An Overview of OR Models for Biomass Supply Chains
Birome Holo Ba, Christian Prins and Caroline Prodhon
ICD-LOSI, Troyes University of Technology, 12 rue Marie Curie, CS 42060, 10004 Troyes, France
Keywords: Biomass Logistics, Supply Chain, Modelling, Simulation, Optimization.
Abstract: The biorefineries of the future will critically depend on efficient supply chains to guarantee continuous
flows of biomass while minimizing logistic costs and environmental impacts. OR techniques can be very
useful to help decision makers to model, evaluate and optimize such complex and large-scale supply chains
at the design stage. This paper provides an overview of the OR models for this recent research domain and
proposes a core-model (mathematical program) for the tactical decision level.
1 INTRODUCTION
The actual biorefineries designed for first-generation
biofuels (like bioethanol from wheat, maize or sugar
cane, or biodiesel from rapeseed or sunflower) raise
criticisms concerning possible pressures on other
crop usages like human food or animal feed
production. This is why the biorefineries of the
future will try to combine various types of biomass,
by valorizing discarded fractions of current crops,
like cotton straw, and using the enormous potential
of plants, like switchgrass and short rotation woods,
to produce non-food crops. Moreover, beyond
biofuels, all these agricultural and forestry resources
will provide renewable raw materials for a broad
range of other products, such as chemicals, fibers,
lubricants, construction materials, etc.
The European Commission has put forward a
proposal for a Directive to achieve by 2020 a 20%
share of renewable energy and a biofuels’ usage
with a target of 10% in transport (European
Commission, 2008).
While research on interesting vegetal species and
biorefinery processes is well developed, the actors
concerned realized only recently that the Achilles'
heel of the planned systems could be the logistic
part. For instance, each type of biomass is produced
during a short period in the year while biorefineries
have a more regular activity. Hence, an efficient
supply chain must be implemented to play the role
of a buffer in between and supply the biorefineries
without shortage. Moreover, as the biomass itself is
relatively cheap, the economic equilibrium of the
whole system critically relies on logistic costs. OR is
an adequate tool to derive quantitative models for
these biomass supply chains, evaluate their
performance and optimize criteria like the total cost
of the chain, the energy consumption and the GHG
(greenhouse gas) emissions.
The goal of this contribution is to depict the OR
models proposed for biomass supply chains, for
readers having a general OR culture but not
specialists in biomass issues. This work is extracted
from a preliminary study conducted by the same
authors in the GENESYS French national project on
the lipids biorefinery of the future. This study has
surveyed more than 150 research articles on biomass
logistics but, due to limited space, only some
representative papers will be cited here, to provide
the interested readers with good entry points. The
papers are selected among recent research papers
considering different decision time frames (i.e.,
strategic, tactical, operational, and integrated) and
proposing some general approaches to model
biomass supply chains.
2 BIOMASS SUPPLY CHAINS
A complete biomass supply chain includes various
activities like cultivation, harvesting, pre-processing
(e.g., drying, baling, granulation), transportation,
handling, storage, conversion processes in the
biorefineries, and distribution to end-users. Figure 1
from Zhang et al., (2013) shows a nice example for a
single biorefinery producing ethanol from a plant
called switchgrass. Although a few authors have
tried to model the whole chain (for instance Feng et
174
Ba B., Prins C. and Prodhon C..
An Overview of OR Models for Biomass Supply Chains.
DOI: 10.5220/0004777001740182
In Proceedings of the 3rd International Conference on Operations Research and Enterprise Systems (ICORES-2014), pages 174-182
ISBN: 978-989-758-017-8
Copyright
c
2014 SCITEPRESS (Science and Technology Publications, Lda.)
Figure 1: Example of supply chain to produce bioethanol from switchgrass (Zhang et al., 2013).
al., (2010) for forest products), a global optimization
is still extremely difficult because very different
actors intervene in the two main parts of the chain,
before and after the biorefineries. Therefore, like in
the vast majority of studies, we consider in the
sequel a supply chain that goes from the fields to the
doors of biorefineries. It is assumed that this chain is
driven by demands issued by refineries for several
types of biomass and that these needs must be
satisfied, if possible.
