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Distributed Space Resource Logistics Architecture Optimization
under Economies of Scale
Evangelia Gkaravela∗
Stevens Institute of Technology, Hoboken, NJ, 07030
Hang Woon Lee†
West Virginia University, Morgantown, WV, 26506
Hao Chen‡
Stevens Institute of Technology, Hoboken, NJ, 07030
This paper proposes an optimization framework for distributed resource logistics system
design to support future multimission space exploration. The performance and impact of
distributed In-Situ Resource Utilization (
ISRU
) systems in facilitating space transportation are
analyzed. The proposed framework considers technology trade studies, deployment strategy,
facility location evaluation, and resource logistics after production for distributed
ISRU
systems.
We develop piecewise linear sizing and cost estimation models based on economies of scale
that can be easily integrated into network-based mission planning formulations. A case study
on a multi-mission cislunar logistics campaign is conducted to demonstrate the value of the
proposed method and evaluate key tradeoffs to compare the performance of distributed
ISRU
systems with traditional concentrated
ISRU
. Finally, a comprehensive sensitivity analysis is
performed to assess the proposed system under varying conditions, comparing concentrated
and distributed ISRU systems.
Nomenclature
A= set of directed arcs
𝐵= facility location matrix
𝑪= spacecraft capacity vector
C= set of commodities
CC= set of continuous commodities
CD= set of discrete commodities
This paper is a substantially revised version of the Paper AIAA 2021-4079, presented at the ASCEND 2021 Conference, Las Vegas, Nevada &
Virtual, November 15-17, 2021.
∗MSc Student, Department of Systems and Enterprises, AIAA Student Member.
†Assistant Professor, Department of Mechanical, Materials and Aerospace Engineering, AIAA Member.
‡Assistant Professor, Department of Systems and Enterprises; hao.chen@stevens.edu. AIAA Member. (Corresponding Author)
𝒄= cost coefficient vector
𝒅= demand and supply vector
E= set of structures
𝑒= structure index
𝐹= structure mass
𝑓= function intercept
G= network graph
𝑔= binary interval variable
𝐻= concurrency matrix
ℎ= binary interval variable
𝑖= node index (∈ N)
J= cost
𝑗= node index (∈ N)
𝑙= number of concurrency constraints
N= set of nodes
𝑃= flow upper bound
𝑄= transformation matrix
𝑞= design quantity
𝑅= number of slopes
𝑟= index of piecewise function interval
𝑀= big constant
𝑀𝑒= bound of piecewise function interval
M= bound of piecewise function interval
T= set of time steps
𝑡= time index (integer)
V= set of spacecraft
𝑣= spacecraft-type index
𝑊= set of time windows
𝑋= demanding mass
𝒙= commodity flow vector
𝑌= manufacturing variable (binary)
𝛼= function slope
2
𝛽= function slope
Δ𝑡= time of flight
I. Introduction
A
slow-cost rocket launch technologies mature, large-scale space infrastructure systems become feasible and
affordable options to support long-term space exploration campaigns. Among these, In-Situ Resource Utilization
(
ISRU
) systems attract the most attention for their ability to generate resources, especially propellants. Multiple studies
on
ISRU
have been conducted, focusing on its chemical processes and standalone system productivity. For example,
Schreiner [
1
] established an integrated molten regolith electrolysis
ISRU
model to analyze oxygen generation leveraging
melted lunar regolith. Meyen [
2
] developed a Mars-atmosphere-based
ISRU
experiment that has been integrated into
the Mars 2020 Perseverance Rover, known as Mars Oxygen In-Situ Resource Utilization Experiment (
MOXIE
). It, for
the first time, produced oxygen on the surface of Mars by solid-oxide electrolysis of atmospheric CO
2
in April 2020 [
3
].
Several testbeds were built by
NASA
[
4
], Lockheed Martin [
5
], and Orbitec Inc. [
6
] based on hydrogen reduction or
carbothermic reduction for oxygen extraction from regolith. These studies demonstrated and evaluated the resource
productivity of different chemical processes during space missions through a concentrated
ISRU
system, where all
subsystems of an ISRU plant are always deployed together.
On the other hand, space logistics research shows the value of the
ISRU
system in supporting long-term space
exploration campaigns by generating propellants for spaceflight. Multiple network-based space logistics optimization
methods [
7
–
9
] demonstrated how
ISRU
infrastructure deployed in earlier missions assists subsequent space transportation.
A multi-fidelity optimization framework was proposed to take into account subsystem-level interactions in the
ISRU
system design and technology trade studies [
10
]. United Launch Alliance also plans to build a cislunar space economy
leveraging lunar water
ISRU
for oxygen and hydrogen generation in its Cislunar-1000 program [
11
]. These studies
only considered the
ISRU
system deployment at a single location and did not fully take advantage of the flexibility of
logistics systems to enable distributed ISRU system operations.
Past literature focused on analyzing concentrated
ISRU
system performances. However, this is not always the case
for certain types of
ISRU
technologies. For example, for a lunar water
ISRU
plant to generate oxygen and hydrogen
based on lunar regolith, two main steps are involved in the operation process. First, water from the lunar regolith is
extracted using the Soil Water Extraction (
SWE
) subsystem, and then the water can be electrolyzed to generate oxygen
and hydrogen using the Direct Water Electrolysis (
DWE
) subsystem. In fact, only the
SWE
subsystem needs to be
deployed on the surface of the moon. The
DWE
subsystem may be deployed on an in-orbit space station between Earth
and the moon, such as at Earth-Earth-Moon Lagrange Point 1 (
EML1
). This placement is used as a demonstration case
to explore the trade-offs and advantages of utilizing EML1 as a logistics hub for water and propellant transportation.
3
This decision can reduce infrastructure deployment costs and simplify propellant logistics processes after production. A
comparison between concentrated
ISRU
systems and distributed
ISRU
systems is illustrated in Fig. 1. In this scenario,
water or ice is transported out of the moon instead of liquid oxygen or hydrogen, which also removes the cryogenic
storage system in space vehicles. However, distributed means decentralized material flow management during the system
operation. More transportation elements and logistics facilities are involved in the mission operation and system design
space. This decentralization introduces another challenge in mission planning, considering the sizing and cost estimation
of multiple types of logistics elements simultaneously. Past studies consider these sizing and cost estimation problems
either through linear models for both sizing and cost estimation [
7
,
8
,
10
] or nonlinear sizing models with pre-defined
cost metrics [
9
]. The former methods sacrifice design fidelity to ensure computational efficiency, whereas the latter
methods are computationally prohibitive for the consideration of multiple sizing models at the same time and limit the
option of cost measures. Previous literature has not effectively addressed the efficient capture of volume discounts for
both structure mass and cost estimation in large-scale elements per unit capacity in the context of economies of scale.
PAC
KSC
Earth Surface Node
Earth/Cis-Lunar System Node
LSP
Earth
Moon
LEO LLO
EML1
Soil Water Extraction (SWE) ISRU
Direct Water Electrolysis (DWE) ISRU
PAC
KSC LSP
Earth
Moon
LEO LLO
EML1
Concentrated ISRU System Distributed ISRU System
KSC: Kennedy Space Center
PAC: Pacific Ocean
LEO: Low-Earth Orbit
LSP: Lunar South Pole
LLO: Low-Lunar Orbit
EML: Earth-Moon Lagrangian Points
ISRU Deployment
Water Transportation
Fig. 1 Concentrated ISRU system v.s. distributed ISRU system.
