International Conference
on Industrial Engineering and Systems Management
IESM’ 2009
May 13 - 15, 2009
MONTREAL - CANADA
The reduction of greenhouse gas emissions from freight
transport by merging supply chains
Shenle PAN1, 2, Eric BALLOT1, Frédéric FONTANE2
1
2
MINES ParisTech, CGS- Centre de gestion scientifique,
60 Bd St Michel 75272 Paris Cedex 06, France
MINES ParisTech, CAOR- Centre de CAO-Robotique, Mathématiques et Systèmes
60 Bd St Michel 75272 Paris Cedex 06, France
Abstract
It is well known that freight consolidation is an effective way to improve the utilization of logistics resources. In fact, at
present this policy is locally and fragmentally implemented at the operational level as it depends on the opportunities taken
by carriers to consolidate freight. In this paper logistical mutualisation at the strategic level (merging supply chains) will be
explored from the environmental point of view. With real data offered by two main French retail chains and through an
optimization model, we are able to estimate the effect on reducing CO2 emissions by merging supply chains. In addition, two
transport modes, road and rail, are the considered in this paper. As regards the general dependency of the emissions produced
by the modes of conveyance on their loads, the emission functions of the two modes are both piecewise linear and
discontinuous functions. Therefore, by nature it is a MIP problem. The conclusions arrived at in this paper show that the
logistical mutualisation proposed in this work is an efficient approach to reducing CO2 emissions. At the same time, rail
transport is an aspect that should be taken into account as well in achieving this objective due to its outstanding performance
in terms of CO2 emissions in some countries.
Key words: Transportation, Merging supply chains, CO2 Emissions, Mixed Integer Programming, Piecewise Linear Function.
1
Introduction
In a context of a global economy and fierce competition, companies made intense use of transport to cope with
the demands from their customers. On the other hand, it is well known that the climate change problem and the
increasing price of energy have garnered worldwide attention over the past decades. As a significant source of
greenhouse gas (GHG) emissions, the transport sector is naturally concerned by global warming. As a result,
improving transport efficiency is among the foremost concerns of supply chain management (SCM) initiatives.
Several studies show that today the lack of satisfaction regarding transport efficiency is based both on the use of
vehicles and on greenhouse gas emissions, see [18, 20, 21]. From this standpoint, the consolidation of shipments
was put forward and has been recently studied in several publications, see [3, 4, 9, 22]; and it has been shown
that freight consolidation may be an efficient way to achieve lower costs and reduce inventories. In fact, at
present this policy is locally and fragmentally implemented at the operational level by using a 3PL for example
because it depends on the opportunities available to carriers to consolidate freight. As shown in [18, 20], despite
the contribution of consolidation, the mean load factor of road transport is about 70% in general, which is
consistent with the result of our data [2]. Thus, new approaches in logistical organization are called for.
Furthermore, the achievement of economies of scale that are profitable for both suppliers and retail chains
requires closer and longer term collaboration, see [11]. A new concept in this same area, the mutualisation of
IESM 2009, MONTREAL – CANADA, May 13 - 15
freight consolidation between supply chains, namely merging supply chains, will be studied in this paper at the
strategic level. As regards sustainable development, this paper aims to evaluate the effect of this mutualisation
on reducing GHG emissions, especially CO2 emissions. The new objective of reducing CO2 emissions by
optimizing the supply chain has not yet been widely studied in logistics. Currently, much more attention is paid
to new fuel economy technologies applied to vehicles to reduce the environmental impact of freight transport.
Nevertheless, concern by the freight transport sector should justifiably have been warranted. In the next part of
our paper, we will take a look at the merging of two large retail chains’ supply chains in France. This second part
will be followed by part 3 that details the preparation of data for the optimization model. Part 4 of the paper
outlines the results and associated analyses with the conclusions following in the last part.
2
2.1
Methodology
Merging retail chains in France
This project was developed in collaboration with a French association called Club Déméter (www.clubdemeter.fr) that provided us with all the data for our research. This support guarantees that the database we
worked on was indeed in agreement with the real network flow of some of the companies in the association. The
data mainly consists of the flow of goods of two major French retail chains in the first 12 weeks of 2006, and
also of the geographic location of both distribution centres of the two retail chains and the warehouses of their
common suppliers. Based on the database offered, we propose that the merging of two supply chains can be
achieved as follows.
