Designing and evaluating sustainable logistic networks

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Int. J. Production Economics 111 (2008) 195–208
www.elsevier.com/locate/ijpe

Designing and evaluating sustainable logistics networks
J. Quariguasi Frota NetoÃ, J.M. Bloemhof-Ruwaard,
J.A.E.E. van Nunen, E. van Heck
Rotterdam School of Management (RSM), Erasmus University, The Netherlands
Received 13 January 2006; accepted 20 October 2006
Available online 26 May 2007

Abstract

Consumers and legislation have pushed companies to re-design their logistic networks in order to mitigate negative
environmental impacts. The objective in the design of logistic networks has changed, therefore, from cost minimization
only, to cost and environmental impact minimization. The objective of this paper is to develop a framework for the design
and evaluation of sustainable logistic networks, in which profitability and environmental impacts are balanced. In this
paper, we review the main activities affecting environmental performance and cost efficiency in logistic networks, we show
the advantages of using multi-objective programming (MOP) to design sustainable networks, we present the expected
computational difficulties of using the MOP approach in the design of sustainable networks, and we introduce a technique,
based on the commonalities between data envelopment analysis (DEA) and MOP, to evaluate the efficiency of existing
logistic networks. The European pulp and paper industry will be used to illustrate our findings.
r 2007 Elsevier B.V. All rights reserved.

Keywords: Supply chain design; Sustainable supply chain; Eco-efficiency; Multi-objective programming; Data envelopment analysis

1. Introduction A number of companies have also pro-actively
acted in favor of a more sustainable development.
In recent years, consumers and governments have Their assertive approach toward the environment
been pressing companies to reduce the environ- has helped them to reap the benefits of an
mental impact of their products and processes environment-friendly image, e.g. to gain or retain
(Thierry et al., 1995). The members of the European environment-conscious consumers, to comply with
Union (EU), for instance, have committed them- the sometimes cumbersome and blurry current
selves to develop, implement and enforce legislation legislation, and to anticipate necessary changes to
that makes producers responsible for the collection, cope with future legal environmental standards.
treatment, recycling and environmentally safe dis- Among those, a group of companies has gone
posal of all electrical and electronic equipment further and achieved economic gains from the
(WEEE/2002/96/EC, 2002). adoption of environment-friendly logistic networks.
IBM, for instance, has profited from its programs
ÃCorresponding author. Tel.: +31 10 408 1781; to receive end-of-use products, promote second
fax: +31 10 408 9010.
hand items internet auctions and dismantle equip-
E-mail address: jquariguasi@rsm.nl ment as a source of spare parts (Fleischmann et al.,
(J.Quariguasi Frota Neto). 2003).

0925-5273/$ - see front matter r 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.ijpe.2006.10.014

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196 J.Quariguasi Frota Neto et al. / Int. J. Production Economics 111 (2008) 195–208

The win-win situations experienced by IBM, This paper is divided as follows: In Section 2
however, are exceptions. Only a limited number of we review the main activities affecting networks
initiatives for environment-friendly production have efficiency in terms of environmental costs. We also
proved to be profitable. Literature and practice present a framework for such networks, including a
suggests that substantial improvement in the en- non-articulated multi-objective model. Non-articu-
vironment is often only possible with substantial lated models are those in which the user or decision
investments that brings none or negative financial maker (DM) do not interact with the model in order
returns (Walley and Whitehead, 1994). As a to find most preferable solutions. For more
consequence, the focus of sustainable logistic net- information on non-articulated models see Climaco
work research and practice has swung from the et al. (1996). A short discussion on computational
search for win-win solutions to the search for results for this formulation is also carried out. In
solutions smartly compromising business and the Section 3 we provide a simple tool to evaluate
environment. Pareto efficiency, using data envelopment analysis
This paper aims to contribute to the design of (DEA) techniques and MOP. In Section 4 we
sustainable logistic networks balancing planet and present an illustrative example of the European
profit. In order to provide a first simple framework pulp and paper sector. Section 5 presents the main
for sustainable networks design, we start by conclusions.
reviewing, from the literature, the main factor
influencing sustainability in logistic networks. 2. Pareto efficiency in logistic networks in terms of
Furthermore, we discuss how the use of multi- the environment and costs
objective programming (MOP) to design sustainable
logistic networks helps to assess the trade-offs In a logistic network, a number of actors will
between the logistic network cost and its environ- influence business costs and corresponding environ-
mental impact, as well as to calculate efficiency of mental impact. Suppliers, manufactures, consumers,
existing logistic networks. We also discuss the logistic operators, as well as third parties operating
expected CPU-time difficulties regarding an MOP in testing, refurbishing, recycling and energy pro-
approach for the design of sustainable logistic duction for the end-of-life products are the main
networks. Finally, we propose our method to assess players. These players perform majority of the
efficiency of existing logistic networks. We illustrate activities impacting business and the environment.
our approach on the European pulp and paper In general terms, the activities performed in a
sector. logistic network are related to manufacturing,

Fig. 1. Framework for a sustainable logistic network. Adapted from Sheu et al. (2005).