The structure of the chain in Figure 1 suggests a
network model with the following node types (recall
that from now on we stop at the biorefineries):
Input nodes or production nodes, where biomass
is produced and harvested;
Output nodes or consumption nodes, where
biomass is consumed (biorefineries);
Intermediate nodes, the main ones being storage
sites, pre-processing facilities, transshipment
nodes (railway stations for instance) and simple
transit nodes (villages traversed).
Compared to an industrial supply chain, several
differences must be underlined:
Biomass supply chains cover a vast collection
territory, with many scattered cultivation areas;
Long planning horizons are involved, because
most crops have a one-year cultivation cycle;
Inputs (biomass productions) and outputs
(biorefinery activities) are desynchronized;
Because of degradations, the crops cannot wait
and must be harvested quickly when ready.
Pre-processing activities lead to a longer preser-
vation (dry forms, granulates, pellets) and/or easier
and cheaper transportation (increase in density). For
instance, harvested switchgrass has a density of 60-
80 kg/m
3
, which becomes 140-180 for a bale and
700-800 for granulates (Sokhansanj et al., 2009).
Simple preprocessing like baling is often done
directly on the field by harvesters, like in Figure 1.
Biomass supply chains can also be described in
terms of activities that involve various resources:
Harvesting Activities. They are possible in a
limited period at input nodes, when the crop is
ready, and they compete for a limited fleet of
machines like harvesters or balers. The yield is
not perfect, with a typical 10 to 20% loss.
AnOverviewofORModelsforBiomassSupplyChains
175
Storage. Storage is required in practice to
synchronize the biomass production calendar
with the production planning of the biorefineries.
It can take place in the fields or forests as simple
stacks, in intermediate storage sites or at the
entry of biorefineries.
Pre-processing. Baling is a simple form of pre-
processing, which can be done directly on the
field by a quader-baler. Stronger compressions
and other transformations are possible, but using
heavier equipments and/or dedicated sites.
Transport. Road transport is often preferred, due
to limited accessibility of some production sites
like forests. However, other modes like trains
can be used. In many cases, the fleet of vehicles
is limited and the number of travels per period is
restricted by various constraints like vehicle
range or driving time regulations.
A real biomass supply chain can be much more
complex than the simple example of Figure 1 : other
activities can be distinguished (e.g., material
handling); several types of biomass and a multi-
period horizon can be added; the locations of some
facilities can be left as decision variables, etc.
Hence, biomass supply chain designers need
modeling tools to cope with this complexity. Before
coming to a total cost, they must understand the
dynamics of the chain and fix many variables, like
the amounts harvested (which type of biomass,
where, when, in which amount), the flows in the
network (amounts transported), the advisable stock
levels, the resources consumed (machines, vehicles,
energy, manpower). Subtle tradeoffs must be found:
for instance, deciding either to densify on the field,
using light equipment, or to get a higher density at a
remote dedicated facility, at the expense of an
additional transportation step.
Like in production management and industrial
logistics, the decisions can be classified into three
levels, according to the time horizon concerned:
Strategic decisions include for instance the
selection of accepted biomass types, the location
and size of biorefineries, storage sites and pre-
processing plants, the transportation modes, the
long-term supply contracts. In general, a single-
period horizon of one year or a multi-period
horizon of a few years is considered.
Tactical decisions correspond to production
planning in industry. A multiperiod horizon of a
few months is involved, with a time period
varying from one day to one month. Examples:
amount of each type of biomass harvested in
each period at each production node, vehicle
fleet size, definition of safety stock levels, etc.
Operational decisions correspond to scheduling
in industry. Contrary to the tactical level, the
order and starting times of tasks are specified.
Examples: vehicle routing and scheduling,
detailed harvesting operations, idle times.
Even if some studies address the operational level
(e.g., truck scheduling in Han and Murphy, 2012),
research on biomass supply chains focuses on the
strategic and tactical decision levels. Indeed, the
goal is to provide decision makers with tools to
model a chain before its implementation, and not to
develop software for day-to-day operations.
Anyway, the data for detailed operations are never
known at the design stage.
Three main approaches presented in the sequel
are used to model biomass supply chains: simple
decision support systems, performance evaluation
tools, and optimization techniques.