In response to this background, this paper proposes a space infrastructure design and deployment optimization
framework to model and analyze the impact of distributed systems for future multi-mission space exploration campaigns.
Piecewise linear sizing and cost estimation models are proposed based on economies of scale. We integrate these
models into network-based mission planning methods as mixed-integer linear programming, whose global optimality is
guaranteed.
There are three main contributions achieved in this paper. First, the proposed resource logistics optimization
framework captures the economies of scale for both structure sizing and cost estimation in a computationally efficient
manner. It enables effective optimization for simultaneously designing multiple transportation elements and plants,
which is the main challenge in mission planning with distributed
ISRU
. Nonlinear parametric cost models can be
4
used directly as the mission design metric. Second, the proposed framework can solve facility location and spacecraft
manufacturing problems together with transportation mission planning. Traditional space logistics optimization methods
focus on transportation flow design. These approaches are sufficient to take into account trade-offs in concentrated
ISRU
. However, facility location problems need to be considered directly in the design space for distributed logistics
systems. Finally, to the best of our knowledge, this paper is one of the first studies to evaluate the performance of
distributed
ISRU
systems compared with concentrated
ISRU
. This research provides an important step in building a
concrete and resilient supply chain for future interplanetary space transportation.
The remainder of this paper is organized as follows: Section II introduces the optimization framework for distributed
resource logistics systems. It develops sizing and cost estimation models based on economies of scale and integrates
them into network-based space logistics optimization methods. A case study on cislunar transportation is conducted in
Sec. III to compare the performance of a distributed and concentrated lunar water
ISRU
system using the proposed
method. Finally, in Sec. IV, we conclude this paper and discuss future directions.
II. Methodology
A. Network-Based Space Logistics Planning Model
Multiple recent studies have shown the effectiveness of converting space mission planning problems into multicom-
modity network flow problems [
7
–
10
]. As illustrated in Fig. 1 in a network-based logistics model, nodes represent orbits
or planets; arcs represent spaceflight trajectories. Then, spacecraft, crew, payload, propellant, etc., are all considered
commodities flowing along arcs.
Consider a network graph, 𝐺, consisting of a set of nodes, denoted by 𝑁, and a set of arcs, denoted by A. We can
write
A={𝑉 , 𝑁 , 𝑇 }
where
𝑉
is the spacecraft set (index:
𝑣
),
𝑁
is the node set (index:
𝑖, 𝑗
),
𝑇
is the time step set (index:
𝑡).
Define the decision variable for commodity flows as
𝒙𝑣𝑖 𝑗 𝑡
, which is a continuous variable denoting the amount of
commodity flow from node
𝑖
to node
𝑗
at time
𝑡
using spacecraft
𝑣
. The transportation mission goals can be represented
by logistics supplies and demands, written as
𝒅𝑖𝑡
for node
𝑖
at time
𝑡
. The mission planning objective is to satisfy the
demands with the lowest mission cost. As a measure of mission cost, we can define a cost coefficient
𝒄𝑣𝑖 𝑗
. We define
a set,
C
, for commodities considered in the logistics planning. It includes continuous commodity variables, such as
propellant, payload, etc., defined by the set C𝑐, and discrete commodity variables, such as the number of spacecraft or
crew members, defined by the set
C𝑑
. Then, there are
|C |
types of commodities in the logistics system, and
𝒙𝑣𝑖 𝑗 𝑡
,
𝒅𝑖𝑡
,
𝒄𝑣𝑖 𝑗
are all vectors of dimension
|C | × 1
. Typical constraints considered in traditional logistics mission planning methods
include the mass balance constraint, the concurrency constraint for flow capacities, and the time-bound constraint for
time windows. We define
Δ𝑡𝑖 𝑗
as the time of flight along the arc from node
𝑖
to node
𝑗
,
𝑄𝑣𝑖 𝑗
as the transformation
5
matrix for commodity conversion and resource generation during space missions,
𝐻𝑣𝑖 𝑗
as the concurrency matrix that
enforces commodity flow bounds, such as spacecraft payload capacity and propellant capacity, and finally
𝑊𝑖 𝑗
as the set
of time windows for mission operation.
The transformation matrix
𝑄𝑣𝑖 𝑗
is a key component of the optimization framework, capturing the relationships
between input and output commodities for spacecraft
𝑣
as they traverse arcs in the logistics network. Each element of
𝑄𝑣𝑖 𝑗
quantifies how resources are transformed during operations, such as ISRU processes or propellant consumption.
The transformation matrix ensures that the conservation of mass and energy principles are maintained across all nodes
and arcs, supporting the feasibility of logistics flows.
The concurrency matrix
𝐻𝑣𝑖 𝑗
models shared capacity constraints among multiple resources flowing through the
same arc. It ensures that the total flow does not exceed the capacity of spacecraft, ISRU plants, or other logistics
elements. This matrix is crucial for mixed-resource missions where commodities like propellant and payloads are
limited by transportation or processing capacity.
The time windows
𝑊𝑖 𝑗
define the operational periods for nodes or arcs, considering environmental and mission
constraints. For example, lunar mining operations may only be active during the lunar day, requiring
𝑊𝑖 𝑗
to capture
these periodic availability intervals.
Based on all the notations defined above and at Table 1, the mission planning formulations can be written as follows.
Minimize the objective function:
J=
(𝑣,𝑖 , 𝑗 ,𝑡 ) ∈ A
𝒄⊤
𝑣𝑖 𝑗 𝒙𝑣𝑖 𝑗 𝑡 (1)
Subject to
The mass balance constraint:
(𝑣, 𝑗 ):(𝑣,𝑖 , 𝑗 ,𝑡 ) ∈ A
𝒙𝑣𝑖 𝑗 𝑡 −
(𝑣, 𝑗 ):(𝑣, 𝑗, 𝑖, 𝑡 ) ∈ A
𝑄𝑣 𝑗 𝑖 𝒙𝑣 𝑗 𝑖 (𝑡−Δ𝑡𝑗𝑖 )≤𝒅𝑖𝑡 ∀𝑖∈ N ,∀𝑡∈ T (2)
The concurrency constraint:
𝐻𝑣𝑖 𝑗 𝒙𝑣𝑖 𝑗 𝑡 ≤0𝑙×1∀(𝑣 , 𝑖, 𝑗, 𝑡 ) ∈ A (3)
The time window constraint:
𝒙𝑣𝑖 𝑗 𝑡 ≥0| C | × 1,if 𝑡∈𝑊𝑖 𝑗
𝒙𝑣𝑖 𝑗 𝑡 =0| C | ×1,otherwise
∀(𝑣, 𝑖, 𝑗 , 𝑡) ∈ A (4)
6
Table 1 Definitions of indices, variables, and parameters
Name Definition
Index
vSpacecraft index
i,jNode
tTime step
lConcurrency index
eStructure index
rIndex for piecewise sizing function intervals
𝛾Index for piecewise cost estimation function intervals
Variables
𝒙vijt
Commodity outflows/inflows. Commodities in
𝒙±
vijt
are considered as continuous or integer variables
based on the commodity type. (p×1)
𝑞𝑒Storage capacity for structure e.
𝐹𝑟
𝑒Mass of structure e.
𝑃vijt Payload utilization along arc (𝑖, 𝑗 )at time 𝑡. Continuous variable.
J
𝑒Manufacturing cost of structure e.
𝑔𝑟
𝑒Binary variable for interval r in piecewise function of structure e.
ℎ𝛾
𝑒Binary variable for interval 𝛾in cost estimation function of structure 𝑒.
