Diagram Slide

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MULTI-OBJECTIVE ANALYSIS OF A

PRODUCTION-DISTRIBUTION SYSTEM

Presented by

Yasoda Sreeram Kalluri

M120408ME

Guide:

Mr. Vinay V Panicker


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Outline of Presentation

Introduction

Literature review

Research gaps identified

Assumptions Problem definition

Work done so far

Further work

Conclusions

References

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Introduction

In manufacturing industries such as automotiveand electronics, distribution cost constitute oneof the largest cost components.

This trend has created a closer interactionbetween the different stages of a supply chain,which increased the practical usefulness of thecoordinated decision models.

This work deals with the coordination ofproduction and distribution functions in a supplychain

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Introduction cont

Production and distribution operations are thetwo most important operational functions in asupply chain

In order to achieve the optimal operationalperformance in a supply chain, it is critical tointegrate production and distributionfunctions

Multi-objectives are obvious in most of thepractical decision making problems

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Introduction cont

In a supply chain, cost and service level are

the two main objectives of interest which are

conflicting in nature

These types of conflicting objectives require

multi-objective analysis

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Literature review

The various research on the production-distribution systems reported in the literatureare categorized based on the following

criteria:1. Problem objective

2. Objective function

3. Solution methodology

4. Decision level5. Integration structure

6. Planning horizon

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Literature review contd

Problem objective: The problem objective

classifies the problem to be a minimization or

a maximization problem.

Objectives include

Maximization or Minimization

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Objective function: The objective function

describes the various decisions to be

considered in the problem analysis.

Objective functions include

Total weighted tardiness

Total distribution cost

Maximum lateness Total flow time

Total completion times, etc.,

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Solution methodology: To solve the

formulated model, researchers adopt

different solution methodologies such as:

Genetic algorithm

Simulated annealing

Tabu search algorithm

Artificial immune systems algorithm, etc.,

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Decision Level: According to Chen (2004), the

decision levels are classified as follows:

Tactical models (A1)

Operational models (A2)

Operational and tactical models (A3)

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Tactical models (A1): In this decisions mainly

involves:

how much to produce

how much to ship in a time period

how long the production cycle/distribution cycle

should be

how much inventory to keep

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Operational models (A2): In this decisions

mainly involves

when and on which machine to process a job

when and by which vehicle to deliver a job

which route to take for a vehicle

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Integration Structure: The integrationbetween production and distributionoperations leads to the following three

types of structures (Chen, 2004): Integration of production and outbound

transportation (B1)

Integration of inbound transportation and

production (B2) Integration of inbound transportation,

production, and outbound transportation (B3)

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Integration of production and outbound

transportation: Products are delivered from

manufacturers to customers after they are

produced by manufacturers.

Integration of inbound transportation and

production: Suppliers supply raw materials or

semi-finished products to manufacturerswhere final products are produced.

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Planning horizon: Based on the planning

horizon, the production-distribution models

can be classified in literature as:

One time period (C1)

Multiple time periods with dynamic demand (C2)

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Reference Problem

objective

Objective

function

Solution

methodology

Decision

level

Integration

structure

Planning

horizon

Vanbuer et

al.(1999)

Minimizatio

n

Cost of owing

trucks and

Operating

costs

Heuristic

search

algorithms

A3 B1 C1

Moon et

al.(2002)

Minimizatio

n

Tardiness Genetic

algorithm based

heuristic

approach

A3 B2 C1

Hall and

Potts (2003)

Minimizatio

n

Total flow

time + total

distribution

cost

Dynamic

programming

algorithm

A2 B3 C1

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Reference Problem

objective

Objective

function

Solution

methodology

Decision

level

Integration

structure

Planning

horizon

Hall and

Potts (2005)

Minimization scheduling

cost + the

delivery

cost

Dynamic

programming

algorithm

A2 B1 C1

Pundoor

and Chen

(2005)

Minimization Delivery

tardiness

and Total

distribution

cost

Heuristics A2 B1 C1

Agnetis et

al.(2005)

Minimization Total

interchange

+ Buffer

storage cost

Efficient

algorithms

A2 B2 C1

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Reference Problem

objective

Objective

function

Solution

methodology

Decision

level

Integration

structure

Planning

horizon

Naso et

al..(2006)