3 SIMPLE SYSTEMS
The simplest decision support systems rely on
spreadsheets and geographical information systems
(GIS). Their apparent simplicity must not hide the
underlying need for many accurate data, e.g.,
biomass production statistics, cost estimates for all
steps and (for the GIS) geographical maps.
A good example of spreadsheet-based system is
described by Delivand et al., (2011) to assess the
supply of rice straw in Thailand. A detailed cost
analysis of a typical rice straw logistic process for
two baling options (small or large rectangular bales)
in three regions shows that the difference in logistic
costs is finally marginal, due to the higher ownership
and operating costs of the equipment for using large
rectangular bales. However, the fuel consumption is
substantially lower for large bales, which induces a
significant reduction of transport costs.
GIS are more powerful and perform non-trivial
calculations for the user. The centroid of a polygon
describing a cultivation area can be easily computed,
e.g., to estimate the Euclidean distance between this
area and a plant. In case of accessibility problem in a
forest, the GIS can find the closest road.
Brechbill et al., (2011) determine up-to-date
biomass production costs using recent prices for all
important cost components including seed, fertilizer,
herbicide, mowing/shredding, raking, baling,
storage, handling, and transportation, from the fields
to the plant gate. The role of the GIS used (ArcMap)
is to map production and supply data over selected
geographical locations.
ICORES2014-InternationalConferenceonOperationsResearchandEnterpriseSystems
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GIS are also used as nice visualization tools on
top of simulation or optimization software. For
instance, Frombo et al., (2009) present a GIS-based
Environmental Decision Support System (EDSS) to
define planning and management strategies for the
optimal logistics for energy production from woody
biomass. The EDSS is organized in three modules
(GIS, data management system, optimization). In
particular, through a GIS-based graphic interface, a
decision maker can visualize the forest parcels of the
territory under concern, select those parcels that can
be used, calculate the distance from each parcel to
the first available road and to the conversion plant
location, and set the parameters related to costs and
technical issues. Then, the optimization module can
be run and the results stored in the database and
displayed on a map.
4 PERFORMANCE VALUATION
The aim of performance evaluation techniques is to
compute performance indicators for real systems
characterized by a complex structure, dynamic
aspects, random variables and/or objective functions
whose each computation is time-consuming (for
instance when these functions have no analytical
formula). The main performance evaluations tools
are simulation methods, stochastic processes like
Markov chains and queuing systems, and Petri nets.
The ones used for biomass logistics are mainly
simulation models. In general, a network-like model
composed of graphical objects (workstations,
queues, random event generators) is defined using
the modelling language of a commercial simulation
software like Arena, then the software simulates in a
few minutes a long period of activity of the real
system.
Sokhansanj et al., (2006) developed a dynamic
Integrated Biomass Supply Analysis and Logistics
model (IBSAL) to simulate the collection, transport
and storage operations and the flow of biomass (corn
stover) from fields to a biorefinery daily throughout
the year. The model includes weather conditions
such as rain and snow which influence the moisture
content and the dry matter loss of biomass through
the supply chain. IBSAL predicts the number and
size of equipment to meet the rate of harvest and
biorefinery demand schedule for feedstock, and also
calculates the costs, energy input and emissions.
IBSAL is very popular as one of the most
sophisticated simulation models, reproducing a
multi-period supply chain with hundreds of
production areas, but with one type of biomass only.
Kumar et al., (2007) applied it to study the logistics
of switchgrass and compare several options for the
collection and transport. IBSAL was also used to
analyze the logistics of different cultures in different
regions (Mani et al., 2006) and (Stephen et al.,
2010). An extended simulation model, called
IBSALMC (IBSAL Multi Crop) was derived from
IBSAL by Ebadian et al., (2011). This model was
developed to evaluate a chain supplying multi-
agricultural raw materials for a proposed cellulosic
ethanol production in Canada.
Ravula et al., (2008) designed a simulation
model to study transport in the logistic network of
cotton, as a possible model for more general biomass
transportation systems. In general, cotton is
collected and compressed into large blocks, known
as modules of cotton transport. Then the cotton
modules built by several farmers are transported to a
gin for processing. Considering a continuous supply
of cotton modules, the originality of this study is to
solve a zero-one knapsack sub-problem which is
solved to optimality to estimate the number of trucks
required in each period. In fact, this work belongs to
the rare publications combining simulation and
optimization.