𝑧𝑒Manufacturing cost of structure 𝑒. Continuous variable.
𝑋𝑒Deployment demand for ISRU plant 𝑒. Continuous variable.
𝑌𝑒Binary variable indicating if structure 𝑒is manufactured.
𝑁water Annual water processing mass for ISRU.
J
Manufacturing Total manufacturing cost for logistics elements. Continuous variable.
Parameters
𝒄vijt Commodity cost coefficient. (p×1)
𝑀𝑟
𝑒Upper bound of 𝑟-th interval in piecewise sizing function for structure 𝑒.
𝑀𝛾
𝑒Upper bound of 𝛾-th interval in cost estimation function for structure 𝑒.
𝛼𝑟
𝑒Slope of 𝑟-th interval in piecewise sizing function for structure 𝑒.
𝛽𝛾
𝑒Slope of 𝛾-th interval in cost estimation function for structure 𝑒.
𝑓𝑟
𝑒Intercept of 𝑟-th interval in piecewise sizing function for structure 𝑒.
𝐽𝛾
𝑒Intercept of 𝛾-th interval in cost estimation function for structure 𝑒.
Hvij Concurrency constraint matrix. (𝑙×𝑝)
𝑑it Demands or supplies of different commodities at each node. (p×1)
Qvij Commodity transformation matrix. (p+1)×(p+1)
Wij Time window vector. (1 ×n, where n is the number of time windows)
Δ𝑡Time of flight along arc (i,j).
𝛽Cost estimation function.
𝒙𝑣𝑖 𝑗 𝑡 =
𝒙C
𝒙𝐷
𝑣 𝑖 𝑗𝑡
𝒙C∈R| C𝑐|×1
≥0,𝒙𝐷∈Z| C𝐷|×1
≥0,∀(𝑣, 𝑖, 𝑗 , 𝑡) ∈ A
7
In this formulation, Eq.
(1)
is the objective function to minimize the mission cost. Constraint
(2)
is the mass balance
constraint to guarantee the commodity outflow is always smaller or equal to the commodity inflow minus the mission
demand. The second term of this mass balance constraint describes the commodity transformation along arcs. Constraint
(3)
is the concurrency constraint to limit the commodity flow because of the capacities of spacecraft or other facilities.
In this constraint,
𝑙
is the number of capacity types considered in the mission operation. Constraint
(4)
is the time
window constraint. Only when time windows are open are commodity flows permitted. For more detailed settings of
each constraint, please refer to Refs. [9, 10].
This network-based logistics planning method focuses on the flow of commodities during space missions. It enables
optimal transportation scheduling and transportation element sizing optimization at the same time. This model is
sufficient for concentrated
ISRU
when the facility location is not part of the tradeoff. Studies integrate nonlinear sizing
models into the formulation through approximation [
9
]. However, the optimization can become easily computationally
intractable when multiple element sizing models are considered simultaneously. The linear cost model in the objective
function also makes it hard to consider volume discounts in the manufacturing of large space structures. In the following
sections, we develop models for economies of scale and manufacturing and facility deployment problems.
B. Economies of Scale Models
We care about the mass and cost of building transportation structures with the desired storage capacity or capabilities
in space logistics problems. The economies of scale describe the volume discounts that large systems have, such as the
lower structure mass or manufacturing cost per unit capacity compared with small structures. An ideal economies of
scale model is a concave function where the marginal mass or cost per unit capacity strictly decreases as the structure
size increases.
We define piecewise linear and concave functions for structure sizing and cost estimation, as shown in Fig. 2.
[
12
–
14
] Define
𝑅
as the number of different slopes in the economies of scale function with index
𝑟=1,2, ..., 𝑅
. We use
the index
𝑒
to represent the structure to be designed and defined by the set
E
, such as spacecraft,
ISRU
plants, or storage
tanks. Let
𝑀𝑟−1
𝑒
and
𝑀𝑟
𝑒
be the lower and upper bound of the
𝑟
th interval, respectively, in the piecewise linear function
with a slope denoted by
𝛼𝑟
𝑒
. Then, we can calculate the function value in each interval using the slope
𝛼𝑟
𝑒
and associated
fixed intercept 𝑓𝑟
𝑒. The function, 𝐹𝑟
𝑒(𝑞𝑒), can be expressed as a function of quantity 𝑞𝑒:
𝐹𝑟
𝑒(𝑞𝑒)=𝛼𝑟
𝑒𝑞𝑒+𝑓𝑟
𝑒∀𝑞𝑒∈ (𝑀𝑟−1
𝑒, 𝑀𝑟
𝑒] ∀𝑟∈ [1, . . . , 𝑅](5)
Note that this concave model assumes that the slopes are strictly decreasing:
𝛼1
𝑒> 𝛼2
𝑒> . . . > 𝛼𝑅
𝑒
. However, the
function and intercept values are strictly increasing: 0< 𝑓 1
𝑒< 𝑓 2
𝑒< . . . < 𝑓 𝑅
𝑒.
To model the piecewise linear function for economies of scale, a binary interval variable
𝑔𝑟
𝑒
is necessary. This
8
𝑓
𝑒
1
𝑓
𝑒
2
𝑓
𝑒
3
𝐹
𝑒(𝑞𝑒)
𝑀𝑒
0𝑀𝑒
1𝑀𝑒
2
𝛼𝑒
1
𝛼𝑒
2
𝛼𝑒
3
𝑞𝑒
Fig. 2 Piecewise linear and concave economies of scale model.
variable indicates whether the quantity
𝑞𝑒
of structure
𝑒
lies within the
𝑟
th interval of the function, defined by the
bounds 𝑀𝑟−1
𝑒(lower bound) and 𝑀𝑟
𝑒(upper bound). It is expressed as:
𝑔𝑟
𝑒=
1,if 𝑞𝑒∈ (𝑀𝑟−1
𝑒, 𝑀𝑟
𝑒]
0,otherwise
(6)
Then, the quantity 𝑞𝑒can be identified as 𝑞𝑒=Í𝑅
𝑟=1𝑞𝑟
𝑒and the following constraints:
𝑅
𝑟=1
𝑔𝑟
𝑒≤1∀𝑒∈ E,(7)
𝑞𝑟
𝑒≤𝑀𝑟
𝑒𝑔𝑟
𝑒∀𝑒∈ E, 𝑟 =1,2, . . . , 𝑅, (8)
𝑞𝑟
𝑒≥𝑀𝑟−1
𝑒𝑔𝑟
𝑒∀𝑒∈ E, 𝑟 =1,2, . . . , 𝑅 . (9)
The binary variable
𝑔𝑟
𝑒
ensures that only one interval is active at a time. The variable
𝑞𝑟
𝑒
represents the portion of
the total storage capacity 𝑞𝑒for structure 𝑒that falls within the 𝑟th interval of the piecewise function.
The function value can be determined using the function:
𝐹𝑟
𝑒(𝑞𝑒)=
𝑅
𝑟=1
(𝛼𝑟
𝑒𝑞𝑟
𝑒+𝑔𝑟
𝑒𝑓𝑟
𝑒) ∀𝑒∈ E (10)
When the economies of scale need to be considered simultaneously for the structure sizing and cost estimation,
we can simply repeat the above steps. For example, if we want to take into account the manufacturing cost in the
optimization of the above logistics structure
𝑒
, then we denote the variable
𝑞𝑒
as the storage capacity and the variable
𝐹𝑒
9
as the structure mass, as calculated by Eq.
(10)
considering constraints Eqs.
(7)
–
(9)
. Here, Eq.
