Supply Chain Modelling: Multi Objective Robust Optimization Model for Facility Layout Design
Summary
TLDR在本次供应链建模小组的会议中,来自印尼大学的Gina Natalia Prayago女士介绍了她的论文《多目标鲁棒优化模型在需求不确定性下的设施布局设计》。该研究强调了设施布局规划在制造业中的重要性,指出操作成本的20%至50%依赖于设施规划和物料搬运设计。论文提出了一种新的多目标鲁棒优化模型,考虑了产品需求的不确定性,并通过优化模型来最小化物料搬运成本、最大化总议程和空间利用率。研究使用了离散场景表示需求不确定性,并通过Kuromori优化器和Python进行求解,展示了模型在实际案例中的应用。最后,演讲者提出未来可以开发启发式算法以获得更高效的运行时间和接近最优解的解决方案。
Takeaways
- 📈 多目标鲁棒优化模型被提出用于在需求不确定性下进行设施布局设计。
- 🏭 设施布局规划对制造业成本有显著影响,约占运营成本的20%至50%。
- ⚙️ 考虑需求不确定性的设施布局优化模型目前研究较少。
- 🔍 产品需求的不确定性影响物料流动频率,进而影响部门的有效定位。
- 📏 使用距离公式计算部门间的物理距离,并用以评估部门间的接近度。
- 📊 通过多目标鲁棒优化方法,考虑生产需求的不确定性,最小化物料搬运成本。
- 🎯 三个目标函数:最小化预期总物料搬运成本,最大化总接近度,最大化空间利用率。
- 🛠️ 模型使用离散场景表示需求的不确定性,并通过二进制变量表示部门的方位。
- 📉 模型包括了多种参数,如部门的尺寸、产品需求、搬运成本等,以及它们之间的函数关系。
- 🔢 通过Kuromoji优化器和Python解决模型,得到最优解,包括部门的位置和方向。
- 📚 论文提出了一个精确模型,并建议开发启发式算法以获得更高效的运行时间和近似最优解。
Q & A
什么是设施布局规划在制造业中的重要性?
-设施布局规划是制造业中的一个重要因素,因为它可以影响制造系统中大约20%到50%的运营成本。有效的设施布局设计可以导致操作成本的显著变化,大约在10%到20%之间。
为什么在设施布局规划中考虑需求的不确定性很重要?
-产品需求的不确定性会影响物料流动频率的不确定性,进而影响部门之间有效定位的重要性。因此,考虑需求不确定性的优化模型对于设施布局规划至关重要。
在设施布局设计中,如何计算部门之间的距离?
-在设施布局设计中,使用距离公式来计算部门之间的距离。每个部门都有一个中心点,用Xi和Yi表示,部门之间的距离会影响其功能需求。
在提出的多目标鲁棒优化模型中,有哪些目标函数?
-在提出的多目标鲁棒优化模型中,有三个目标函数:第一是最小化预期的总物料搬运成本;第二是最大化总的接近度;第三是最大化空间利用率。
如何使用离散场景来表示产品需求的不确定性?
-在模型中,使用离散场景来代表产品需求的不确定性。每个场景都与一定的概率相关联,这些概率用于在模型中表述需求的不确定性。
在模型中,如何考虑部门的取向?
-部门的取向通过考虑部门的长度和宽度以及它们相对于x轴的方向来定义。取向影响部门之间的距离,进而影响设施布局规划。
在提出的模型中,如何确保部门的布局既有效又符合空间限制?
-模型通过一系列约束来确保部门布局的有效性和符合空间限制,包括部门的尺寸、部门之间的距离、以及部门在x和y轴方向上的位置。
在模型中,如何考虑物料搬运成本?
-模型中考虑物料搬运成本是通过计算从一个部门到另一个部门搬运单位物料的距离乘以搬运成本来实现的。
在提出的模型中,如何量化部门之间的接近度?
-部门之间的接近度是通过评估部门之间的距离和它们之间的关系来量化的。接近度用一个介于0到5之间的数值来表示,其中5表示最大程度的接近。
在实际应用中,如何使用Kuromobi优化器来解决这个多目标鲁棒优化问题?
