Fast Pick Area

8/12/2019 Fast Pick Area

1/26


2/26

The fast-pick or forward-pick orprimar-pick area

!eser"es

#rea

$orward pick#rea

!ecei"ing

!estocking%rimarpicking

!eser"espicking

hipping


3/26

The ma'or trade-offs (ehind theesta(lishment of a forward pick area

) # forward pick area increases thepick densit(

concentrating a large n*m(er of +s within a small

phsical space.

) n the other hand, it introd*ces the acti"it of restocking.

) #lso, in general, a forward pick area concerns the picking

of smaller /*antities and in"ol"es more sophisticated

e/*ipment than the picking acti"it taking place in the

reser"es area. o, its deploment re/*ires some capital

in"estment in e/*ipment and 0e1tra2 space.


4/26

3a'or iss*es to (e resol"ed

) 4hich +s to store in the fast-pick area5 062

) How m*ch of each + to store5 02

) How large sho*ld (e the fast-pick area5 082


5/26

# fl*id model for determining theoptimal allocation of forward-pick

storage to a pre-determined set of +s) 9i"en

: ;< ;ol*me of entire forward-pick storage area 0e.g., in c*(ic ft2

: f=i< $low of + i, 0e.g., in c*(ic ft > ear2

: c=r < replenishment cost 0?>replenishment trip2) Determine

: *=i< storage "ol*me to (e allocated to + i, i@,A,n 0c*(ic ft2

s.t. total restocking cost 0rate2 is minimied 0?>ear2

) #dditional ass*mptions: !eplenishment for each + occ*rs at lots e/*al to *=i, and occ*r

instantaneo*sl *pon the complete depletion of the pre"io*s lot


6/26

%ro(lem form*lation

min

=i c=r 0a"erage n*m(er of replenishments per earfor + i2 @

=i c=r 0f=i > *=i2s. t.

=i *=i ; *=i , i

ptimal ol*tion =k f=k2 ;


7/26

#ccommodating minim*m 0andma1im*m2 allocation constraints

) 0e.g., we cannot allocate to an + a "ol*me less than thatre/*ired for storing at least one *nit2

) ol*tion algorithm for accommodating minim*mallocation constraints: Edentif those +s that recei"ed less than their minim*m

re/*ired space, when sol"ing the pro(lem witho*t consideringthese constraints.

: Encrease the allocations of these deficient +s to their minim*mre/*irements, and remo"e them as well as their allocated spacefrom an f*rther consideration.

: !e-allocate the remaining space among the remaining +s.) # similar tpe of logic can (e applied for the

accommodation of constraints imposing a ma1im*mallocation


8/26

!emarks

) The fraction of fast-pick storage de"oted to + i =k f=k) ptimal n*m(er of replenishment trips per ear for + i *=i @ 0f=i =k f=k2 > ;

) Fach *nit of the fast-pick storage sho*ld (e restocked atthe same rate *=i2 > *=i @ f=i > 0*=i2G6 @ 0=k f=k2G6 > ;G6

i.e., independent of i. This res*lt can (e *sed for a /*ickassessment of the optimalit of the c*rrent allocation in afast-pick area, ( considering how 0spatiall2 (alanced isthe replenishment effort.


9/26

ther he*ristics *sed in practice for resol"ingthe fast-pick storage allocation pro(lem

) F/*al-pace #llocation< #ssign each + the same

amo*nt of space, i.e.,

*=i @ ; > n, i

) F/*al-Time #llocation =k f=k2 ;, i

Hence, n*m(er of trips per ear for + i,f=i > *=i @ 0=k f=k2 > ;


10/26

Comparing the performance of thehe*ristics and the optimal optimal sol*tion

) %erformance of the optimal sol*tion *=i @ 0=i f=i2G6 > ;) %erformance of the e/*al-space allocation he*ristic *=i @ n 0=i f=i2> ;) %erformance of the e/*al-time allocation he*ristic *=i @ n 0=i f=i2> ;


11/26

# statistical assessment of the s*(-optimalitof the e/*al-space>time allocation

%erf. of he*ristics > %erf. of optimal sol. @ =i f=i > n

0=i f=i > n2G6

#ss*me that each f=iis an independent sample from a random

"aria(le with mean mand "ariance sG6. Then, the a(o"e ratio is

appro1imated ( ear2: c=r< cost of each restock trip 0?>trip2

: s< the sa"ing realied when a pick is done from the forward arearather than the reser"e 0?>pick2

: p=i< the e1pected ann*al picks for + i 0picks>ear2

: *=i< storage "ol*me to (e allocated to + i, i@,A,n 0c*(ic ft2Then, the net ann*al (enefit of allocating fast-pick storage *=i to +i, is *=i2 if *=i L 0?>ear2


13/26

%lotting the net (enefit f*nction

*=i

c=i0*=i2

0c=rf=i2 > 0sp=i2 < minim*m "ol*me to (e stored, if an


14/26

%ro(lem $orm*lation

ma1=i c=i0*=i2s.t.

=i *=i ; *=i , i

# near-optimalit condition

f=i.


15/26

#lgorithm for comp*ting a near-optimalsol*tion

) ort all +s from most "isco*s to least 0p=i > f=i2

) $or k @ to n 0total n*m(er of +s2 ='@Gk f='2 ;Gk 2: the res*lting total (enefit

0e.g., =i@GkMs0;Gk2 p=i - c=r f=i > *=iGk N 2) %ick the "al*e of k, denoted ( k, that corresponds to the

ma1imal total (enefitO set ; @ ;G0k2 and

*=i @ *=iG0k2, for i@ to kO , otherwise


20/26

Designing a fast-pick area for pallet storage*=i that we *sed for small-item picking2.

h i i h di


22/26

nthesiing the correspondingnet-(enefit f*nction

) %arameters

: P @ sie of the fast-pick area 0in pallet storage locations2: p=i @ n*m(er of less-than-f*ll-pallet picks for + i

: d=i @ n*m(er of pallets mo"ed ( less-than-f*ll-pallet picks for + i

: %=i @ n*m(er of f*ll-pallet picks for + i

: D=i @ n*m(er of pallets mo"ed ( f*ll-pallet picks for + E 0D=i @ %=i2

: *(=i @ ma1im*m on-hand in"entor for + i 0in n*m(er of pallets2: s @ sa"ings per pick when picking from fast-pick area 0?>pick2

: c=r @ cost of restocking trip 0?>trip2

) %rimar Decision "aria(les: 1=i @ n*m(er of pallets from + i to (e stored in the fast-pick area

) The net-(enefit f*nction for + i

Documents

Fast Pick Area