Zhang et al., (2012) also selected a simulation
approach to take into account the main activities of
the supply chain of biomass, including harvesting,
processing, transportation and storage. Their model
considers the cost of raw materials delivered, energy
consumption and GHG emissions as criteria for
measuring system performance. Compared to the
authors previously cited, this work includes the
distribution sub-network, i.e., beyond the refinery.
Compared to mathematical programming
models, the main advantages of simulation
approaches are the following:
A fine-grain modelling is possible, tackling for
instance resource conflicts, queues of vehicles
waiting for loading in the fields, biomass
production variations or delays due to
unexpected climatic conditions, etc.
System dynamics can be appraised.
Stochastic events are possible.
The operational level can be handled.
Large and complex chains can be modelled.
Practitioners like this kind of models, that they
can easily understand and even modify.
However, simulation models have also some limits:
The running time can be huge for large supply
chains or long time horizons.
No optimization is possible: the user defines the
input parameters and obtains the corresponding
AnOverviewofORModelsforBiomassSupplyChains
177
performance indicators.
In practice, it is possible to evaluate only a few
scenarios to select the best one. For instance, if a
biorefinery is not yet located, a simulation model
can be used to compare a few possible locations,
while ad-hoc variables in a mathematical
program can lead to an optimal location.
5 OPTIMIZATION MODELS
5.1 Principles and Main Works
The formalism used in optimization models is quite
different. The decisions must be described in terms
of variables while the constraints to satisfy are
expressed as equations which link these variables.
Most works consider mixed integer linear programs
(MILP) with a single objective function.
Tembo et al., (2003) are worth citing as one of
the first complete models. They developed a multi-
region, multi-period MILP handling alternative
feedstock, feedstock production, field losses,
harvests, storage, storage losses, transport, bio-
refinery size, and biorefinery location. To take into
account the fluctuations in biomass availability, one-
month time slots are considered. The solution
minimizing logistic costs indicates the best locations
and sizes of warehouses, the storage policies, the
flow of biomass in the logistic network, the planning
of annual crops, the required vehicle fleet, and the
optimal location of the biorefinery.
More recently, Ekşioğlu et al., (2009) proposed
another MILP model that uses agricultural and
woody biomass to produce ethanol. Their multi-
period model prescribes strategic decisions such as
the location, number and size of refineries and
collection sites, and tactical decisions like material
flows. The objective is to minimize over one year a
sum of costs concerning biomass (harvest, storage,
transport, conversion) and the distribution of
ethanol. Ekşioğlu et al., (2010) extended this study
to different modes of transport. The objective was to
identify locations for refineries, transportation
modes to use, transport planning and biofuel
production scheduling to minimize the total cost for
delivering the fuels to end-customers.
Zhu et al., (2011) designed also a MILP for a
single product (switchgrass) supply chain, involving
strategic decisions about the design of the supply
chain and tactical decisions over an annual schedule.
The planning horizon is discretized into one-month
time slots. The MILP takes into account biomass
seasonality, harvesting and transport operations,
energy consumption, and residue handling. The
model determines the best location and capacity for
new warehouses, an effective policy for storage, the
flows of switchgrass transported in the logistic
network, the timing of annual harvest and the best
configuration from a set of candidates bio-refineries.
Zhu and Yao (2011) extended the previous work to a
biorefinery accepting three types of biomass
(switchgrass, corn stover and wheat straw). An
original aspect of their study is that additional
biomass can be purchased from external sources.
The previous papers consider as objective
function a linear combination of various costs,
which is not considered as a true multi-objective
optimization. Multi-objective approaches in Pareto's
sense are all very recent. For instance, Santibañez-
Aguilar et al., (2011) investigated a multi-objective
optimization model for the optimal planning of a
biorefinery, considering various types of production
technologies, raw materials and products. The model
was applied to a case study of a refinery in Mexico.
It simultaneously maximizes the profit and
minimizes the environmental impact.