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J.Quariguasi Frota Neto et al. / Int. J. Production Economics 111 (2008) 195–208 197

transportation, usage and end-of-life products’ maximizing profits) and minimizing environmental
destination. Fig. 1 depicts these activities. The impact. There is little done integrating these two
decisions regarding these activities will, therefore, formulations (Bloemhof-Ruwaard et al., 2004).
determine the network costs and environmental The drawbacks of such perspectives is straight-
impact. These decisions are strategic (e.g. location forward: they do not capture the trade-offs between
of factories), tactical (e.g. the destination of the logistics network costs and its respective
products end-of-life) as well as operational (e.g. environmental footprint. We propose the optimiza-
the choice of suppliers, third parties, etc.). tion of both objectives simultaneously, in order to
Furthermore, it is clear that choosing the right make it possible for DM, in logistic networks
activities in modeling specific logistic networks is with centralized control, to evaluate his choice and
crucial. The combinatorial and multi-objective select, out of a number of solutions provided by the
nature of designing sustainable logistic networks model, the one that best capture his objectives in
requires, besides smart algorithms, parsimonious terms of the environment and cost. Another
conceptual models in order to keep the problem important application is the definition of an upper
CPU-time tractable, without losing its explanatory bound for networks with multiple agents. The
power. In problems with low inverse flows, like the importance of defining and efficient frontier is
reverse logistic of cameras, the model might exclude threefold:
the decision regarding the location of manufactur-
ing plants, and leave the location-allocation pro- (1) Evaluation of the current situation in terms of
blem to the end-of-use facilities (Fleischmann, the system’s efficiency relative to environmental
2000). Table 1 presents, in broad terms, the main impact and costs. It is possible, for instance, to
activities influencing the environmental impact and calculate efficiency indexes for existing network
costs in logistic networks. configurations using DEA techniques. For
Literature into logistic network design is mostly further description of DEA see the seminal
divided in two approaches: minimizing costs (or paper of Charnes et al. (1978).
(2) Determination of the trade-offs between the
resulting environmental impact and costs in a
Table 1 logistic network.
Main activities influencing costs and environmental impact in
(3) Evaluation of the necessity of policies and
logistic networks
efficiency assessment of different legislations.
Type of factor Variables We also prove general rules for different
legislations, using the same concept of Pareto
1. Transportation 1.1. Transport from supplier to
manufacturer and vice versa
optimality.
1.2. Transport from supplier to The idea of exploring the best alternatives is
consumers and vice versa based on Pareto optimality. The Pareto-optimal
1.3. Transport from supplier to end-of- frontier is composed of the set of the images of
life facilities and vice versa all efficient solutions of the network regarding
1.3. Transport from manufacturers to
consumers and vice versa
two objectives: optimize economic and environ-
1.4. Transport from manufacturers to mental goals, like cost minimization and waste
end-of-life facilities and vice versa minimization, respectively. An MOP is denoted
1.4. Transport from consumers to end- by (Steuer and Piercy, 2005):
of-life facilities and vice versa
maxfc1 x ¼ z1 g . . . maxfck x ¼ zk g s:t.
2. Manufacturing 2.1. Manufacturing at suppliers
2.2. Manufacturing at manufacturers
fx 2 Rn jAxpb; b 2 Rm ; xX0g, (1)
3. Product use 3.1. Product use by consumers
where k is the number of objectives. A solution
4. Testing 4.1. Testing x 2 S & Rn is efficient if and only if there is no
^
5. End-of-use 5.1. Re-use x 2 S such that: ci xXci x for all i, and there is at
^
alternatives least one ci x4ci x.
^
5.2. Refurbishing
5.3. Recycling
5.4. Energy production
In our formulation, c1 x represents the environ-
mental impact of a certain solution. We assess the

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coefficients of the environment impact function via
the following three steps:

