Supply Chain Modelling: Multi Objective Robust Optimization Model for Facility Layout Design

Summary

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

00:00

😀 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。

05:02

📈 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。

10:05

🔍 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。

15:08

🏆 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。

Keywords

💡供应链建模

供应链建模是用于分析和管理供应链中的产品流、信息流和资金流的一种方法。在视频中，它与会议的主题相关，即讨论如何在需求不确定性下进行设施布局设计。

💡多目标鲁棒优化

多目标鲁棒优化是一种在不确定性条件下寻找最优解的数学方法，它考虑了多个目标函数并试图找到平衡这些目标的解决方案。视频中提到的模型旨在最小化物料搬运成本、最大化总议程价值以及最大化空间利用率。

💡设施布局设计

设施布局设计是确定制造系统中各个部门或设施的物理位置的过程。它对运营成本有显著影响，视频中提到，大约20%至50%的运营成本取决于设施规划和物料搬运设计。

💡需求不确定性

需求不确定性指的是产品需求在未来可能变化的不确定性。视频中强调了在设施布局设计中考虑需求不确定性的重要性，因为它影响物料流动的频率和部门的有效定位。

💡物料搬运成本

物料搬运成本是指在生产过程中，将原材料、半成品或成品从一个地点移动到另一个地点所产生的成本。视频中提出的模型旨在最小化这一成本，这是制造系统中一个重要的考虑因素。

💡工业工程

工业工程是一门应用数学、物理学和社会科学原则于生产和运营过程的学科，旨在提高效率和生产力。视频中的演讲者来自工业工程系，他们研究的设施布局设计问题属于工业工程的研究范畴。

💡优化模型

优化模型是一种数学模型，用于在给定的约束条件下找到最优解，以最大化或最小化一个或多个目标函数。在视频中，优化模型被用来处理设施布局设计问题，特别是在需求不确定的情况下。

💡目标函数

目标函数是优化问题中用于评估解决方案质量的数学表达式。视频中提到的模型包含三个目标函数：最小化预期总物料搬运成本、最大化总议程价值和最大化空间利用率。

💡离散场景

离散场景是描述不确定性的一种方法，通过定义一系列可能的未来状态来表示不确定性。视频中的模型使用离散场景来表示需求的不确定性，并以此来构建鲁棒优化模型。

💡部门间关系

部门间关系指的是组织内部不同部门之间的相互作用和依赖。在设施布局设计中，部门间的关系影响物料流动的频率和路径，视频中提到的“代理因素”就是用来量化这种关系的。

💡位置决策

位置决策是确定组织内各个部门或设施在空间上的确切位置的过程。视频中的模型通过多目标鲁棒优化来制定位置决策，考虑了需求不确定性和部门间的关系。

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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whether you can share and without any

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