WH of
Supplier i
WH of
Supplier j
WH of
Supplier k
DC of
Retailer m
DC of
Retailer n
DC of
Retailer l
After merging
WH of
Supplier i
WH of Supplier j
/ Upstream hub
WH of
Supplier k
DC of
Retailer m
DC of Retailer n
/ Downstream hub
DC of
Retailer l
Direct flows (before merging)
Upstream flows
Midstream flows
Downstream flows
Fig. 1. Example of the merging supply chains
As illustrated in Fig. 1, originally the flows from the suppliers’ (i, j and k) warehouse or plant (WH) are directly
shipped to retailers’ (m, n and l) distribution centres (DC). To achieve the merging of the supply chains, we
create two kinds of hub in this network, an upstream hub and a downstream hub. Further, two assumptions are
made to simplify the problem: (1) the hubs are respectively among the set of WH or DC in the database; (2)
goods are allowed to be transported from WH to DC directly or to be consolidated at upstream hubs,
downstream hubs or both. Hence, the merged network here is a three-echelon hub network, with the upstream
path between WH and the upstream hub, the midstream path between the upstream hub and the downstream path
between the downstream hub and DC. More details are discussed in the formulation section. The possibility of
reducing CO2 emissions obviously depends on the consolidation of a mass of flows that will be shipped together
between the different supply chains in order to increase the truck load factor of each shipment.
IESM 2009, MONTREAL – CANADA, May 13 - 15
2.2
Construction of the database
The database mentioned above consists of a large number of diverse goods’ flows (several thousands lines in
Excel) concerning the most important 106 common suppliers of the two French retail chains. Initially, to be able
to identically analyze the flows, they are all measured in number of pallets. This means that the flows are
converted into quantities of equivalent full pallets.
First the flows are subdivided into three classes according to the different types of products involved: CARE
(pharmaceuticals, cosmetics/perfume and hygiene), GRO (grocery) and LIQ (liquids). The main reason for this
subdivision is that these classes of product require different handling through the transportation due to their
varying logistic behaviour. For example, a warehouse for liquid products will not have the same construction
features as that for cosmetics. This classification in the French supply chains is maintained in this paper.
According to the first study of this project [2] using the same data, it was shown that mixing flows with very
different sizes should be avoided. Moreover, after the classification of products, the suppliers’ warehouses in
each class are divided into three groups based on the size of flows in the warehouse, since the flows of each
warehouse (even of the same supplier) are independently dealt with in our case. In order to obtain a balanced
amount of variables in each group, the boundaries of the groups are respectively 0-200, 200-600 and >600
pallet/week. Note that the flow per week involved here is an average of the flows covering the 12 week period
studied. This decomposition doesn’t exactly follow the real volume breakdown, but help the optimization
process. It could be seen as a limitation of this work. Finally the initial problem is broken down into 9 subproblems in which the number of suppliers is showed in table 1.
Table 1
The number of warehouses (or plants) in each group under classification
CARE
GRO
LIQ
Group pal<200
8
25
21
Group pal=200-600
9
29
25
Group pal>600
13
27
34
As mentioned above, the procedure of classification and grouping to reduce the extent of the problem, which
also determines the framework of the database, is important to decrease the computational time of an
optimization model presented in next part.
3
Problem formulation
To be able to calculate and minimize CO2 emissions from freight transport, we must first define an emission
function according to mode of transport, as well as an optimization model.
3.1
Emission functions
Two modes of transport, road and rail, are taken into account in this research. The emission function of their
mode of transportation is based on several reports in this field, e.g. the MEET report [12, 15] and the COST 319
project [16]. Furthermore, CO2 emissions factors in France applied to these functions can be found in some
reports of the ADEME (Agency of Environment and Energy Management in France: www.ademe.fr), see [8, 14,
21]. In these reports, CO2 emissions are as a rule measured in terms of ton-km freight transported, which is also
adopted in our case, but the ton-km is changed into pallet-km due to the form of the database. In this section, we
simply indicate the final formulas to calculate emissions that are applied to the optimization model.
