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Master Thesis Midway
DefendingJob-shop Scheduling Approach
to Order-picking Problem
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Ad'isor( Assoc)Prof) *o ThanhPhongStudent( Tran +uoc Dat
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,ontents
%-,ompleted ,ontents
") elationship between OrderPicking and Jobshop
) Ob.ecti'e
/) Modelling
0)elationship between modules %%-Ongoing ,ontents
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Acti'ities in logistic center
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")" elationship between OrderPicking and Jobshop Problem
Order-Picking JobShop Problem
Order Job
Shelf or %tem Machine
Se1uence of picking products Process se1uence
Picking time Machine time
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") Ob.ecti'e
2uild a decision support tool for Order PickersScheduling in the warehouse(
Minimize Travel Distance for each
picker
Balance the work load among pickers-Min Deviation
Minimize Makespan of all pickers
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")/ Mathematical formulation
Minimize Distance between ! items"
Parameter"
s( source node
t( target node
di.( distance between item i and item .
#ariables"
4i.( binary 'ariable5 e1ual " if arc 6i5.7 is inthe shortest path and e1ual # otherwise)
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")/ Mathematicalformulation
Minimize Distance between !items"
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s. t :
1, if ;
1, if ;
0, otherwise.
ij ij
ij A
ij ji
j j
minimize x
i
d
s
x x i t
=
= =
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")/ Mathematicalformulation
Minimize Distance for each Batch
Parameter"
ci.( minimum distance from item i toitem .
9:;#5
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")/ Mathematicalformulation
Minimize Distance for each Batch
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0 # , j 0
0, #
0,i#j
min . (1)
s. :
1 (2)
1 (3)
0 1, interger
n n
ij ij
i j i
n
ij
i i j
n
ij
j
ij ij
c x
t
x
x
x x
= =
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")/ Mathematicalformulation
Minimize Deviation between batches Parameters
J( the set of customer orders5
%( the set of feasible batches5
,( the capacity of the picking de'ice5 c.(the capacity re1uired for order . 6. @ J75
di( the length of the picking tour in which all orders of a batch iare collected)
#ariable
ai.( binary 'ariable5 an order . is included in a batch i 6ai.: "7or not 6ai.: #75
4i( binary 'ariable5 if a batch i is chosen 64i: "7 or not 64i: #7)
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")/ Mathematicalformulation
Minimize Deviation betweenbatches
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")/ Mathematicalformulation
Minimize Makespan for all batches
Parameters"
9( the set of all operations 6i5 .7
A( the set of all routing constraints 6i5 .7 6h5 .7
pi.( processing time of .ob . on machine .
#ariables"
,ma4( Makespan
yi.(the starting time of operation 6i5 .7
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")/ Mathematicalformulation
Minimize Makespan for allbatches
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max
max
Min ;
s . t :
-Makespan is the argest !ompetion time:
( , )
-"onj#n!ti$e ar!s:
( , ) ( , )
-%isj#n!ti$e ar!s :
ij ij
hj ij ij
ij ik ik
ik ij ij
C
C y p for all i j
y y p for all i j h j A
y y p or
y y p for
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-&on-negati
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al
r al
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")0 elationship betweenmodules
% code by ,B language) %nclude /main Module(
-2atching Module
-TSP Module
-Jobshop Module
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")0 elationship betweenmodules
Batching Mod$le TSP Mod$le JobshopMod$le
Data%np$t
-9umber of Order-Total %tems-Cist item for each
Order-9umber of2atch6Picker7-Minimum Distance ineach 2atch
-DistanceMatri4
between%tems 6Cayout7-Cist %tems ineach 2atch
-Se1uences%tems in each
2atch-Distance Matri4between %tems6Cayout7
DataO$tp$t
-Cist Orders in each2atch6 -%nput to Job-shop Module7-Cist %tems in each2atch 6%nput to TSPModule7
-Se1uences%tems in each
2atch
-Order PickingPlan
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%%-Ongoing ,ontents
")Cink between TSP and 2atchingModule
)Cink between 2atching ' JobshopModule
/) Testing with diEerent layouts6D-/D7
0) ,ompare other schedulingmethods)
3) Simulate Model in AF9A software!"#!"$ %nternational &ni'ersity "8
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eferrences
[1]Job-shop Scheduling Approach to Order-picking Problem,Yukiyasu Iwasaki, Ikuo Suzuki, Masahito Yamamoto and MasashiFurukawa, Vol. 26, No. , !!. 1"#1"$, 2"1.
[2] Batching orders in warehouses by minimizing travel distancewith genetic algorithms, %hih&Min' (su, )ai&Yin' %h*n, Mu&%h*n %h*n,
+!!liations o- *n*ti +l'orithms in Industry, Volum* /6, Issu* 2,
F*0ruary 2""/, a'*s 16$#13 [] Solving Travelling Salemans Problem sing !enetic Algorithm
Based On "euristic #rossover And $utation Operator, Int*rnational4ournal o- 5*s*arh in n'in**rin' 7 8*hnolo'y, Vol. 2, Issu* 2, F*02"19, 2&9
[9] $ulti-Ob%ective routing and scheduling o& order pickers in awarehouse, :al;zs Moln;r and yor'y
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