(10)
is the economies of
scale function for structure sizing. The manufacturing cost of structure
𝑒
, denoted by
J
𝑒
, is estimated based on the
structure mass variable
𝐹𝑒
. Similarly, we build economies of scale model with independent variable
𝐹𝑒
, dependent
variable
J
𝑒
, interval index
𝛾=1,2, . . . , Γ
, slopes
𝛽𝛾
𝑒
, intercepts
𝐽𝛾
𝑒
, and binary interval variable
ℎ𝛾
𝑒
. Here,
Γ
is the
number of linear intervals used to approximate the structure cost function under economies of scale. The cost estimation
function for the structure 𝑒can be expressed as:
J
𝑒(𝐹𝑒)=
Γ
𝛾=1𝛽𝛾
𝑒𝐹𝛾
𝑒+ℎ𝛾
𝑒𝐽𝛾
𝑒∀𝑒∈ E (11)
Define the lower and upper bounds of
𝛾
-th interval of this cost estimation function as
M𝛾−1
𝑒
and
M𝛾
𝑒
. Then, the
optimization constraints associated with Eq.(11) can be written as:
Γ
𝛾=1
ℎ𝛾
𝑒≤1∀𝑒∈ E,(12)
𝐹𝛾
𝑒≤ M𝛾
𝑒ℎ𝛾
𝑒∀𝑒∈ E, 𝛾 =1,2, . . . , Γ,(13)
𝐹𝛾
𝑒≥ M𝛾−1
𝑒ℎ𝛾
𝑒∀𝑒∈ E, 𝛾 =1,2, . . . , Γ.(14)
C. Manufacturing and Facility Deployment Problems
The previous section builds the relationship between the structure design quantity
𝑞𝑒
and the structure mass
𝐹𝑒
and
between the mass
𝐹𝑒
and the manufacturing cost
J
𝑒
. Then, there are two problems left for logistics mission planning: 1)
whether the structure should be manufactured and 2) how we can integrate the demand in the formulation for facilities to
be deployed at a specific location. The structures we discuss here include immovable infrastructure, such as
ISRU
plants,
and mobile transportation elements, such as spacecraft and transportation tanks. The only difference between
ISRU
and
spacecraft is that an
ISRU
plant should be added to the system at a specific node as a demand, while a spacecraft should
be launched from Earth and added to the system as a supply. Therefore, for simplicity, we discuss them using the same
set of notations below.
1. Manufacturing Problem
First, we have to determine whether the structure
𝑒
should be manufactured in the logistics system. We define the
following binary variable:
𝑌𝑒=
1,if a structure is manufactured
0,otherwise
∀𝑒∈ E (15)
10
For the purpose of this study, all ISRU plants and spacecraft are assumed to be manufactured on Earth. This
assumption reflects the reliance on advanced manufacturing facilities and resources available on Earth. The challenge of
this problem comes from the calculation of the total manufacturing cost in the optimization objective. We know that the
manufacturing cost for structure 𝑒is J
𝑒. Then, the total manufacturing cost can be expressed as:
J
Manufacturing =
𝑒∈ E
𝑌𝑒J
𝑒(16)
Because both
𝑌𝑒
and
J
𝑒
are decision variables in the optimization problem, Eq. (16) contains quadratic terms,
which makes the problem nonlinear. Fortunately, this is a quadratic term of multiplication between a binary variable
and a continuous variable. We can define the final manufacturing cost of structure 𝑒as 𝑧𝑒. We get:
𝑧𝑒=𝑌𝑒J
𝑒∀𝑒∈ E (17)
Using a big constant 𝑀, Eq. 17 can be converted into mixed-integer linear constraints as follows:
𝑧𝑒≤𝑀𝑌𝑒∀𝑒∈ E (18)
𝑧𝑒≤ J
𝑒∀𝑒∈ E (19)
𝑧𝑒≥ J
𝑒− (1−𝑌𝑒)𝑀∀𝑒∈ E (20)
𝑧𝑒≥0∀𝑒∈ E (21)
2. Facility Deployment Problem
After determining the structure to be manufactured for the logistics, we need to generate demand for the
ISRU
plant deployment or the spacecraft supply. Now, we consider the deployment of
ISRU
plants and spacecraft separately
because the demand for
ISRU
plants is a continuous variable, while the supply of spacecraft is a discrete variable. We
can represent the set of structures as
E=[EISRU,ESC]⊤
, where
EISRU
denotes the set of
ISRU
plants and
ESC
denotes
the set of spacecraft or transportation tanks.
For ISRU deployment demand, define the demanding mass for ISRU plant 𝑒as:
𝑋𝑒=𝑌𝑒𝐹𝑒∀𝑒∈ EISRU (22)
Then, we define a binary facility location matrix
𝐵𝑖𝑒𝑡
where
𝑖
is the node index of the
ISRU
facility deployment site.
The binary elements of
𝐵𝑖𝑒𝑡
are determined in advance depending on the
ISRU
operation requirement and landing site
environment. Specifically,
𝐵𝑖𝑒𝑡 =1
indicates that
ISRU
structure
𝑒
is deployed at node i at time step t, while
𝐵𝑖𝑒𝑡 =0
11
indicates that the structure is not deployed. We can get the total
ISRU
demand mass to be deployed at node
𝑖
at a specific
time 𝑡as:
𝑑ISRU,𝑖𝑡 =−
𝑒∈ EISRU
𝐵𝑖𝑒𝑡 𝑋𝑒∀𝑖∈ N ∀𝑡∈ T (23)
Note that based on the definition of the mass balance constraint Eq.
(2)
, all supplies are positive and demands are
negative in the demand vector
d𝑖𝑡
. In Eq.
(23)
,
𝑋𝑒
is a product of a binary variable and a continuous variable. Similarly,
Eq.(23) can be linearized by following mixed-integer linear constraints:
𝑋𝑒≤𝑀𝑌𝑒∀𝑒∈ EISRU (24)
𝑋𝑒≤𝐹𝑒∀𝑒∈ EISRU (25)
𝑋𝑒≥𝐹𝑒− (1−𝑌𝑒)𝑀∀𝑒∈ EISRU (26)
𝑋𝑒≥0∀𝑒∈ EISRU (27)
For spacecraft supply, because all spacecraft need to be launched from Earth, the spacecraft supply can be expressed
as:
𝑑SC,𝑖 =
Í
𝑒∈ ESC
𝑌𝑒,if 𝑖=Earth
0,otherwise
(28)
We can also include additional demands for spacecraft if we want to specify the target orbit of spacecraft launching.