3.1.1
Road transport emissions
First of all, the mode of road transport here refers to transport by HDV truck only (32-40 ton for general
merchandise). According to the emission function for the truck given by [12, 14], some assumptions are made:
(a) The average speed is 80 km/h; (b) The gradient of a road is not taken into account; (c) In general the truck
IESM 2009, MONTREAL – CANADA, May 13 - 15
considered here is fully loaded with 25 tons for weight or 33 pallets for volume. Particularly, for the care and
grocery classes, it is assumed that the truck is fully loaded at the same time by weight and volume (33 pallets
weighting 25 tons). However for the liquid class which is doubtless heavier than the others, the truck is fully
loaded only with 23 pallets weighing 25 tons. As a result, the final CO2 emission function with the variable of
load is:
(1)
where:
: is the CO2 emissions from a vehicle in kg/km with the variable of load x in pallet;
: is the CO2 emissions of a fully loaded (by weight) vehicle, which is
: is the CO2 emissions of an empty vehicle, which is
= 1.096 kg/km for HDV truck;
= 0.772 kg/km for HDV truck;
c: is the volume capacity of a vehicle; as said above, which is 33 pallet/vehicle for the care and grocery classes
and 23 pallet/vehicle for the liquid class.
3.1.2
Rail transport emissions
According to the data from Fret SNCF (www.fret.sncf.com), 90% of the freight train locomotives in France are
electrically driven, thus only the eclectically powered locomotive is considered here. The emission of air
pollutant related to rail transport is calculated in two steps. The first step is the estimation of the energy
consumption of a train in KJ per ton-km, which is required to move the train. After this step, the amount of
emissions can be calculated according to the energy required. Consequently, the pollutant emission function
related to energy consumption is as follows:
(2)
where:
Ei: is the total emission of air pollutant i in kg;
WSEC: is the weight specific energy consumption of the train in KJ/ton-km;
Tkm: is the amount of freight transported by the train in ton-km;
Tpt: is the load factor of the train, in ton-km/total train ton;
BSEFi: is the brake specific emission factor in g/kWh of energy produced.
Formula (2) which is corrected and validated by the main author of the MEET report [15] is the general form of
calculation of air pollutant emissions. In this study, we focus on CO2 emissions as the most representative of the
emissions of electricity production. In France, according to the report of the ADEME [14], the BSEFco2 of EDF
in 2007 was 42 g/kWh. Some assumptions are also made here to simplifier the problem: (a) The average speed is
100 km/h; (b) The mean distance between stops is 100 km; (c) A train is composed of 13 wagons which is the
minimum actual size for chartering a half full train; (d) Because of the large weight capacity of the wagon (56
ton/wagon), a wagon is only fully loaded by a volume equivalent to 36 pallets. The assumption (c) and (d) imply
that the volume capacity of train here is 468 pallet/train. Similar to formula (1), formula (3) given below is used
to calculate CO2 emissions from rail transport.
(3)
where:
: is the CO2 emissions from a train in kg/km with the variable of load x in pallet;
: is the CO2 emissions of a fully loaded (by volume) train, which is
classes and
= 0.96 kg/km for the care and grocery
= 1.16 kg/km for the liquid class;
: is the CO2 emissions of an empty train, which is
= 0.498kg/km;
c : is the volume capacity of a train; as said above, which is c = 468 pallet/train.
IESM 2009, MONTREAL – CANADA, May 13 - 15
To compare the CO2 emissions of these two transport modes, illustrated in Fig.2, it is assumed that one pallet
weighs one ton, which means that the ton-km and pallet-km units are now equivalent. The conclusion, here very
favourable to rail transport, should be considered with respect to the source of production of electricity that emits
very little CO2/kWh in France.
Fig. 2. Comparison of CO2 emissions between road and rail transport
Due to the upper integer part of x/c, functions (1) and (3) are in fact piecewise linear and discontinuous
functions. That is also the foundation of the optimization model, which will be presented in the next section.
3.2
Optimization model
Since the purpose of our optimization project is to minimize the CO2 emissions related to freight transport in two
large supply chains, the emission functions are adopted in the optimization model via an objective function. The
discontinuity of the functions results in a Mixed Integer Linear Programming (MILP) problem in our case.
3.2.1
Formulization
Croxton [5] cites three models, namely the IM (Incremental Model), the MCM (Multiple Choice Model) and the
CCM (Convex Combination Model) to describe a formula for the piecewise linear function. Furthermore,
according to this article and another one concerning the knapsack problem [17], these three MIP models for
nonconvex piecewise linear minimization problems are equivalent. The MCM model is adopted in our case
because it is adapted to the fact that the emission produced by freight transport in an arc depends on the sum of
the flow of pallets on this arc and noted x.
x
Fig. 3. Variables for each emission segment
As described in part 2, the merging supply chains in this case is carried out by way of a three-echelon network.