-通过将问题输入到Kuromobi优化器中,并使用Python编程语言来求解,可以得到最优解,包括部门的最佳位置和取向。
在演讲中提到的数值例子中,可用区域的尺寸是多少?
-在数值例子中,可用区域的长度是55单位,宽度是40单位。
在演讲中,对于模型的运行时间和效率有什么建议?
-演讲中提到,虽然使用的是精确模型,但为了获得更高效的运行时间和接近最优解,可以开发启发式算法。
Outlines
😀 会议介绍与开场
本段介绍了会议的背景和参与者。会议在印尼的3号房间举行,主题是供应链建模。会议由Imam主持,他是来自IBS的专业人士,也是Kujawan的同事。第一位演讲者是来自印尼拉比大学(University of Rabbii)的Gina Natalia Prayago小姐。她的论文标题是“需求不确定性下的多目标鲁棒优化模型:设施布局设计”。演讲者Tina Natalia和她的同事Olivia来自苏拉巴亚工业工程系,他们将介绍设施布局规划的重要性,以及如何通过考虑需求不确定性来优化设施布局设计。
📈 设施布局规划的多目标鲁棒优化模型
这一段深入讨论了设施布局规划的多目标鲁棒优化模型。模型考虑了需求的不确定性,旨在最小化总的物料搬运成本。模型包括两个主要部分:一是解决方案的稳健性,二是模型的广泛性。使用离散场景来表示需求的不确定性。模型有三个目标函数:最小化预期总物料搬运成本、最大化总议程价值和最大化空间利用率。模型还包括了各种参数和约束条件,如部门间的代理因子、部门的尺寸和方向、产品需求数据等。
🔍 模型开发与应用示例
本段介绍了多目标鲁棒优化系统模型的开发过程,以及如何将其应用于实际的设施布局问题。模型考虑了产品类型、生产过程流程、部门间的关系以及代理因子。模型使用了一系列的索引、函数和数据,如概率场景、移动成本、部门间距离、可用面积的尺寸和重量、产品类型的需求数量等。通过一个数值例子,展示了如何使用Kuromobi优化器和Python来解决这个问题,并得到了最优解,包括部门的位置和方向。
🏆 结论与讨论
在最后一段中,演讲者总结了提出的多目标鲁棒精确模型,并讨论了模型的应用。他们提到,尽管模型基于成本最小化,但并没有考虑吞吐量作为随机变量,而是假设为一个阶段。演讲者提出,未来可以开发启发式算法以获得更高效的运行时间和接近最优的解决方案。最后,演讲者感谢听众的注意,并邀请听众通过虚拟鼓掌来表达对演讲的赞赏。
Mindmap
Keywords
💡供应链建模
💡多目标鲁棒优化
💡设施布局设计
💡需求不确定性
💡物料搬运成本
💡工业工程
💡优化模型
💡目标函数
💡离散场景
💡部门间关系
💡位置决策
Highlights
会议由Imam主持,他来自IBS,是Kujawan的同事。
第一位演讲者是来自印尼拉比大学工业工程系的Gina Natalia Prayago女士。
论文标题为'需求不确定性下的多目标鲁棒优化模型:设施布局设计'。
设施布局规划在制造业中非常重要,因为它影响着制造系统中约20%至50%的运营成本。
研究提出了一种考虑需求不确定性的多目标鲁棒决策模型。
模型使用距离公式计算部门之间的距离,并考虑了部门的接近度。
模型采用鲁棒优化来表述需求的不确定性,并最小化总物料搬运成本。
模型包含三个目标函数:最小化预期总物料搬运成本、最大化总接近度和最大化空间利用率。
模型使用离散场景来表示需求的不确定性,并通过Python和Kuromobi优化器求解。
通过数值例子展示了模型的应用,包括可用区域尺寸、部门间距离、产品流程和需求数据。
模型考虑了部门规格、方向以及部门间的功能关系,这些参数将影响部门间的距离。
模型使用了显著正数'big M'作为约束条件之一,以确保部门间不会重叠。
模型的决策变量包括部门的中心位置、长度和重量。
模型通过二进制变量来表示部门的朝向,平行于x轴方向为1,垂直于x轴方向为0。
模型的约束条件包括部门长度和宽度的设置,以及部门在x轴和y轴方向上的一般位置。
通过线性化维护距离公式,模型能够处理部门间距离的约束。
演讲者提到,虽然模型主要基于成本最小化,但并没有将吞吐量作为目标函数的一部分。
演讲者建议未来研究可以开发启发式算法,以获得更高效的运行时间和接近最优解。
Transcripts
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trouble
okay that's good okay please stay there
because you will be the first one okay
okay let's we'll start okay we'll start
okay everybody thank you very much thank
you very much for joining this session
this is uh in room 3 uh with the group
of supply chain modelings
okay it's a 335 noise in indonesia
we would like to start with the first
presenter thank you everybody for
coming in and thank you for observing
also coming in here
uh in this session the first presenters
by the way my name is imam i'm from ibs
i'm the colleague of professional human
kujawan
okay so the first presenter is
mr miss gina natalia prayago from
university of rabbi indonesia
uh the pep the title of the paper is
multi-objective robust optimization
model
for facility layout design under demand
uncertainties
is yours
okay thank you uh
thank you for everybody good afternoon
uh
thank you for this time given to
us to present our paper with the title
multi-objective robust optimisation
model
for facility level design under demand
uncertainty
my name is tina natalia and my friend is
olivia
we are from uh department of industrial
engineering university of surabaya
indonesia this is again
our presentation uh start a introduction
followed by a problem statement and
model development
discussion of the research of
implementation of this model
and finally we have a conclusion
for the first introduction facility
layout
planning is an important factor
in the manufacturing industry because
around 20 percent
up to 50 of the operational costs
in the manufacturing system depend on
facility planning and material handling
design
material rendering costs efficiency from
an optical
facility layout with resulting
operational cost shifting
of approximately 10 to 20 percent
so far few uh researchers has
been done on the optimization model of
facility layout planning
that took into account the uncertainty
of demand for
its type of support
the uncertainty of product demand has an
impact
on the uncertainty of material movement
frequency
between batman which affect
the every effective positioning of the
department as a
component of material handling of course
therefore this paper will propose a
mother
multi of objective robust of the
decision model for