D. Distributed Logistics System Optimization Framework
In this section, we integrate the economies of scale model proposed in II.B and the manufacturing and deployment
formulation proposed in II.C into the network-based logistics planning model. Based on the notations mentioned above,
the optimization framework for the distributed logistics system can be written as follows:
Min J=
(𝑣,𝑖 , 𝑗 ,𝑡 ) ∈ A
c⊤
𝑣𝑖 𝑗 𝒙𝑣𝑖 𝑗 𝑡 +
𝑒∈ E
𝑧𝑒(29)
Subject to:
section 1 (space logistics flows)
(𝑣, 𝑗 ):(𝑣,𝑖 , 𝑗 ,𝑡 ) ∈ A
𝒙𝑣𝑖 𝑗 𝑡 −
(𝑣, 𝑗 ):(𝑣, 𝑗, 𝑖, 𝑡 ) ∈ A
𝑄𝑣 𝑗 𝑖 𝒙𝑣 𝑗 𝑖 (𝑡−Δ𝑡𝑗𝑖 )≤
𝒅𝑖
𝑑ISRU,𝑖
𝑑SC,𝑖
𝑡
∀𝑖∈ N ∀𝑡∈ T (30)
12
𝐻𝑣𝑖 𝑗 𝒙𝑣𝑖 𝑗 𝑡 ≤ 𝑅
𝑟=1
𝒒𝑟
sc!𝑥sc,𝑣𝑖 𝑗 𝑡 ∀(𝑣, 𝑖, 𝑗 , 𝑡) ∈ A (31)
𝒙𝑣𝑖 𝑗 𝑡 ≥0| C | × 1if 𝑡∈𝑊𝑖 𝑗 ,
𝒙𝑣𝑖 𝑗 𝑡 =0| C | ×1otherwise
∀(𝑣, 𝑖, 𝑗 , 𝑡) ∈ A (32)
section 2 (sizing model) Eqs. (7)-(10)
section 3 (cost model) Eqs.(11)-(14)
section 4 (manufacturing cost) Eqs.(18)-(21)
section 5 (demand generation) Eqs.(23)-(28)
𝒙𝑣𝑖 𝑗 𝑡 =
𝒙𝐶
𝒙𝐷
𝑣 𝑖 𝑗𝑡
,𝒙𝐶∈R|𝐶𝑐|×1
≥0,𝒙𝐷∈Z| CD|×1
≥0,∀(𝑣, 𝑖, 𝑗 , 𝑡) ∈ A
𝑔𝑟
𝑒, ℎ𝛾
𝑒∈ {0,1} ∀𝑒∈ E,∀𝑟, 𝛾 𝑞𝑟
𝑒, 𝐹𝛾
𝑒, 𝑧𝑒, 𝑋𝑒∈R≥0∀𝑒∈ E,∀𝑟, 𝛾
In this formulation, Eq.
(29)
is the objective function to minimize the total mission cost. The first term covers all
transportation costs determined by commodity flows, including the facility deployment cost. The second term covers
all manufacturing costs of
ISRU
plants and transportation elements. The objective function, Eq.
(29)
combines the
transportation cost, incurred incrementally during the mission, and the non-recurring plant manufacturing cost. While
this formulation can be used for lifecycle cost estimation, its validity depends on mission duration, plant type, and reuse
potential. If the ISRU plant is reusable across missions, its manufacturing cost should be spread across its lifecycle. In
this research, we focus on cost estimation during the mission time span and assume the deployed ISRU will only be used
for the proposed mission scenarios.
Additional demand and supply generated by the
ISRU
and spacecraft deployment are added to the demand vector of
the mass balance constraint, Eq.
(30)
. Equation
(31)
is the concurrency constraint that limits the commodity flow because
of the capacity of structures. We can consider the payload and propellant capacities from spacecraft, transportation
tanks, or
ISRU
storage systems. The vector variable
𝒒𝑟
has a dimension of
|X | × 1
. It is the vector form of the capacity
of commodities. The flow variable
𝑥𝑠𝑐 ,𝑖 𝑗𝑡
is a binary variable defined specifically for the spacecraft
𝑣
. When we
consider spacecraft sizing, the spacecraft set
V
is equal to
E𝑆𝐶
. The expression
Í𝑅
𝑟=1𝒒𝑟
determines the capacity of the
spacecraft 𝑣during spaceflight. We can define a |V | × 1capacity vector variable 𝑪for all spacecraft in the set V.
𝑪=
𝑅
𝑟=1
𝒒𝑟(33)
13
Then, the right-hand side of the concurrency constraint Eq.
(31)
can be expressed as
𝑃𝑣𝑖 𝑗 𝑡 =𝐶𝑣𝑥𝑠𝑐 ,𝑣𝑖 𝑗 𝑡
. This is also
a product of a binary variable and a continuous variable. We can express this term equivalently using the following
mixed-integer programming formulations:
𝑃𝑣𝑖 𝑗 𝑡 ≤𝑀 𝑥𝑠𝑐, 𝑣𝑖 𝑗 𝑡 ∀( 𝑣, 𝑖, 𝑗 , 𝑡) ∈ A (34)
𝑃𝑣𝑖 𝑗 𝑡 ≤𝐶𝑣∀( 𝑣, 𝑖, 𝑗 , 𝑡) ∈ A (35)
𝑃𝑣𝑖 𝑗 𝑡 ≥𝐶𝑣− (1−𝑥𝑠𝑐, 𝑣𝑖 𝑗 𝑡 )𝑀∀(𝑣, 𝑖, 𝑗 , 𝑡) ∈ A (36)
𝑃𝑣𝑖 𝑗 𝑡 ≥0∀( 𝑣, 𝑖, 𝑗 , 𝑡) ∈ A (37)
When spacecraft or transportation tank sizing problem is considered, Eqs.
(34)
-
(37)
need to be added into the optimization
framework to replace the right-hand side of Eq.
(31)
by
𝑃𝑣𝑖 𝑗 𝑡
. A similar technique was used in Ref. [
9
] to handle the
multiplication of spacecraft capacity and spacecraft flow variables.
III. Cislunar Transportation Case Study
In this section, we develop a case study on cislunar logistics to compare the performance of distributed
ISRU
and concentrated
ISRU
systems using the proposed optimization framework. We first introduce mission operation
assumptions and economies of scale models used in the case study in Section III.A. Then, we show mission planning
results and discuss mission performances in III.B.
A. Mission Scenarios
The mission planning scenario considered in this paper is a series of transportation missions in the cislunar
system. The transportation network model is shown in Fig. 3. This transportation network includes Earth, Low Earth
Orbit (
LEO
), Geostationary Earth Orbit (
GEO
),
EML1
, and the moon. The trajectory
Δ𝑉
along each arc is also shown
in Fig. 3. In this case study, we assume that the time of flight along each arc is always one-time step. The mission goals
are to deliver 25,000 kg payload to GEO and 15,000 kg payload to the moon from Earth every year. At the same time,
the logistics system needs to satisfy 5,000 kg oxygen annual demands at
EML1
and
GEO
that can be used for astronaut
activities or as the propellant oxidizer. To structure the timeline of these mission activities, we define the Mission
Start Time (
MST
) as the initial reference point from which all mission operations are measured. All subsequent time
steps, such as annual demands and mission events, are defined relative to
MST
. This framework allows for a consistent
comparison of different ISRU strategies, including their setup phases and operational efficiencies.
The oxygen can be delivered from Earth, generated by the lunar
ISRU
system on the Moon, or generated by a
distributed
ISRU
system on-site. This case study aims to analyze the ability of
ISRU
to support transportation logistics
in the cislunar system and compare the performance of concentrated and distributed
ISRU
systems. The mission
14
demands and supplies are summarized in Table 2. All ISRU plants are assumed to be manufactured on Earth, similar to
spacecraft. Also, all resources are supplied from Earth in infinite quantities. However, we need to pay corresponding
costs for the rocket launch, spaceflight operation, and system manufacturing to use these resources.
Earth Low Earth Orbit
(LEO)
Earth Moon
Lagrange Point 1
(EML1)
Moon
Geostationary Earth Orbit
(GEO)
Earth Moon
Δ𝑉 in [km/s]
Δ𝑉 = 3.77 Δ𝑉 = 2.52
Δ𝑉 = 1.4
Geostationary Earth Orbit
(GEO)
Low Earth Orbit
(LEO) Earth Moon
Lagrange Point 1
(EML1)
Fig. 3 Cislunar transportation network model.
Table 2 Mission Demands and Supplies.