Thus the problem actually involves minimizing the sum of CO2 emissions of the three sections of transport
(upstream, midstream and downstream). To simplify the problem, the flows would only be considered for one
period and only one mode of transport would be involved. The optimization problem is stated as follows (for
notation refer to the Fig.3):
IESM 2009, MONTREAL – CANADA, May 13 - 15
with
(5)
Piecewise linear constraints
,
(6)
,
(7)
,
(8)
,
(9)
Flow-balance constraints
,
(10)
,
(11)
,
(12)
,
(13)
,
(14)
Hub selection constraints
,
(15)
,
(16)
,
(17)
,
(18)
,
(19)
,
(20)
where:
Z: a constant large enough;
K: set of commodities; and each has at least one specific origin and destination node that are respectively called
warehouse and distribution centre;
O, M, N, D: denote respectively the set of WH (source nodes), candidate upstream hubs, candidate downstream
hubs, DC (destination nodes);
Au, Am, Ad : subsets of arc set A, of which Au is the arc set on the upstream flow, Am on the midstream and Ad
on the downstream .
a: The set of arc subsets above
;
dij: the distance of arc
;
: piecewise linear function of CO2 emissions related to the flow x;
: quantity of commodity
supplied at WH
;
: quantity of commodity
required at DC
;
Sa: represents the number of segments on each
s: piecewise linear segment
on each
;
;
: nonnegative fixed value of the intercept of segment
on arc
, in our case the piecewise function
is identical on each arc, so the intercept of the same segment on every arc is always the same according to the
mode of transport, such as 0.772 for road transport and 0.489 for rail;
IESM 2009, MONTREAL – CANADA, May 13 - 15
: slope of segment
on each arc
. Because of the fact that all the segments are parallel, the slope
here is constant with the same product and transport mode, such as
classes and
for the care and grocery
for the liquid products in road transport. With regard to rail transport; similarly we
have
for care and grocery, and
: binary variable on each arc
for liquid products;
, with
if segment
contains a nonzero flow, and
otherwise;
: lower and upper bounds of total flow lie in segment
we assume that
and
on each arc. In particular, for every arc
; and also for each segment s,
(which represents the
capacity of conveyance depending on the pallet’s density and area of the conveyance);
: the total flow on arc
if that flow lies in segment
and
;
and decision variables:
: quantity of shipment of commodity
: binary variable, with
on arc
if commodity
;
supplied at WH
is converged at hub upstream
, and 0 otherwise;
: binary variable,
if DC
is served by the downstream hub
, and 0 otherwise;
Constraints 6-10 which come from the MCM [5] assure that the total product flow on arc a must lie between the
lower and upper bounds of that segment; and at most one segment contains a nonzero flow on each arc.
Equations 11-14 are the flow balance constraints in the three-echelon multicommodity network. Constraints 1520 correspond to the assumption that each supplier must have at most one related upstream hub to where his
flow will be shipped; and each DC must be served by at most one downstream hub. This assumption is to
simplify flow management at each stock point. In addition, if we take into consideration both transport modes
(truck and train) in the model at the same time, the objective function, as well as the number of variables, is
doubled, as a result of the selection between road and rail transport. Moreover, another additional constraint to
bound the minimal flow by train exists only in the case of rail transport.
3.2.2
Approaches to reduce the optimization problem
This MILP transportation problem is a NP-Hard problem[1], so the computing time of this problems could be
influenced by its size. As a representative factor of the size of an instance of a problem, the number of variables
is about 23000 in the biggest problem among the sub-problems presented. This leads us to explore the possibility
of being able to reduce the size in order to solve the problem. Thus, in the model we made several assumptions
as follows:
a. As stated in part 3, the emission functions are nonconvex piecewise linear and discontinuous, and the number
of segments depends on the size of flow. Concerning similar problems, some articles based on analyzing
piecewise function efficacy indicate that some attributes of the function deeply influence computational time,
e.g. the continuity and the number of segments, see [7, 17, 19]. Therefore, to simplify the function in road
transport for example, we assume that a truck is fully loaded in an arc with a shipment above a volume
equivalent to 5 trucks in one week. In other words, the maximum number of segments is set at 6 (so Sa=6 and
s≤6), in addition, the slope of the sixth segment is 0.3321 for the care and grocery classes, and 0.476 for
liquids. Due to a significant difference in load capacity between trucks and trains, the function in rail
transport is reduced to 2 continuous segments, which represent the case that trains are always fully loaded
above one train. The slope of the second segment in rail transport is 0.002 for the care and grocery classes,
and 0.00248 for liquids.