A few authors have studied non-linear
programming formulations, although they can be
quite hard, computationally speaking. A good
example can be found in Shabani and Sowlati
(2013), who designed a nonlinear mixed integer
program (MINLP) to optimize the supply chain of a
biomass power plant in Canada. Biomass
procurement, storage, energy production and ash
management are considered at the tactical level to
maximize the profit. The model provides estimates
of the amount of biomass to be purchased, stored
and consumed in each month, over a one-year
planning horizon.
The mathematical models solved by commercial
solvers are still limited to small networks in terms of
nodes, contrary to simulation models for instance.
However, still very few authors have proposed
metaheuristics to tackle larger problems. For
instance, Vera et al., (2010) compared a Binary
Particle Swarm Optimization (BPSO) metaheuristic
and a genetic algorithm (GA) to efficiently
determine the optimal location of a biomass power
plant, avoiding a greedy exhaustive search which
would be too time-consuming. The proposed
approach allows to get the location, plant size and
supply area that offer the best profitability from the
investor's perspective.
Optimization models offer the following
advantages compared to simulation:
Optimal decisions can be taken;
Tactical and strategic levels are easily tackled;
ICORES2014-InternationalConferenceonOperationsResearchandEnterpriseSystems
178
Commercial solvers with a high-level modelling
language are available.
But they have still some drawbacks:
The model is difficult to modify for end-users.
The running time may be excessive when integer
variables or non-linearity are involved.
Commercial solvers fail on large instances and
dedicated algorithms must be designed, e.g.
metaheuristics or decomposition approaches.
Handling stochasticity and multiple objectives is
not obvious, although ad hoc extensions exist.
5.2 A Detailed Example
To fix ideas, we propose a tactical model of biomass
supply chain, inspired by the different models from
the literature but more general and flexible. We
allow both a multi-period planning horizon , a set
of biomass types (e.g., corn straw, switchgrass), a
set of biomass forms or "products" (e.g., straw
bales, straw pellets, switchgrass briquettes), a set of
production zones , a set of storage sites , a set of
transformation (pre-processing) sites and a set of
biorefineries .
The supply chain structure is described by a
digraph with a node-set ∪∪∪ and
an arc-set . models the real road network but
simple transit nodes are removed and each arc ,
stands for a path from node to node in the actual
network, with a length
pre-computed by a
shortest path algorithm. The chain considered covers
a biomass basin corresponding to one French
department, so any implicated arc is traversed in a
single period. It is assumed that each production
node, storage node and preprocessing node is
dedicated to a single product (several products are
easily handled by placing several nodes at the same
location). Our model involves the following data.
For each type of biomass ∈:
set of products for this biomass, e.g.,
bales and pellets from wheat straw.
For each product ∈:
type of biomass of origin, e.g. wheat straw
for straw bales and straw pellets;
density in tons/m
3
;
dry fraction, e.g. 0.8 for 20% humidity.
For each production zone ∈:
delivered product;
harvest window (set of consecutive periods);
amount available in tons;
harvesting capacity in tons/period;
harvesting cost in €/ton.
For each storage site ∈:
stored product;
storage capacity in tons;
storage cost in € per ton and per period.
For each preprocessing site ∈:
input product;
output product (same biomass of origin);
weight conversion factor (e.g., 0.9 if 10
tons on input yield 9 tons on output);
transformation capacity in tons/period;
transformation cost per ton.
For each refinery ∈:
set of accepted biomass types in ;
demand for biomass type in period ,
in dry tons.
For each arc , ∈ :
arc length in km;
transportation cost in € per ton of product .
Variables (amounts in tons)
0,∀∈,∀∈
∶ amount harvested per
zone and period;
0,∀∈,∀∈: stock level for each
storage node and period;
0,∀∈,∀∈: amount of input product
treated for each transformation node and period;
0,∀
,
∈,∀∈,∀∈: flow for
each arc, product and period.
The minimization of the different costs of the chain
can be modeled by the linear program given on next
page, in fact a kind of multi-commodity, minimum
cost flow problem (declarations of variables are not
recalled).