(1) Assessment of the environmental impact in each
activity. For each activity affecting the environ-
mental impact of the proposed logistic network
(i.e. transportation of 1 kg of wasted paper per
km) we calculate the associated environmental
impacts, namely: global warming, ecotoxidity,
photo-chemical oxidation, acidification,
nitrification and solid waste. The coefficients
(e.g. global warming potential (GWP) per kilo-
gram per kilometer of paper transported) are
obtained via life cycle analysis (LCA), a
Fig. 2. Pareto-optimal frontier. Adapted from Huppes and
standard technique for evaluating environmen- Ishikawa (2005).
tal impact.
(2) Normalization. The scores obtained for each
class of environmental impact are normalized
dividing them by a reference level. In our study objective. The principle of such heuristics is to
we take the larger contributor as the reference rationally explore different weights for the objective
level. functions, avoiding weight indifference regions.
(3) Weightening. We propose equal weight for each Despite the term ‘‘heuristic’’ the final subset is
of the environmental impacts. For more details composed of optimal solutions, only. We apply the
on the assessment of the proposed environmental term ‘‘heuristic’’ in this particular case to designate
index see Bloemhof et al. (1996). a non-comprehensive exploration of the subset
The assessment of the environmental footprint analyzed. The cardinality of this subset is defined
can be as well performed with different methods, by model parameters, but is obviously upper
such as Eco-Indicator99s , for instance. bounded by the number of non-dominated solutions
in an MOP formulation. An estimation for the latter
The second objective function c2 x represents the can be found in Steuer and Piercy (2005). Eq. (2)
respective total cost ðk ¼ 2Þ. Our objective is to gives the equivalent LP of Eq. (1), for problems with
explore, completely or not, the set of efficient two objective functions:
logistic network configurations. In other words, we
are interested in supply chains in which it is not minfc1 xl1 þ c2 xð1 À l1 Þg s:t.
n m
possible to decrease costs or environmental impacts fx 2 R jAxpb; b 2 R ; xX0g. ð2Þ
without a trade-off between them. Fig. 2 illustrates
the efficient frontier. For mixed linear and integer problems (e.g. decision
The Pareto frontier can be completely defined by regarding disassembly, location-allocation) not
a set of all extreme points in an MOP in a only with the frontiers will the frontier defined
formulation with two objectives. Although deter- ‘‘heuristically’’, but also the points defining the
mining these points is the only task to be performed frontier (or via approximation schemes). It is
to obtain the frontier, its accomplishment is evident that in case where the single objective
extremely CPU-time consuming. The complete problem is NP-complete, the multi-objective
exploration of all extreme efficient solutions for formulation will never be P; NPaP. The literature
large networks is intractable, even for linear models. on solving both linear and combinatorial multi-
For CPU-time processing details see Steuer (1994) objective problems is relatively scarce if compared
and Steuer and Piercy (2005). For integer (i.e. to its single objective pair. For multi-objective
location-allocation) models, computational efforts combinatorial problems, Ehrgott (2000) and Ehr-
are much higher, as expected. gott and Gandibleux (2000) present a detailed
In order to obtain a subset of efficient network review on such methods. A survey on multi-
configurations, it is possible to formulate the MOP, objective meta-heuristics is available in Hansen
for the linear case, as several problems with a single (1998) and Jones et al. (2002).