b. According to Croxton [6], with the data in our case we can tighten the LP relaxation of the model by limiting
the maximum bound of each product’s flow in any arc in the network.
c. Considering the fact that consolidation would not occur if the distance between WH and the upstream hub or
between the downstream hub and DC is too great, a condition of distance in both upstream and downstream
paths is introduced to filter candidate upstream and downstream hubs. In other words, the possible hubs are
IESM 2009, MONTREAL – CANADA, May 13 - 15
situated within a certain radius from WH or DC. We studied the sensibility of the solution according to radius
variation, and 100 km was shown to be the best compromise between computing time and solution quality.
3.2.3
Lower limit of emissions
Aside from the model presented to minimize CO2 emissions, it might also be valuable to calculate the lower limit
of the emissions in transport, meaning that all shipments are direct from WH to DC with an absolutely fully
loaded transport mean. As a result, equation (5) in the optimization model will be replaced by a completely
linear objective function.
The assumptions made allow all the sub-problems to be solved by coding and executing a computational
programme. The results obtained are discussed in the next part.
4
Results and discussions
The model presented is coded in ILOG’s OPL 6.1 software with CPLEX 11.2 and run on Quad CPU Q6700
(2.66 GHz) hardware having 4 GB of RAM. The MIP problem is solved with OPL’s default settings, except
Memory Emphasis parameter to true to deal with the large size of the problems, refer to [13]. Furthermore, all
the results obtained showed a variance of less than 3% between the best integer solution and the upper bound.
Note that all the values exhibited in the following tables are measured in tons. It should also be recalled that, as
stated in the methodology part, the suppliers in each class are divided in 3 groups: Group A < 200 pallet/week,
Group B 200-600 pallet/week and Group C > 600 pallet/week.
4.1
Road transport
Initially, road transport is the exclusive transport mode involved in the optimization problem. In the framework
of the 9 sub-problems presented, the purpose of this section is to evaluate the performance of merging supply
chains in terms of CO2 emissions (Emissions / merging in the tables) using the optimization model, by
comparing results with the emissions from the actual transport system (Actual emissions in the tables).
Additionally, the lower limit of emissions (Minimum emissions in the tables) will also be introduced as the
optimum situation in which either the trains or trucks are absolutely fully loaded (linear emission function).
Table 2
Emissions from road transport per week (ton CO2)
Groups of suppliers in CARE
A
B
Actual emissions
51
93
Emissions / merging
28
62
Reduction
Absolute
23
31
Relative
45%
33%
Minimum emissions
11
45
Reduction
Absolute
40
48
Relative
78%
52%
Groups of suppliers in GRO
Actual emissions
Emissions / merging
Reduction
Absolute
Relative
Minimum emissions
Reduction
Absolute
Relative
A
132
67
65
49%
29
103
78%
B
309
219
90
29%
147
162
52%
C
319
290
29
9%
266
53
17%
Σ
463
380
83
18%
322
141
30%
C
670
628
42
6%
568
102
15%
Σ
1111
916
195
18%
744
736
33%
IESM 2009, MONTREAL – CANADA, May 13 - 15
Groups of suppliers in LIQ
Actual emissions
Emissions / merging
Reduction
Absolute
Relative
Minimum emissions
Reduction
Absolute
Relative
A
183
93
90
49%
39
144
79%
B
291
255
36
12%
177
114
39%
C
1257
1193
64
5%
1134
123
10%
Σ
1731
1541
190
11%
1350
381
22%
The results in the tables show that the approach of merging supply chains significantly reduces CO2 emissions
from transport, despite the fact that its gain in emissions is about half the maximum gain defined by the lower
limit, namely the theoretical minimum emissions. Furthermore, it is obvious that the relative reduction in group
C is much less than the other groups. This situation can be explained by the fact that at present the suppliers with
massive flows logically make more effort to saturate their means of transport. Besides the reduction of CO2, it is
also important to indicate that the number of transport paths falls because of the mutualisation, as shown in the
Fig.4.