The objective function (1), to be minimized, is
the total cost of operations, composed of four terms:
harvesting costs, storage costs, preprocessing costs
and transportation costs. Constraints (2) to (4)
concern production zones: equations (2) mean that
the sum of product flows leaving the zone is equal to
the amount harvested, equations (3) ensure that this
amount does not exceed harvesting capacity, while
equations (4) state that the total amount harvested
while the crop is ready cannot exceed crop
availability. Constraints (5) guarantee the inventory
balance at each storage site while constraints (6)
prevent storage capacity overflows. Constraints (7)
mean that the amount processed at each
AnOverviewofORModelsforBiomassSupplyChains
179
preprocessing plant corresponds to the sum of
incoming flows. Constraints (8) say that this amount
is equal to the sum of outgoing flows after
preprocessing. The capacity of preprocessing plants
is respected via constraints (9). Finally, biorefineries
are handled by constraints (10), which state that the
demands expressed in dry weight for each accepted
biomass type and each period are satisfied.
This model is very flexible because the user may
interleave freely storage nodes and transformation
nodes between the input layer (production zones)
and the output layer (refineries).
Figure 2: Example of supply chain tackled by our model.
Figure 2 shows an example of possible network
with seven sites: three production zones, two
preprocessing plants and two biorefineries (BR),
respectively symbolized by circles, inverted
triangles and squares. All these sites have local
stocks depicted by triangles.
Production zones PZ1 and PZ2 supply straw
already packed into bales while PZ3 yields loose
switchgrass. Refinery BR1 accepts straw and
switchgrass, but refinery BR2 switchgrass only.
Straw bales can be sent directly to BR1, or to the
first preprocessing plant for pelletization.
Switchgrass can be shipped to BR1 and BR2, or to
the other preprocessing plant to give briquettes. Both
plants have local stocks on input and output.
The core-model has been tested on such
examples, using the OPL-STUDIO modeling
environment from IBM (based on CPLEX) and
providing some preliminary results.
6 CONCLUSIONS
This short review indicates that interesting
optimization problems are raised by the design of
biomass supply chains. Compared to industrial
logistics, many input nodes scattered over vast
territories have to continuously supply output nodes
with biomass produced by slow-growing crops,
which leads to large-scale models.
min
∙
∈
∈
∙
∈∈
∙
∈∈
∙
∙
∈,∈
(1)
∀ ∈ ,∀ ∈
:
,,,
∈
(2)
∀ ∈ ,∀ ∈
:
(3)
∀ ∈ :
∈
(4)
∀ ∈ ,∀ ∈ :
,
,,
,
∈
,,
,
∈
(5)
∀ ∈ ,∀ ∈ :
(6)
∀ ∈ ,∀ ∈ :
,,
,
∈
(7)
∀ ∈ ,∀ ∈ :
∙
,,
,
∈
(8)
∀ ∈ ,∀ ∈ :
(9)
∀ ∈ ,∀ ∈
,∀∈:
∙
∈∈
(10)
ICORES2014-InternationalConferenceonOperationsResearchandEnterpriseSystems
180
Our analysis of literature has shown that the
genericity of proposed models is still insufficient.
Very few can cope simultaneously with several
types of biomass, a multi-period horizon, strategic
and tactical decisions. We are also surprised by a
majority of articles that neglect storage nodes,
contrary to our model.
Moreover, most authors belong to laboratories of
agriculture, chemistry or energy. Their models are
often solved on small instances, using commercial
software. OR scientists can contribute to the field by
designing dedicated methods based on relaxation or
metaheuristics to solve larger instances in acceptable
running times, and by designing more advanced
models which could incorporate further criteria such
as economic, environmental and social measures,
and further features as uncertainty and sustainability
issues. The next step of our work is to enrich our
model to make it more generic and scalable, and to
study decomposition techniques, relaxation methods,
and a metaheuristic for large problems.
ACKNOWLEDGEMENTS
This work was carried out, in partnership with the
SAS PIVERT, in the frame of the French Institute of
Excellence in the field of Low-Carbon Energies
(IEED) PIVERT (www.institut-pivert.com) selected
as an Investment for the Future ("Investissements
d’Avenir"). This work was supported, as part of the
Investments for the Future, by the French
Government under the reference ANR-001.
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