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3. Evaluating Pareto efficiency in logistic networks efficient in DEA terms (the same does not hold with
combinatorial problems). After this step, we calcu-
Intuitively, we can think of the efficient solutions late efficiency based on the efficient measure
explored in the last section as benchmarks for proposed by Cooper et al. (1999). We use the
existing logistic networks. Comparing the mapped projection of Cooper et al. (1999) due to the fact
environmental impact and costs of the current that it provides a more robust measure when
configuration to the theoretical optimal provides compared to the traditional radial projection as
an indicator of efficiency in the existing logistic proposed by Charnes et al. (1978). The projection
network. If the actual environmental impact and we use avoids projections in Pareto-inefficient
costs are close to the frontier, for instance, there will parts of the frontier, providing a measure that
be no need for configuration changes. Furthermore, assess the inefficiency of all dimensions at analysis
it is possible to give a measure of efficiency for (in our case environmental impact and logistic
existing networks. In order to do so, we need the network costs).
following lemmas: It is also possible to explore other projections
for such problems, allowing the DM to more
^
Lemma 1. Each image of an efficient x solution in (1) freely explore the efficient frontier. For interactive
ðc1 x1 ; . . . ; ck xk Þ is an efficient Decision Making Unit
^ ^
and non-articulated methods for finding radial
(DMU) in a DEA problem with DMUs projections see Halme et al. (1999), Quari-
ðc1 x1 ; . . . ; ck xk Þ for x 2 S & Rn in (1).
^ ^ guasi Frota Neto and Angulo-Meza (2007), Tha-
Proof. For a problem with a continuous set of nassoulis and Dyson (1992) and Zhu (1996).
images of efficient solutions, the linear convex Furthermore, it is easy to see that every non-radial
combinations of these images also map a real projection in the DEA formulation maps a real
solution in the original problem. In that case, once solution in the original logistic network. For
the convex combinations are part of the images of mixed-integer problems, the set of unsupported
the solution set for the problem at question, the efficient solutions are not efficient in a DEA
posterior addition of such solutions will not perspective, as proved in Lemma 2. In this case,
dominate any previously existing non-dominated we say that the solution is Pareto-efficient iff it is
solution. Once no convex combination will result in not dominated by any other solution provided by
a solution that dominates the original non-domi- the mixed-integer formulation. This can be done,
nated set, the efficient solutions will map efficient in polynomial time on the number of solutions,
DMUs in a DEA problem. & via simple pairwise comparison between the solu-
tion being tested and all the efficient (supported
^
Lemma 2. Every image of an efficient x solution in and non-supported) solutions of the multi-objective
(1) ðc1 x1 ; . . . ; ck xk Þ is an efficient DMU in a DEA
^ ^ mixed-integer problem. A measure for ineffi-
problem with DMUs ðc1 x1 ; . . . ; ck xk Þ for x 2 S & Rn
^ ^ ciency for combinatorial MOP is, as far as we
in (1), in case we require x 2 S & Z n , iff x is also
^ know, not available in the literature. The minimal
supported distance necessary to bring the inefficient point
Proof. For non-supported solutions, there exists at into the non-dominated set would be an alternative.
least two supported solutions that makes the non- We propose the following mixed and non-linear
supported solution inefficient in DEA terms. For formulation:
supported solutions, no convex combination of qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
other supported solutions dominates it. & min d2 þ d2 ;
1 2

s:t: ða À d1 À aj Þo0 or (3)
For an in-depth discussion of such properties
of DEA and MOP, see Korhonen et al. (2003). We ðb À d2 À bj Þo0 8ðaj ; bj Þ 2 ND;
first formalize our approach, for linear models
(allocation) and then extend for mixed-integer where ða; bÞ is the point at analysis, ND is the set of
models. all non-dominated points for the mixed-linear
We map every image of the non-dominated formulation, and d1 and d2 are the minimum
solutions as an efficient DMU of a DEA formula- necessary reductions in, respectively, environmental
tion, using Lemma 1. Once the problem is linear, all impact and costs, to eliminate inefficiency. In order
efficient solutions are supported, and are, therefore, to eliminate the quadratic and logical terms, we

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reformulate as follows: More precisely, the convex combinations not
only do not provide the efficient frontier in
min y
Pareto terms, but also do not map real net-
s:t: works. The concept of frontier may therefore be
d ja ða À d1 À aj Þ þ d jb ðb À d2 À bj Þo0 8ðaj ; bj Þ 2 ND relaxed and efficiency tested in terms of dom-
inance with the solutions of the mixed-linear
d ja þ d jb ¼ 1 8ðaj ; bj Þ 2 ND
multi-objective formulation. In the case of non-
d1 b À d2 a ¼ 0 exhaustive exploration of the efficient solutions,
d1 b À y ¼ 0 the frontier is an upper bound of the real
d ja ; d jb 2 f0; 1g 8ðaj ; bj Þ 2 ND: efficient frontier, and its closeness to the real
theoretical frontier will depend on the number
(4) of non-dominated vertexes explored.
The new variables d ja and d jb
are dummies intro- (2) Calculate the efficiency of the logistic network.
duced to eliminate the logic constraints. Note that The current situation is bound by the efficient
now the model search for the minimal necessary frontier and is a convex combination of the
equi-proportional reduction of ða; bÞ for eliminating efficient points or an inefficient DMU in DEA
dominance. The optimization and evaluation of the terms. It is possible, furthermore, to evaluate the
sustainable logistic networks, as illustrated in Fig. 3, efficiency of the current situation through
can be summarized in the following steps: standard DEA techniques for end-of-use deci-
sions and allocation problems. For location-
allocation problems we need a new metric, as
(1) Explore, partially or completely, non-dominated
presented before, such as the minimal equi-
points of the logistic network. When completely
proportional reduction of environmental impact
exploring the extreme efficient solutions in a
and costs to bring the dominated point into the
linear models, it is possible to construct a convex
non-dominated set.
piecewise linear frontier. For mixed-integer
(3) Assess the efficiency of a specific mandatory
models, the frontier is likely to be no longer
legislation by its capacity of locking-out envir-
convex, as presented before, and cannot be
onmentally harmful solutions, without deterior-
explored via the standard DEA techniques.
ating the proposed frontier, and evaluate the
impact of a market-based legislation. In some
cases, it may be possible to improve the efficient
frontier, providing cheaper and more environ-
ment-friendly solutions, as well as locking out
harmful environment logistic network con-
figurations, through adequate market-based
legislation.