Minimization Overall cost

(transportati

on,

outsourcing,overtime,

hiring

trucks)

Meta-heuristic

approach based

on genetic

algorithm

A3 B1 C1

Demirli and

Yimer

(2008)

Minimization Overall

operating

costs

Mixed-integer

fuzzy

programming

A3 B3 C2

Wang and

Cheng

(2009)

Minimization Make span Heuristics A3 B3 C1

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Reference Problem

objective

Objective

function

Solution

methodology

Decision

level

Integration

structure

Planning

horizon

Kumar et

al.(2010)

Minimization Tardiness Fuzzy

incorporate

artificial

immune system

algorithm

A2 B1 C1

Hall and

Liu (2010)

Minimization Total cost Proportional

allocation

algorithms

A3 B1 C2

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Literature review contd..

Reference Problem

objective

Objective

function

Solution

methodology

Decision

level

Integration

structure

Planning

horizon

Steinrucke

(2011)

Minimization Production

cost +

transportation

cost - bonuspayments

Mixed-integer

decision-making

model and

Relaxing and/orfixing Heuristic

A3 B3 C1

Cakici et al

(2011)

Minimization Total weighted

tardiness

+

total

distribution

cost

Heuristics based

on a genetic

algorithm

A2 B1 C1

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Research gaps identified

1. Most of the production-distribution problem

assumes a homogenous fleet of vehicles.

There can be heterogeneous fleet of vehicles

in the model.

2. The production-distribution problem uses a

direct shipping strategy from supplier to

each customer. Routing can be considered inthe model.

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Research gaps identified cont

3. Researchers consider a penalty cost for

tardiness, while a bonus/penalty can be

incorporated for earliness.

4. Multiple orders are received by one

manufacturer but there can be multiple

customers with multiple manufacturers. This

situation needs further study.

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Assumptions

1. Jobs are available at the beginning of planninghorizon

2. All the machines are available throughout thescheduling period

3. An order once taken up is completed fully beforeanother order is taken

4. An operation is not stopped in the midway foranother operation

5. Processing times for all orders are known anddeterministic

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Assumptions cont..

6. All orders are processed in a single

production line

7. No limitation for availability of vehicles

8. For every order one vehicle is dedicated for

its delivery whether it is assigned or not

9. Capacity of vehicle is more than maximum

quantity of one order

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Problem definition

Make-to-order production-distribution systemwith one manufacturer and one or morecustomers. Customers places orders to

manufacturer. Orders are received bymanufacturer are processed on a singleproduction line and delivered to the customeraccording to the weight associated with the

order. By relaxing the assumptions 8 and 9 and

implementing the research gaps 1,2 and 3.

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Work done so far

The production distribution problem specified

in Cakici et al. (2011) is adopted for further

study

The mathematical model present in that

problem is modeled in an optimization

modelling software, LINGO 11.0

Global optimum solution was found

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Work done so far cont..

Problem: Considering same problem

statement without relaxing any assumptions.

Each order is associated with

Volume of the jobs

Due date of the order

Penalty cost associated with the order for late delivery

Processing time of order

Time required to perform trip

Distribution cost associated with trip

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Objective is to minimize the total weighted

tardiness and distribution cost

Scalarization or weighted-sum method is

applied to combine both the objectives by

assigning weights to each objective and

change the whole problem as a single-

objective optimization problem (Caramia andDellolmo, 2008).

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-time required to perform the trip b B

-distribution cost for trip b B

-time at which orderj J finishes its required

processing

-time at which trip b B starts its delivery

-time at which job j J finishes its required

processing

time job j J is delivered

processing time of the orderj J

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penalty for orderj J

volume of the orderj J

due date of orderj J

tardiness of orderj J weight associated with total weighted tardiness

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=1, if job i J immediately precedes job j J

=0, otherwise.

=1, if job j J is assigned to trip k B

=0, otherwise =1, if trip b B is performed

=0, otherwise.

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Objective function: The objective function of

this production distribution problem is to

minimize the total weighted tardiness (TWT)

of all jobs and total transportation cost (TC) ofall deliveries.