Payload Type Node Time, [days] Demand (-)/Supply(+),
[kg]
Payload GEO Annually -25,000
Oxygen GEO Annually -5,000
Oxygen EML1 Annually -5,000
Payload Moon Annually -15,000
Propellant, ISRU
Maintenance, spares Earth All the time +∞
In this case study, we focus on the analysis of lunar water
ISRU
. For simplicity, we assume the
ISRU
system is mainly
made up of two components: 1) The
SWE
system to extract water from lunar soil; 2) The
DWE
system to electrolyze
water into oxygen and hydrogen. As we can see, depending on the working environment, the
SWE
system needs to be
deployed on the lunar surface. In contrast, the
DWE
system can be deployed either together with
SWE
or on-site at the
place of resource demand. In this mission scenario, the problem is whether we should deploy a concentrated
ISRU
on the moon or deploy a distributed
ISRU
system with the
SWE
system on the moon and the
DWE
system on
EML1
.
Based on the
ISRU
subsystem-level modeling established in Ref. [
15
], for 5.6% water concentration lunar regolith, a 1
kg
SWE
reactor can extract 31.4 kg water per year, and a 1 kg
DWE
reactor can electrolyze 105.2 kg water per year. We
assume a continuous operation of
ISRU
systems during the space mission. The
ISRU
system also contains multiple
subsystems to support the operation of the reactors, such as the power system, storage system, soil extraction system, etc.
In this analysis, we assume these subsystems are integrated into the
SWE
and
DWE
systems. As a result, we added
a 200% overhead mass for these subsystems as the baseline
ISRU
productivity. Therefore, 1 kg of
SWE
reactor can
15
extract 10.5 kg of water per year, and 1 kg of
DWE
system can electrolyze 35 kg of water per year. For the economies
of scale model, the
ISRU
plant mass is a concave function of the
ISRU
productivity. However, in logistics mission
planning,
ISRU
structure is part of the commodity flow variables. Therefore, we switch the x and y axes to create a
model where the
ISRU
productivity is a function of the
ISRU
structure mass. The economies of scale model derivation
is still valid. With the increase of system mass, we assume the
ISRU
productivity will increase 10% per 3000 kg of
structure mass. The baseline manufacturing cost is assumed as the same for both the
SWE
system and the
DWE
system
based on the structure mass, $10,000/kg [
15
]. As the increase of the structure mass, the
ISRU
system manufacturing
cost per unit mass will decrease 10% per 3000 kg [16, 17]. The sizing and cost models of ISRU are shown as follows:
𝑁water (𝐹SWE)=
10.5𝐹SWE ∀𝐹SWE ∈ (0,3000]
𝑁water (3000) + 10.5× (1+10%)(𝐹SWE −3000) ∀𝐹SWE ∈ (3000,6000]
𝑁water (6000) + 10.5× (1+10%)2(𝐹SWE −6000) ∀𝐹SWE ∈ (6000,9000]
.
.
.
(38)
𝑁water (𝐹DWE)=
35𝐹DWE ∀𝐹DWE ∈ (0,3000]
𝑁water (3000) + 35 × (1+10%) (𝐹DWE −3000) ∀𝐹DWE ∈ (3000,6000]
𝑁water (6000) + 35 × (1+10%)2(𝐹DWE −6000) ∀𝐹DWE ∈ (6000,9000]
.
.
.
(39)
J
ISRU(𝐹ISRU)=
J
ISRU(1000) ∀𝐹ISRU ∈ (0,1000]
J
ISRU(1000) + 10000(𝐹ISRU −1000) ∀𝐹ISRU ∈ (1000,3000]
J
ISRU(3000) + 10000 × (1−10%) (𝐹ISRU −3000) ∀𝐹ISRU ∈ (3000,6000]
J
ISRU(6000) + 10000 × (1−10%)2(𝐹ISRU −6000) ∀𝐹ISRU ∈ (6000,9000]
.
.
.
(40)
The nonlinear functions in Eqs.
(38)
-
(40)
represent piecewise-defined economies of scale relationships, where each
interval accounts for different structural efficiencies and cost scaling factors. Equations
(38)
-
(40)
are depicted in Fig. 4.
In these functions,
𝑁water
is the annual water processing mass of the
ISRU
system,
𝐹ISRU
is the structure mass for
SWE
and
DWE
systems, and
J
ISRU
is the
ISRU
manufacturing cost. The maintenance of the
ISRU
system is also considered.
It is assumed that the maintenance spares required are equal to 5% of the
ISRU
structure mass, and the manufacturing
cost of maintenance spares is always $10,000/kg.
After resources are generated, we need spacecraft to deliver them to the demanding node. For the simplicity of the
16
0 1000 2000 3000 4000 5000 6000 7000 8000 9000
F
0
50000
100000
150000
200000
250000
300000
350000
Nwater
Piecewise Functions
Nwater
and
ISRU
Nwater
(
FSWE
) (0-3000]
Nwater
(
FSWE
) (3000-6000]
Nwater
(
FSWE
) (6000-9000]
Nwater
(
FDWE
) (0-3000]
Nwater
(
FDWE
) (3000-6000]
Nwater
(
FDWE
) (6000-9000]
0
10000000
20000000
30000000
40000000
50000000
60000000
70000000
80000000
ISRU
ISRU
(
FISRU
) (0-3000]
ISRU
(
FISRU
) (3000-6000]
ISRU
(
FISRU
) (6000-9000]
Fig. 4 Sizing and cost models of ISRU.
optimization, we do not consider the concurrent sizing of spacecraft in this paper. Instead, we use spacecraft with a fixed
design. Based on the design of Advanced Cryogenic Evolved Stage (
ACES
) [
11
] spacecraft and Centaur [
18
] spacecraft,
the propulsive stage of this spacecraft uses LO2/LH2as the propellant. Therefore, the oxygen and hydrogen generated
by the
ISRU
can also support the spaceflight of the spacecraft. The propellant mass ratio of oxygen and hydrogen is
5.5:1. The structure mass of the spacecraft is assumed as 6,000 kg, and it has a propellant capacity of 65,000 kg. The
manufacturing cost of one spacecraft is $150M, and the operation cost per spaceflight is $0.5M. We assume that there
are two spacecraft available on the Earth at the beginning of each time window. We assume that water and LO
2
/LH
2
propellant are both delivered and stored through specific water and propellant tanks. The water tank capacity ratio
is assumed as 40 kg of
H2O
per kg of tank mass and its cost is $800/kg. However, the transportation of oxygen and
hydrogen requires cryogenic cooling systems to prevent boil-off. The LO
2
/LH
2
propellant tank capacity ratio is assumed
as 1.478 kg of LO
2
/LH
2
per kg of tank and its cost is $1,869/kg. The assumptions for mission operation are summarized
in Table 3.
17
Table 3 Assumptions of mission operation.
Parameter Assumed Value [11, 15]
Mission Operations
Propellant LO2/LH2
𝐼𝑠 𝑝 420 s
Time window Every 6 months
Spacecraft propellant capacity 65,000 kg
Spacecraft structure mass 6,000 kg
Available spacecraft each time window 2 spacecraft
Water Tank Capacity Ratio 40 kg of H2O capacity per kg of tank
Propellant Tank Capacity Ratio 1.478 kg of LO2/LH2per kg of tank
ISRU maintenance 5% plant mass/year
Cost Models
Rocket launch cost $5,000/kg
Spacecraft manufacturing cost $150M each
Spaceflight operation cost $0.5M/flight
Water Tank Cost $800/kg
Propellant Tank Cost $1,869/kg
LO2cost on Earth $0.15/kg
LH2cost on Earth $5.97/kg
ISRU maintenance spares cost $10,000/kg
B. Results and Analysis
1. Mission Planning Results
We perform mission planning to satisfy the transportation mission demands defined in Table 2 for three consecutive
years. To compare the performances of concentrated and distributed
ISRU
systems during their steady-state operations,
we assume the deployment of an initial 1000 kg
ISRU
plant at the start of the mission. This initial deployment aims to
mitigate the impact of the setup phase, particularly for distributed
ISRU
systems, which require longer times to become
fully operational.