Source nodes
Destination nodes
Upstream hubs
Downstream hubs
Road transport
Fig. 4. Example of transportation network before and after merging by road transport (CARE Group C)
4.2
Transport by the road and the rail
This section aims to determine the effect of joint road/rail transport in reducing CO2 emissions. This means that
road and rail transport are alternative transport modes to be chosen according to the size of flows and their
performance in terms of emissions. To reflect practical situations in transportation, a lower limit of flow for rail
transport is fixed at 468 pallets which is a volume equivalent to half of a train of 26 wagons.
Table 3
Emissions from joint road and rail transport per week (ton CO2)
Groups of suppliers in CARE
A
B
C
Σ
Actual emissions
51
93
319
463
Emissions / merging
28
44
157
229
Reduction
Absolute
23
49
162
234
Relative
45%
53%
51%
50%
Groups of suppliers in GRO
Actual emissions
Emissions / merging
Reduction
Absolute
Relative
A
132
67
65
49%
B
309
210
99
32%
C
670
257
413
62%
Σ
1111
534
577
52%
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Groups of suppliers in LIQ
Actual emissions
Emissions / merging
Reduction
Absolute
Relative
A
183
93
90
49%
B
291
247
44
15%
C
1257
471
785
62%
Σ
1731
812
919
53%
According to the results in table 3, especially in group C, it can be concluded that joint road and rail transport is
a significant way to reduce CO2 emissions, provided the electrically powered train generates low emissions in
France thanks to the low emission electricity production mainly nuclear and hydro. However, it should be noted
that the problem of rail transport here is to obtain a (consolidated) flow that simultaneously meets the weekly
demand of retailers and the minimum flow for rail transport (468 pallets for 13 wagons). That is to say that the
weekly stock level of retailers can not be challenged. Comparing to the Fig.4, we can easily remark in the Fig.5
that the introduction of the rail transport simplifies the transport network and indicates that it is the means of
transport of massive flows.
Source nodes
Destination nodes
Upstream hubs
Downstream hubs
Road transport
Rail transport
Fig. 5. Example of transportation network before and after merging by joint transport (CARE Group C)
5
Conclusion
This paper explored the effect of merging supply chains on reducing CO2 emissions from transport with two
possible modes, i.e. road and rail, in the context of a national distribution network of two major French retailer
chains. We first pointed out the principal drawback of current freight consolidation, namely that it currently
takes place in a local and fragmentary manner by using carriers and 3PL. This inspired us to search for another
approach to achieve more efficient consolidation. In the aim of reducing CO2 emissions from freight transport,
we were interested in merging supply chains at the strategic level, an approach that demands further and longterm collaboration between the actors of supply chains (suppliers and retailers in this case) as defined in [10].
In this article geographical merging was proposed, namely geographical consolidation among suppliers or
retailers. Moreover, an optimization model with a piecewise linear objective function was set up to quantitatively
evaluate its impact on reducing CO2 emissions. Benefiting from our association with Club Déméter, we tested
the model with the real data of merchandise flows over 12 weeks in a large national distribution network
composed of two French retailers’ supply chain. Due to the great size (more than 100,000 variables in all) of the
problems, it was necessary to make some assumptions to reduce the problems’ size in order to obtain a solution
with a gap of less than 3% in CPLEX. Finally, we obtained the results in tables 2 and 3, which globally yield a
relative reduction of CO2 emissions of 14% exclusively with road transport and of 52% with joint road and rail
transport (with the French railway system described here). It should be recalled that all the results obtained in
this paper are conditional upon an unchanged weekly service rate to retailers. Consequently, it can be concluded
that merging supply chains as studied here provides a significant solution to reducing CO2 emissions from
freight transport. However, one must recall that certain factors present in actual supply chain situations such as
the capacity of each stock point and arc, the empty truck runs and some other operational constraints, were not
taken into consideration in this paper in the initial phase of our project.
Apart from the environmental aspect, future research in the framework of this project could focus on an
economic aspect concerning transportation and reloading costs. Furthermore, the impacts of logistical
IESM 2009, MONTREAL – CANADA, May 13 - 15
mutualisation on shipment frequency, as well as inventory level and organization at stock points are also
considerations of value that might be explored.
6
Acknowledgments
Playing an indispensable role in our research, we gratefully acknowledge the support provided by the Club
Déméter Association. The authors are also grateful to the R2DS program of the Ile-de-France Region that
provided us with funding for this project.
7
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