MinimizeZ= ; + 1 ;

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Subjected to the constraints

1. Jobs are assigned to a single production line(machine) with a unique predecessor and a uniquesuccessor,

; = 1, for all iJ

; = 1, for all iJ

2. In order to process jobjimmediately after job i, job iJcompletes time units before jobj J:

- +(1-)M, for all i J, jJ, j 0, i j

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3. Jobs are assigned to one of the available trips that

are associated with the same customer

= =1, for alljJ

4. Vehicle capacity constraint

= ,for all kB

5. A vehicle cannot start its delivery until all jobs to

be delivered in the corresponding batch havefinished their processing

- (1-)M, for all i J, bB, i0.

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6. is the delivery start time plus the delivery time

+- (1-)M, for all i J, bB, i0.

7. Each possible trip should be performed if any job

is assigned to it

, for all bB.

8. The tardiness of the jobs is calculated using the

following relationship

Tardiness=Max{0,( -)} or

-, for all iJ.

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Generation of input data

The vehicle capacity is assumed to be 50 units

Weight () is a continuous value between (0,1)

The processing times, job due times,

transportation times, transportation costs, penalty

for late delivery are randomly generated following

DU [1,10] Volume of the order is randomly generated

following DU[10,20]

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Results and Discussion

The possibility of job iprecedes itself is eliminated

by using a membership filter operator in LINGO

11.0 Two dummy orders one at the starting and other

at the ending are considered for sake of jobs

starting at time zero

With the creation of these two dummy orders

always the number of orders are increased by two

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If customer places n orders to manufacturer while

solving this problem by LINGO the number of

input orders enters for each attribute become n+2

For dummy orders, the values for theattributes such as the penalty, processing

time, due date, time required to perform trip

and size of the order are assumed as zero.

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Since it is a minimization problem the

distribution cost for dummy jobs is assumed a

large value otherwise all jobs are assigned to

dummy trips whose cost is zero.

Example for n=5 and =0.6

Processing times=0 3 5 7 0

Weight(penalty cost)= 0 9 7 6 0

Volume of order= 0 15 20 15 0

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Due date= 0 2 1 2 0

Transportation time=0 4 3 2 0

Delivery cost=M 2 4 2 M

Capacity of vehicle= 50

=0.6

Optimal solution is found using LINGO

Objective value= 122.6 (TWT=119.4.8,TC=3.2)

Production sequence

1-2-3-4-5-1 (X12=X23=X34=X45=X51=1)

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Completion times= 0 3 8 15 0

Order(j) assigned to trip(k)=Yjk Y14=Y24=Y33=Y42=Y54=1

Delivery times=7187 5 11 19 1035

Trip performed

Z1=Z5=0; Z2=Z3=Z4=1

Tardiness values=7187 3 10 17 1035

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Work done so far cont

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1 1

2

Del-11

2

W=9, p=3

2

T=4

1

3W=7, p=5

3T=3

3Del-8

4W=6, p=7

4T=2

4Del-5

5 5 5

Manufacturer Trucks Customers


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The computational time taken to obtain a

solution with =0.6 for different number of

orders in LINGO is tabulated.

All the tests are performed on PC with an Intel

Core 2 Duo processor(3 GHz) with 3 GB RAM.

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* Solver is interrupted to get a feasible solution


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It is inferred from the table that as number of

orders increases, the computational time also

increases

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Sl no Number of ordersfrom customers (n)

Computationaltime (hh:mm:ss)

1 2 00:00:00

2 3 00:00:11

3 4 00:06:32

4 5* 10:36:27

5 6* 12:15:51

6 7* 15:10:32


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To investigate the effect of the weight associatedwith total weighted tardiness on thecomputational time, the weight is varied from 0to 1 in steps of 0.1. The change of computationaltime with respect to the weight is depicted

It is understood that the computational time highas the weight (=0.8).

The computational time is less when the priorityfor distribution cost is high compared totardiness.