unequal uh real facility layout training
by considering the uncertainty of
productive men
as you know it is a facility like our
for example we have several
departments with its apartment
we have a center of
its departments still in x y
and x i and y i as a centroid of its
abutment
in this case uh we use the distance
formula to calculate the distance
between uh
and each department uh have agency uh
requirements uh that's your uh
distance about uh between the
department the objective requirement uh
we're not uh using nation a e
i o u and x uh
the appreciator distance uh
between uh department is uh
for example uh approximately or
extremely
disabled closers uh so we use the
extensive value
scores is five as a maximum
and zero is the minimum or undisabled
closely between two departments
and descendants of uh adjective vectors
uh
will depend on the this this distance uh
between
department i and g
maximum adjective factor is one and
which
minimum is zero
we use robust optimization our model
to formulate the uncertainty uh
demand in our
minimize the total uh
material handling cost uh in this model
we have
uh two uh terms the first term is using
solution of and second terms is used to
characterize the
model of vastness we use a discrete
scanner to represent
our answer demand
as a problem statement for each project
we have a process flow uh and
its department uh required to process
that product
and unit load between a department
they also have a product uh demand data
uh that in this case uh consider
the uncertainty uh demand this uh
three data will influence the frequency
between
the movement frequency between
department
and we have the department specification
and orientation department orientation
means
we use the length of batman
in parallel x-axis direction or in
particular
x-axis orientation
and we have a functional relationship
that uh
influencer agency requirement uh this
parameter will influence the distance
between
departments and to find the
facility of planning
we use multi-objective robust
optimization we have three
uh objective function what the first is
minimize the expected total material
handling cost
second objective function is maximize
the total
agendas and the third is maximize
space utilization ratio
now we uh done to the water
uh development the development of the
multi
uh objective robust of the system model
for
unequal uh a real facility layout
problem is carried by considering demand
uncertainty for its uh type of product
uh the production process flow uh for
its
uh product type catalyst of its
department departmental
relationship which is stated in the
agency factor between departments
this model has indices uh i
n g uh as a set of apartment k
as a function
and s discrete scanners
some data as a motor parameters needed
in these models
probability for its scenario
we use discrete scenarios and
cost of moving criteria perfume
unit distance between apartment i to
department
and vitamin g g and
adjacent value of department i to
department j
uh length and weight of available area
number of demand for product type
p in scenario s and
unit load from department id department
for each type product
minimum and maximum line of batman i
required for department i minimum and
maximum
weight of department minimum uh
weight of ether between the batman i to
department
in x-axis direction
and y-axis direction and
big m as a significant positive number
the decision numbers consists of x
i and y i see the centroid of position
of the atom and i
in x and y that is a direct direction
and length or uh of department i
uh weight of department i uh as a
decision variable
uh jesus function uh between the vitamin
i and department
and g uh the function of a distance or
between the batman eye and the vitamin c
that is we calculate using health and
distance function
decent function distance between
the centroid of the batman either the
centroid of the vitamin c
in x direction and y axis direction
and the orientation you have five
minutes
okay thank you thank you
we use uh type of orientation
uh we use a binary forever one
one or zero if the line of department is