In the next section we illustrate the use of the
proposed methodology to optimize the logistic
networks in terms of the environment and costs,
as well as the efficiency of the current one, and the
impact of mandatory legislation.

4. The European paper and pulp sector case study

In order to illustrate the concepts presented in
the last sections we take the European pulp and
paper industry as a case study. The sector has
significant impact in both environment and business
Fig. 3. Steps to calculate the Pareto-efficient frontier and to for the EU. For Scandinavian countries, for
assess eco-efficiency in sustainable logistic networks, as well as to instance, it corresponds to a significant part of the
evaluate environmental legislation. industrial activity and generates a considerable

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portion of the GDP. In Finland, the forest sector the efficient frontier, and from that, as presented in
represents 7% of the GDP and approximately one- Section 2:
fifth of industrial production in the country (FFI-
Association, 2006). For the environment, the Provide an upper bound for a system from a
impacts are also significant and they appear in game theoretical perspective. Modeling environ-
different parts of the life cycle: forest management, mental legislation is an example of a bi-level
pulp production, pulp bleaching, paper consump- game: the government creates legislation to
tion, waste management and transportation mitigate environmental impact, without dama-
(Bloemhof et al., 1996). The magnitude of waste ging the economy, while companies adapt to such
paper produced is impressive: in Europe, waste legislation—working to minimize the associated
paper responds for 35% of the total waste by additional costs. For the European Govern-
volume (Buwal, 1991). ments, for example, the efficient frontier provides
We describe the re-organization of the European insights on the best alternatives for the used
pulp and paper logistic network as a multi-objective paper. Presently, such decisions are highly biased
linear problem, with the network cost and environ- by the economic interests of the members, as well
mental impact objectives to be optimized. We as by the belief that some (supposedly) environ-
consider facility locations as fixed, which lead us ment-friendly alternatives should be preferred.
to a problem of allocation and end-of-use decision. Scandinavia advocates that the production of
This formulation can be extended to include facility clean virgin pulp is both environmentally and
allocation decisions. For an operational perspective, economically preferable over recycling. France
however, it is reasonable to assume that the location favors incineration, while Germany goes for
of energy generation plants, paper recycling or recycling (Bloemhof et al., 1996). An example
paper production will not change in a short period of applications of Game Theory in Legislation is
of time. found in Amouzegar and Moshirvaziri (1999).
The model divides the EU in six regions: Determine the cost of decreasing environmental
Scandinavia, Germany, France, UK, Italy and impact for the pulp and paper sector. This is key
Iberia (Portugal and Spain). These six regions are information for DMs in private and public
responsible for 80% of the paper consumption and sectors. For governments, this particular infor-
production in the EU. In order to assess ecological mation is useful as an input for decisions
impact we use the environment index proposed regarding subsidizing or taxing activities (e.g.
proposed in Bloemhof et al. (1996). The index uses incineration, transport or recycling) of the
LCA, considering the diverse emissions in the logistic network, for instance. In cases where
supply chain regarding the pulp and paper sector, the environmental improvements come at a low
namely global warming, human toxicity, ecotoxi- cost, subsidizing clean logistic networks is
city, photochemical oxidation, acidification, nitrifi- recommended. In cases where decreasing envir-
cation and solid waste, and provides a single onmental impact comes at a high cost, taxation
weighted measure for environmental impact for and investment in other sectors may be more
each phase of the supply chain. The economic appealing.
objective function is the sum of the cost of the Determine the efficiency of the sector relative to
following activities: transportation, production, the environment and costs. The efficiency will tell
recycling and incineration. Data from environmen- us how much the system can be improved with
tal impact is directly taken from Bloemhof et al. initiatives integrating and directing the players
(1996). We also use secondary data for the costs within the logistic network. This re-design of the
from production, recycling and incineration of logistic network can happen directly, by a self re-
paper (FFI-Association, 2006). organization of the players (in that case, con-
The logistic network we describe has multiple sidering cooperative players), as well as indirectly
agents: producers, consumers, third parties working via a leader, from a game theoretical perspective.
on recycling, incineration and energy generation. For example, governments may take the role of a
At a higher level, governments can also be leader—projecting the actual inefficient system to
considered players, for their role in legislation. We the frontier via legislation.
model the system, however, for a centralized control Determine ‘‘optimal’’ configurations for the
perspective. This approach allows us to explore European pulp and paper sector. The results

