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P1, P2 – product 1, product 2;

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S1, S2 – supplier 1 and supplier 2; WWTP – wastewater treatment plant.

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References

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Carawan, R.E., Chambers, J.V. and Zal, R.R., 1979. Spinoff on dairy processing water

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Highlights 1. Approach for “green” products’ portfolio design of dairy complex is proposed.

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2. Curd production, supply chain and environmental impact models are interconnected.

3. Assessments for CO2 and wastewater produced are defined in terms of costs.

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4. Optimal “green” products portfolio and profit products’ portfolio are obtained.

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5. The “green” products portfolio is restricted by environmental consideration.