in parallel with x
axis direction or vertical with x-axis
direction
it's a formula of multi-objective
in our model
the first is minimizes the total uh the
expected total
cost of moving the between department
uh in planning horizon uh horizon
and the second is maximizing the total
attention values between department
based on the relationship and the
distance between departments
and the lessons maximize the utilization
ratio of the music area for all
departments to
available area
there are some constants to be
considered in our
model because we use a robust
optimization of the first is
the expected total cost of material
transparency with apartments
and we comfortable linearization
epsilon of the distance and the
frequency
of transfer department people different
department
for its scenario in constant six
my attention function is to calculate
the
distance between department in concern
seven constraints eight and
9 set the length
and which rings for its batman
and constrained tan and 11 is the
general position
of its department in x
and y axis direction
uh constraint 12 up to
14 to
ensure that its apartment is without uh
of for wrapping in both uh
dimension and the relationship between
the position department and the system
uh distance between departments is uh
still in the constraint 15 to 17
and maximum distance between departments
stated in the
constraint 18 and all the
decisions for er performance we
studied the constraint 19 up to
25 linearization of the maintenance
distance formula
is followed we use a numerical example
to see the uh application of this model
uh the available area uh with the length
of 55 units and the width is 40
units it's in
x and y direction between departments
is three units
this is the data for the sequence
of production process flow for its
type of products we have 12
product processes in the
8 departments this is the demand
for each scenario the unit load
between uh department for its project
the determinations rings in uh length
and width of
the its pro department the lower and
upper
length and lower and upper width
for its apartment and material handling
costs for
unit 15 apartments
the example for scenario 1 the frequency
of transfer between department
and here in this step
and we solve this problem using a kurobe
optimizer python and get the
optimal solution uh the position uh
and the orientation uh so the uh
orientation is showing a binary uh
variable
set eye one is the uh the
line of department is uh parallel the x
uh
x is the direction and zero for
department three and
uh department uh seven and eight is uh
particular with the x axis direction
which is the distance between apartment
and the consequence of jensen texture
between department
so means department one should go
between department one and the first one
it
[Music]
with the three objective function as a
conclusion
um multiple uh objective robust
precision has been proposing this uh
paper
uh we use uh three objective or function
uh as
mentioned before and this in this paper
we
use a exact model uh so for the
next reasons we can develop
the heuristic of materialistic uh to get
more efficient runtime with the near
optimal solution
sometimes we use it and
thank you for your attention
thank you very much mr
for her presentations and
yeah could you please give applause to
miss dina by using
virtual applause clicking reaction and
below the screen
okay uh before we move on to the next
presenter i would like to
invite everyone if you have any question
to miss dana
the questions perhaps uh i have one
question before we move on
uh miss dinah you measure the uh
this model based on cost minimizations
what about what about the throughput do
you also
measure the throughput of this uh
layer on
yes because the time uh
we do not consider as a stochastic
so the top of this uh effects in this uh
problem we assume is phase so we now
measure as a objective in our mortar
okay okay thank you very much
okay thank you okay thank you miss dino
for your presentations
the next one thank you yes
thank you
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