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provide a clear guideline for the configurations of Table 2
production, transport and end-of-use destination Variables for the European pulp and paper model
for paper. Indexesa
i; j; k 2 I ¼ Indices for the six regions
The multi-objective formulation for the European v2V ¼ Index for the four virgin pulp types
pulp and paper sector is presented in Tables 2 and 3. p2P¼ Index for the seven paper types

Objective (3) minimizes environmental impact of Decision variables:
virgin pulp (both in Europe and North America), VPiv Virgin pulp production of type v in region i
VTijv Virgin pulp transport type v, from region i to
recycled pulp production, waste paper incineration, region j
and transport. Objective (4) minimizes the costs for VDiv Virgin pulp demand in region i of type v
the same activities. Constraints (5) are the capacity RPi Recycled pulp production in region i
constrains for wood pulp. Constraints (6) and (7) PDi Recycled pulp demand in region i
PTijp Paper transport of paper p, from region i to region j
define flow conditions for virgin pulp and recycled WTij Waste paper transport, from region i to region j
pulp. Constraint (8) defines the allowable share of WIi Waste paper incinerated in region i
recycled pulp in order to satisfy conditions for paper WPi Waste paper ‘‘production’’ for recycling in region i
types. Constraint (9) defines the allowable share of WDi Waste paper demand for recycling in region i
Lip Share of recycled pulp in furnish of paper type p in
recycled pulp in order to satisfy conditions for paper region i
types. Constraint (10) represents the natural bound
Exogenous variables
on the share of recycled pulp in the overall
vsi Virgin pulp wood supply in region i
furnishing of paper products. Constraint (11) ppip Paper production of type p in region i
defines flow condition for paper. Constraint (12) pdip Paper demand for paper type p in region i
defines the destination of collected waste paper to be wsi Waste paper supply for recycling or incineration to
either incineration or recycling. Constraint (13) non EU-countries
peip Paper import from non-EU countries to region i
defines flow conditions for waste paper. Constraint
(14) considers the yield from waste paper for Other parameters
recycled pulp. Constraints (4) and (6) allow us to eviv Environmental impact of virgin pulp production of
type v in region i
represent all paper produced in one variable. eri Environmentalimpact of recycled pulp production
Constraint (7) uses the same rationale to reduce in region i
the number of technologies used for virgin pulp eii Environmental impact of incineration of waste
paper in region i
processing. Fig. 4 represents the network flow for
etij Environmental impact of transport from region i to
one European region. For the paper and pulp sector region j
we assume that: rp Total share of pulp in the inputs of paper type p
(yield of paper from pulp)
mvp Furnish rate of virgin pulp type v wrt to total virgin
The production and consumption of paper is
pulp share in paper product p
constant. This implies that the virgin and lmax
p Maximum share of recycled pulp in the furnish of
recycling pulp demand, as well as the waste paper type p
generation are maintained in the actual levels. dp Long-term consumption rate for paper type p
sp Sewage rate of waste paper for paper type p
The production of virgin pulp making is limited
yip Collection rate of waste paper originating from
by the capacity installed in each region. Further- paper type p in region i
more, the formulation does not allow increase of w Estimated fiber yield of waste paper
capacity. Economic parameters
The proportion of paper produced newsprint cviv Production cost of virgin pulp production of type v
14%, printing quality paper 36%, liner 12%, in region i
fluting 9%, boxboard 9%, household 5% and cri Productioncost of recycled pulp in region i
cii Costs of incineration of waste paper in region i
others 15% is fixed. ctij Transport cost from region i to region j
The proportion of virgin pulp production tech-
Waste paper supply for either recycling or incineration i is defined as
nology (sulphate bleach, sulphate unbleach, follows:
sulphite bleach and TMP bleach) used is fixed. P
wsi ¼ p2P ð1 À lp Þð1 À sp Þ Ã yip Ã pdip
The proportion between the actual use of
a
recycled fiber and its maximum value is The set I þ :¼I [ NA relates to the OECD-Europe regions plus
North America.
equal for each paper. The bigger the maximum
of recycled pulp allowed (this is a technical