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0

2

4

6

8

10

12

=

0

=

0.1

=

0.2

=

0.3

=

0.4

=

0.5

=

0.6

=

0.7

=

0.8

=

0.9

=

1Co

mputationaltime

insec

Number of orders = 3

Number of orders =2

0

100

200

300

400

500

600

700

800

900

Com

putational

tim

einsec

Number of orders = 4


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Work done so far cont

Cakici et al.(2011) Proposed model Multi objective problem is

considered as it is

Multi objective is converted into

single objective by scalarization

method (i.e., by assigning some

weights(priority) to each objective)

Priority of the orders are

considered in the form of weights

Penalty of late delivery is

considered in the form of weight

Problem is solved by using non

dominated sorting genetic

algorithm (NSGA-II)

Problem is solved by using LINGO

11.0 an optimization modelling

software NSGA-II used doesnt assure

optimal solution gives only near

optimal solution for production-

distribution problem.

LINGO 11.0 assures an optimal

solution for production-

distribution problem.

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Further work

Investigate the possibility of revising constraints

for better computational time

Search for an efficient heuristic to get near

optimal solution within less computational time

Formulate the constraints for heterogeneous

fleet of vehicles instead of homogeneous fleet.

To incorporate the bonus/penalty payment forearly delivery

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Further work contd

To incorporate the routing for delivery of

orders to customers instead assigning one

vehicle to each trip whether it is assigned or

not.

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Conclusions

From the literature review different problem

environments its associated assumptions and

research gaps are perceived

The production distribution problem adoptedfrom Cakici et al. (2011) was modelled in LINGO

and a global optimum solution was found

Analysed the solutions obtained by differentweights associated with total weighted tardiness

() with respect to computational time.

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References

Agnetis, A., Hall, N. G., & Pacciarelli, D., 2006.Supply chain scheduling: Sequence coordination.Discrete Applied Mathematics, 154, 20442063

Alebachew D., & Demirli, Y. K., 2008. Fuzzy

scheduling of a build-to-order supply chain.International Journal of Production Research, 46,39313958.

Cakici,E., Mason,S.J.,&Kurz, M.E., 2011.Multi-

objective analysis of an integrated supply chainscheduling problem. International Journal ofProduction Research 50 (10), 26242638

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References cont

Caramia, M., and Dellolmo, P., 2008, Multi-objectivemanagement in freight logistics increasing capacity, servicelevel and safety with optimization algorithms, Springer-Verlag London Limited., ISBN-13: 9781848003811, pp. 14-25.

Chen, Z. L., (2004), Integrated Production and DistributionOperations: Taxonomy, Models, and Review. In D. Simchi-Levi, S. D. Wu, & Z. J. Shen (Eds.), Handbook of quantitativesupply chain analysis: modelling in the e-business era, pp.711746

Hall, N.G. & Potts, C.N., 2003. Supply chain scheduling:Batching and delivery. Operations Research, 51, 566584

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References cont

Hall, N.G. & Potts, C.N., 2005. The coordination ofscheduling and batch deliveries. Annals ofOperations Research, 135, 4164

Halls, N. G. & Liu, Z., 2010. Capacity allocation

and scheduling in supply chains. Operationsresearch. 58 (6), 17111725

Kumar, V., Mishra, N., Chan, F. T. S., & Verma, A.,2011. Managing warehousing in an agile supply

chain environment: an F-AIS algorithm basedapproach. International Journal of ProductionResearch. 49 (21), 64076426

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References cont

Moon, C., Kim, J., & Hur, S., 2002. Integrated processplanning and scheduling with minimizing total tardiness inmulti-plants supply chain. Computers & IndustrialEngineering, 43(1-2), 331-349

Naso, D., Surico, M., Turchiano, B., & Kaymak, U., 2007.

Genetic algorithms for supply-chain scheduling: A casestudy in the distribution of ready-mixed concrete. EuropeanJournal of Operational Research, 177(3), 2069-2099

Pundoor, G. & Chen, Z.L., 2005. Scheduling a production-distribution system to optimize the tradeoff between

delivery tardiness and distribution cost. Naval ResearchLogistics, 52, 571-589

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References cont

Steinrucke, M., 2011. An approach to integrateproduction-transportation planning and scheduling inaluminum supply chain network. International Journalof Production Research. 49 (21), 65596583

Van Buer, M. G., Woodruff, D.L., & Olson, R. T., 1999.Solving the medium newspaperproduction/distribution problem. European Journal ofOperational Research. 115(2), 237-253

Wang X. & Cheng, T.C.E., 2009. Production scheduling

with supply and delivery considerations to minimizethe makespan. European Journal of OperationalResearch. 194 (3), 743752

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Thank you

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