As seen in Table 4, the total mission cost using concentrated
ISRU
is $2.922B, and an 11,028 kg
ISRU
system is
deployed in total. In comparison, the total mission cost using distributed
ISRU
is $2.916B, and a 11,601 kg
ISRU
system is deployed.
Figures 5 and 6 illustrate detailed mission planning solutions using concentrated and distributed ISRU systems.
Comparing these two figures, first, we can find that for the deployment demand at
GEO
, the logistics system chooses
a LEO-EML1-GEO logistics path instead of a LEO-GEO logistics path. This is because spacecraft can get refueled
at
EML1
from the lunar
ISRU
, which makes the spaceflight from
EML1
to
GEO
get rid of relying on the propellant
launched from Earth. However, as shown in Fig. 6, part of the payload is still deployed through the LEO-GEO path.
This is caused by the long setup phase of the distributed
ISRU
system. In this mission scenario, the
SWE
system needs
18
to extract water from the lunar surface. Then, part of the water is electrolyzed by the
DWE
plant deployed on the moon,
and the remaining water needs to be transported to the
DWE
plant deployed on
EML1
to generate propellant. The lead
time of water logistics delays the propellant generation, which elongates the setup of the distributed ISRU system.
ISRU = 11028 [kg]
1
1
1
ISRU = 11028 [kg]
Time
Step
LEO
Earth
EML1
Moon
GEO
MST
(Day) 360
0123
720
0123
012
0
3
1
2
1
11
1
4
Payload=40000[kg]
1
2
Payload=40000[kg]
2
1
11
Propellant
Payload ISRU
ISRU plant deployed
MST: Mission Start Time
Holdover arc
Maintenance
NSpacecraft: ACES
(N is number of spacecraft)
1
1080
0123
1
4
Payload=40000[kg]
1
1 1
Payload Delivered
1
1 1
1
1
1
Fig. 5 Mission planning using concentrated ISRU.
ISRU =11601[kg]
1
1
1
ISRU = 10965 [kg]
Time
Step
LEO
Earth
EML1
Moon
GEO
MST
(Day) 360
0123
720
0123
012
0
3
1
1
1
11
4
1
Payload=40000[kg]
1080
0123
1
1
Payload=40000[kg]
1
211
2
1
Payload=40000[kg]
1
1
540
01
11
5
1
1
Propellant
Water ISRU
SWE ISRU plant
MST: Mission Start Time Maintenance
NSpacecraft: ACES
(N is number of spacecraft) DW E ISRU plantHoldover arc
Payload
Payload Delivered
ISRU =636 [kg]
4
1
1
1
1
1
1
1
2
1
1
Fig. 6 Mission planning using distributed ISRU.
2. Impact of a Setup Phase
To evaluate the impact of the
ISRU
system setup phase, we consider mission planning with a one-year setup
phase where mission demands are satisfied starting from the second mission. The mission planning solutions using
concentrated and distributed
ISRU
systems are shown in Fig. 7 and Fig. 8, respectively. When a long setup phase is
considered at the beginning of the mission, the total mission cost using a distributed
ISRU
system, $2.083B, is lower
19
than using a concentrated ISRU system, $2.147B. As we can see in both solutions, the transportation to
GEO
always
receives support from the propellant generated by ISRU.
1
1
ISRU = 6300 [kg]
1
1
1
ISRU = 6300 [kg]
Time
Step
LEO
Earth
EML1
Moon
GEO
MST
(Day) 720
0123
012
0
3
2
2
1
1
4
1
Payload=40000[kg]
1080
0123
1
1
Payload=40000[kg]
1
1
4
1
1
1
Propellant
Payload ISRU
ISRU plant deployed
MST: Mission Start Time
Holdover arc
Maintenance
NSpacecraft: ACES
(N is number of spacecraft) Payload Delivered
1
Fig. 7 Mission planning using concentrated ISRU with setup phase.
ISRU = 9295 [kg]
1
1
1
ISRU =8154 [kg]
Time
Step
LEO
Earth
EML1
Moon
GEO
MST
(Day) 360
0123
720
0123
012
0
3
1
2
1
1
1
1
4
Payload=40000[kg]
1080
0123
2
2
Payload=40000[kg]
1
1
1
1
4
1
5
1
1
Water ISRU
SWE ISRU plant
MST: Mission Start Time Maintenance
NSpacecraft: ACES
(N is number of spacecraft) DWE ISRU plantHoldover arc
Payload
Payload Delivered
Propellant
ISRU = 1141 [kg]
1 1
Fig. 8 Mission planning using distributed ISRU with setup phase.
This result analysis shows that with a proper setup phase, a distributed
ISRU
system can support the cislunar
logistics processes with multiple deployment demands at a lower cost. Note that the conclusion from this case study is
20
Table 4 Comparison of ISRU systems
Concentrated ISRU Distributed ISRU
Without Setup Phase
Total Mission Cost $2.922B $2.916B
ISRU Mass Deployed 11,028 kg 11,601 kg
With Setup Phase
Total Mission Cost $2.147B $2.083B
ISRU Mass Deployed 6,300 kg 9,295 kg
based on the specific mission demands and mission operation assumptions. It may not be valid for the performance of
distributed
ISRU
in general. However, the main contribution of this paper is to enable such a trade study to compare the
performance of distributed ISRU and concentrated ISRU in supporting a complex multi-mission logistics campaign.
3. Sensitivity Analysis
The sensitivity analysis in this study explores the variability of
ISRU
total mission costs under different operational
conditions. This analysis explores how changes in key parameters, such as the mission duration,
ISRU
productivity
rates, setup phase inclusion, and production efficiency, impact the overall mission cost.
The sensitivity analysis begins by examining the relationship between mission cost and duration for both concentrated
and distributed ISRU systems, as shown in Fig. 9. The results indicate that while costs increase with mission duration,
distributed ISRU consistently achieves lower costs. The baseline at year 3 marks a turning point where cost trends begin
to diverge, highlighting the long-term benefits of distributed ISRU’s multi-location deployment strategy.
Beyond mission duration, another critical factor influencing total mission cost is the productivity rate of ISRU
systems, which determines resource extraction and processing efficiency. The baseline productivity rates of the
ISRU
systems, exploring how different levels of resource processing efficiency impact mission costs. The
ISRU
productivity
rates of resource utilization for extraction and processing were varied across different scenarios to evaluate their impact
on total mission costs. Figure 10 shows the correlation between total mission costs and
ISRU
productivity rates for both
concentrated and distributed
ISRU
systems, considering the inclusion and exclusion of the setup phase. We notice that as
the productivity rates increase, the mission costs for all
ISRU
systems decrease significantly. Notably, distributed
ISRU
with the setup phase shows a steeper reduction in costs compared to scenarios without the setup phase, highlighting that
incorporating the setup phase strategically or optimizing its duration can significantly enhance cost-effectiveness.