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Table 3
Mathematical formulation for the European pulp and paper model
!#
P P P P P P PP P (3)
min eviv VPiv þ eri RPi þ eii WIi þ etij VTijv þ etij PTijp þ WTij
v2V i2I i2I i2I þ j2I v2V i2I j2J p2P
!#
P P P P P P PP P (4)
min cviv VPiv þ cri RPi þ cii WIi þ ctij VTijv þ ctij PTijp þ WTij
v2V i2I i2I i2I þ j2I v2V i2I j2J p2P
P
s:t: VPiv pvsi ; 8i 2 I (5)
v2V
P P
VTijv þ VPjv ¼ VDjv þ VTjkv ; 8j 2 I; v 2 V (6)
iaj2I þ iaj2I
RPj ¼ DRj ; 8j 2 IV (7)
P
VDiv ¼ mvp ð1 À Lip Þ Ã rp Ã ppip 8i 2 I; v 2 V (8)
p2P
P
RDi ¼ Lip Ã rp Ã ppip ; 8i 2 I (9)
p2P
Lip plmax
p 8i 2 I; p 2 P (10)
P P
pijp þ PTijp þ ppjp ¼ pdjp þ PTjkp þ pejp ; 8j 2 I; p 2 P (11)
i2I;iaj k2I;kaj
wsi ¼ WIi þ WPi ; 8i 2 I
P P (12)
WTij þ WPj ¼ WDj þ WTjk ; 8j 2 I (13)
i2I;iaj k2I;kaj
RPi ¼ w Â WDi ; 8i 2 I (14)

Fig. 4. Network ﬂow model for the European pulp and paper model.

restriction: papers such as printing accept a The decision variables for the problem are there-
maximum of 50% recycling pulp), the bigger fore: the transportation of virgin pulp, paper and
the proportion in relation to the overall recycled waste paper among the six described regions, the
pulp used. import and export of, respectively, pulp and paper
The network ﬂow conditions involving virgin and from outside EU, and the destination of the end-of-
recycled pulp, paper and waste should be use paper.
respected. Furthermore, we consider that there We understand that the problem is more complex
is no transport of recycled pulp. than is portrayed in the paper, but as said,

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assumptions presented can be relaxed. The reason dominated by virgin pulp production associated
for such simplification is that we are more interested with incineration. Despite the common belief that
in showing an application of the proposed metho- recycling is always cleaner, solutions with high
dology than provide results for decision making in recycling proportions are not always more environ-
such industry. We believe that the illustrative model ment-friendly for the particular case of the Eur-
works properly for that purpose. opean pulp and paper sector. The positive marginal
environmental impact of incineration for energy
5. Results generation, if compared to fuel fossil energy
generation, as well as the carbon emission from
We first analyze the efficient frontier for the the transportation of wasted paper from the
European pulp and paper sector in order to consumption centers to the recycling facilities
determine the theoretical trade-offs between envir- explains such results. Recycling is, on the other
onmental impact and costs, as described in Section hand, present in the lower costs configurations.
2. Furthermore, we use the frontier to find a Mandatory recycling quotas, therefore, may bring
measure of efficiency for the actual logistic network, no positive results for the environment.
as described in Section 3. Figs. 5–7 show three efficient configurations for
The minimization of costs gives a total cost of the European pulp and paper sector, and their
approximately 60% the cost for the configuration respective environmental impact and costs. Note
with minimum environmental impact. On the other that, although they do not differ much in terms
hand, the environmental impact for the logistic of the environment and cost results, they present
network with minimum cost is 90% higher than the quite different configurations. The solution with
minimum feasible environmental impact. Note that lowest costs has no incineration, and significant
the objective function values, in percentage terms, flows of wasted paper, besides the expected flow of
differ much among the efficient solutions, despite new paper from the Scandinavian countries to the
the impact of transportation, which is simulta- rest of Europe. The solution with the highest cost is
neously optimized for both objectives. Another a mix between virgin pulp utilization, incineration
interesting observation is that the parts of the side and recycling. Also, there is no flow of wasted
of the frontier which maps the costly solutions, are paper. An intermediate solution presents both

Fig. 5. Configuration of the logistic network for minimum environmental impact. Volumes are represented in 1000 t.

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Fig. 6. Configuration of the logistic network compromising environmental impact and costs. Volumes are represented in 1000 t.

