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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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Literature review contd
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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Literature review contd
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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Literature review contd
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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Literature review contd
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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Literature review contd
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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Literature review contd
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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Literature review contd
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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Literature review contd
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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Literature review contd
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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Literature review contd
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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Literature review contd
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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Literature review contd
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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Work done so far cont..
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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Work done so far cont..
-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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Work done so far cont..
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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Work done so far cont..
=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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Work done so far cont..
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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Work done so far cont..
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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Work done so far cont..
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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Work done so far cont..
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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Work done so far cont..
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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Work done so far cont..
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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Work done so far cont..
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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Work done so far cont..
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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Work done so far cont..
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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Work done so far cont..
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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Work done so far cont..
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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Work done so far cont..
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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Work done so far cont..
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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Work done so far cont..
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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