The baseline
ISRU
productivity rate at 1.0
×
marks a point where distributed
ISRU
begins to outperform or closely
match concentrated
ISRU
in cost savings. Beyond this baseline, the cost benefits of further productivity increases
continue to grow, highlighting even greater potential for cost savings through enhanced
ISRU
efficiency. This analysis
shows the strategic advantage of distributed
ISRU
systems in achieving significantly lower costs for large-scale missions,
especially when the setup phase is optimized or minimized, allowing for more efficient and cost-effective missions.
21
2345678910
Mission Duration, years
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
Mission Cost, $B
Baseline
Total Cost Concentrated ISRU w/o setup phase
Total Cost Distributed ISRU w/o setup phase
Total Cost Concentrated ISRU
Total Cost Distributed ISRU
Fig. 9 Total cost vs mission duration (with/without setup).
0x 0.25x 0.5x 0.75x 1x 1.25x 1.5x 1.75x 2x
ISRU Productivity Rates
1.8
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
3.6
3.8
4.0
Mission Cost, $B
Baseline
Total Cost Concentrated ISRU w/o setup phase
Total Cost Distributed ISRU w/o setup phase
Total Cost Concentrated ISRU
Total Cost Distributed ISRU
Fig. 10 Total Cost vs ISRU Productivity Rates (With/Without Setup).
22
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
Volume Discount Productivity
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
Mission Cost, $B
Baseline
Total Cost Concentrated ISRU w/o setup phase
Total Cost Distributed ISRU w/o setup phase
Total Cost Concentrated ISRU
Total Cost Distributed ISRU
Fig. 11 Total Cost vs ISRU Volume Discount (With/Without Setup).
Following this, the effect of volume discount on productivity was assessed, highlighting how increased production
volumes can reduce costs. Figure 11 examines the impact of volume discounts on
ISRU
productivity, indicating that as
volume discount of productivity increases, mission costs decrease substantially. The graph demonstrates that while
the exclusion of a setup phase initially leads to higher costs, the advantages of volume discounts become increasingly
evident in distributed ISRU systems as the scale increases.
Next, the impact of cost discounting due to economies of scale is analyzed, and Fig. 12 evaluates the effect of
cost discounts on mission expenses across various
ISRU
configurations. The analysis reveals that while cost discounts
contribute to lowering mission costs, their impact is relatively modest compared to improvements achieved through
productivity rate increases and volume scaling.
Finally, the analysis considered the effect of different mass scaling intervals for the
ISRU
systems, providing insights
into how changes in the economies of scale on deployed systems influence overall mission costs. A larger ISRU mass
scaling interval means that volume and cost discounts occur at a higher ISRU system mass. Figure 13 compares the
total mission cost and ISRU mass for distributed and concentrated
ISRU
systems across various mass scaling intervals.
The concentrated
ISRU
, with lower system mass, has a higher mission cost, which reflects the challenge of deploying a
centralized infrastructure entirely on the lunar surface. This approach leads to higher expenses despite the reduced mass.
In contrast, the distributed ISRU has a higher system mass, but achieves lower mission costs. This occurs due to the
strategic deployment of some subsystems closer to Earth, such as
EML1
, reducing the logistics and transportation costs.
23
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
Volume Discount Cost
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
Mission Cost, $B
Baseline
Total Cost Concentrated ISRU w/o setup phase
Total Cost Distributed ISRU w/o setup phase
Total Cost Concentrated ISRU
Total Cost Distributed ISRU
Fig. 12 Total Cost vs ISRU Cost Discount (With/Without Setup).
This shows that while distributed
ISRU
requires more mass to be deployed in the discussed mission scenarios, it is
cost-saving due to the flexibility of multi-location deployment strategy. Moreover, when the ISRU mass scaling interval
becomes larger, meaning a weaker economies of scale effect, the distributed
ISRU
deployment strategy leads to a lower
mission cost.
This approach offers a deeper understanding of the interplay between ISRU productivity, volume and cost discounts,
and mass scaling, ultimately guiding the identification of optimal operating conditions and cost-saving strategies in
mission design.
C. Discussion
This study examines the trade-offs between concentrated and distributed ISRU architectures, considering their cost,
mass, and logistical complexities. While distributed ISRU reduces reliance on Earth-launched propellant, it introduces
operational complexity due to transportation constraints between the lunar surface and
EML1
. Unlike a concentrated
ISRU
system, a distributed
ISRU
requires additional logistical coordination, increasing the risk of transportation
disruptions and delays in resource delivery. Given that the cost difference between concentrated and distributed ISRU is
relatively small and less than 5%. This is within the range of uncertainty typical for space mission cost estimates, and
thus additional flexibility in logistics planning is required to mitigate potential risks.
While distributed ISRU introduces greater complexity, it strengthens mission robustness by providing multiple
24
1000 1500 2000 2500 3000 3500 4000 4500 5000
ISRU Mass Interval (kg)
2.90
2.91
2.92
2.93
2.94
2.95
2.96
2.97
Mission Cost, $B
Baseline
Total Cost Concentrated ISRU
Total Cost Distributed ISRU
5000
6000
7000
8000
9000
10000
11000
12000
13000
14000
15000
ISRU Mass (kg)
ISRU Mass Concentrated
ISRU Mass Distributed
Fig. 13 Impact of ISRU Mass Scaling on Cost and System Mass without setup phase.
supply nodes and reducing dependence on Earth-based launches. To further quantify the impact of uncertainties in
transportation, operational constraints, and
ISRU
system performance, a sensitivity analysis was conducted, extending
the mission horizon beyond three years to determine whether distributed ISRU remains advantageous over longer
durations. The results indicate that even as uncertainties are introduced, distributed ISRU continues to demonstrate
long-term benefits in resource availability and cost efficiency.
The inherent uncertainties in cost modeling for space hardware must also be acknowledged. Specifically, cost
estimates are influenced by technology readiness levels, operational constraints, and economies of scale, which introduce
significant variability. Figures 9 and 13 further highlight that distributed ISRU remains favorable under assumed scaling
relationships, though real-world deployment scenarios may introduce unexpected cost and mass deviations.
IV. Conclusion
This paper proposes an optimization framework for distributed resource logistics system design. It integrates
piecewise linear sizing and cost estimation models developed based on economies of scale into network-based space
logistics optimization methods. This framework enables concurrent optimization for
ISRU
technology trade studies,
deployment strategies, facility location evaluation, and resource logistics after generation, considering nonlinear sizing
and cost models. A cislunar logistics case study is conducted to demonstrate the value of the proposed method. The
results show that distributed
ISRU
can support a multi-demand cislunar logistics mission at a lower cost than the
25
concentrated
ISRU
under the assumed mission scenario. This case study also indicates that decision-makers can evaluate
potential logistics architectures and ISRU technologies using the proposed optimization framework.
The sensitivity analysis highlights the benefits of distributed
ISRU
systems, showing that enhanced
ISRU
productivity
rates and effectively managing the setup phase can significantly reduce mission costs. Enhanced productivity and
strategic setup in distributed
ISRU
lead to lower costs than concentrated
ISRU
systems. Economies of scale, including
volume and cost discounts, further contribute to cost reductions, underscoring the strategic advantage of distributed
ISRU for large-scale, long-duration missions and optimizing overall cost efficiency.
Future research directions include assessing the resilience of distributed and concentrated
ISRU
systems under
uncertainties and analyzing the impact of these uncertainties on the transportation system. Research can also be done
to consider the interactions among different
ISRU
plants in the cislunar system, further refining the optimization of
resource logistics for space missions.
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