Fig. 7. Configuration of the logistic network with maximum environmental impact. Volumes are represented in 1000 t.

incineration and recycling, but no flow of wasted In order to calculate the network efficiency, we
paper. There are also flows of paper from Scandi- use the measure of inefficiency proportions (MIP)
navia to the rest of Europe and virgin pulp to proposed in Cooper et al. (1999). The logistic
Germany. network measure of inefficiency is equal to 0.24,

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which mean that an weighted average of 24% and incorporates all inefficiencies in the model.
improvement in the environmental impact and costs Figs. 8 and 9 show, respectively, the two projections.
in the logistic network is necessary to reach The efficiency calculation and the optimization
efficiency. Note that we do not use radial projection, phase, are modeled as linear systems, and therefore
despite the easier interpretation of results, due to the performed in polynomial time. CPU-time is negli-
risk of projecting in inefficient parts of the frontier. gible for both problems, the assessment of the
This is a well-known problem in the literature, and efficient frontier and the calculation of the efficiency
occurs for the data of this specific study case. of the existing logistic network configuration.
Furthermore, the model proposed by Cooper et al. We also analyze the impact of legislation on the
(1999) gives a single real value as efficiency measure efficient frontier. We explore four scenarios: in the

Fig. 8. Radial projection for the European pulp and paper industry.

Fig. 9. Cooper et al. (1999) projections for the European pulp and paper industry.

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Fig. 10. Pareto-optimal frontier for the European pulp and paper industry with mandatory legislation.

first scenario we have no mandatory recycling. The recycling are examples of initiatives to reduce
second scenario is the 20% mandatory recycling environmental impact in logistic networks. Unfor-
scenario for the members of the EU. Here we tunately, win-win solutions for the environment and
suppose that the parliament decides to, based on the business are very elusive in practice.
actual directives for wasted paper, to mandate The adoption of cleaner solutions is generally
this percentage of recycled pulp. We expand our bounded by an increase in costs. Companies aiming
analysis for the 50% scenario. We also analyze the to decrease the environmental impact of their
result of 100% mandatory recycling legislation in logistic networks should, then, look for good
Germany. trade-offs between environmental impact and costs.
The Pareto optimal configuration, including the The game is, therefore, smartly compromising the
scenarios, is presented in Fig. 10. Note that two P’s: Planet and Profit. The same rationale is
mandatory policies for recycling may deteriorate true for governments: effective legislation should
the Pareto-optimal frontier. It is also worth to take into consideration specific trade-offs of the
highlight that environment-friendly scenarios were logistic network in question, as well as the efficiency
locked out, instead of the expected effect to lock out of the existing logistic network.
unfriendly ones. In this paper we review the main family of
The adoption of mandatory legislation for 20% activities influencing the environment and costs in
of recycled pulp does not highly deteriorate the logistic network, namely: transportation, manufac-
Pareto-efficient frontier, but locks-out environment- turing, product use, testing and end-of-use alter-
friendly alternatives. The effect of 50% use of natives. Furthermore, we present a framework for
recycled pulp in the EU and 100% in Germany is optimizing the design of efficient logistic networks,
similar: locking-out environment-friendly alterna- based on multi-objective programming (MOP), in
tives and deteriorate the Pareto frontier. terms of the environment and costs. We also discuss
the expected computational challenges of such
6. Conclusions approach for the design of sustainable logistic
networks. Applications and further developments
The concern of consumers, companies and of such frontier are also discussed.
governments with the environment has steadily In addition, we introduce a new methodology to
increased in the last years. Cleaner process, re-use evaluate efficiency in logistic networks, based on the
of products and components, re-manufacturing and properties shared by MOP and data envelopment

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analysis. We also pinpoint the main mathematical Ehrgott, M., Gandibleux, X., 2000. An annoted bibliography on
characteristics of such an efficiency indicator. The multiobjective combinatorial optimization. Technical Report,
indicator tells the decision maker, in companies, Report in Wirtschaftsmathematik.
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environmental legislation. Ph.D. Thesis, Erasmus University.
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background for presenting the methodologies pro- Integrating closed-loop supply chains and spare-parts man-
agement at IBM. Interfaces 33 (6), 44–56.
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for such sector, as well as the trade-offs between the A value efficiency approach to incorporating preference
environment and costs. Furthermore, we show that information in data envelopment analysis. Management
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lock out bad environmental solutions, and will Hansen, M.P., 1998. Metaheuristics for multiple objective
combinatorial optimization (working paper). Technical Re-
deteriorate the efficiency of the sector in terms of the port, Technical University of Denmark, Denmark.
environment and business. We also show that the Huppes, G., Ishikawa, M., 2005. A framework for quantified eco-
actual system has space for win-win gains. The re- efficiency analysis. Journal of Industrial Ecology 9 (4), 25–41.
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