Gomez Aparicio Juan Miguel - Gestion Logistica Y Comercial

4 La gestión de las existencias

Caso práctico 4 (continuación)

Frecuencia N.º de pedidos Cantidad Stock medio Coste de Coste de pedido Coste total
del periodo Np D total (Q) Q mantenimiento y transporte Q ⋅ Cp + Cg ⋅ Np
Q 2 2
Q ˜ Cp (Cg · Np)
2
) \ŠY *00 )&((( -(( -/&.(($(( -/&.*-$((
* \ŠYk ),, *&((( )&((( *-$(( *0&0(($(( *0&0-($((
+ \ŠYk 1. +&((( )&-(( -($(( )1&*(($(( )1&*/-$((
/-$((
– – – – – –
) k]eYfY . \ŠYk! ,0 .&((( +&((( – 1&.(($(( 1&/-($((
* k]eYfYk *, )*&((( .&((( )-($(( ,&0(($(( -&)(($((
+ k]eYfYk ). )0&((( 1&((( +(($(( +&*(($(( +&.-($((
) e]k , k]eYfYk! )* *,&((( )*&((( ,-($(( *&,(($(( +&((($((
.(($((
– – – – – –
. k]eYfYk 0 +.&((( )0&((( – )&.(($(( *&-(($((
1(($((
– – – – – –
2 meses 6 48.000 24.000 – 1.200,00 2.400,00
+ e]k]k , /*&((( +.&((( 0(($(( *&.(($((
, e]k]k + 1.&((( ,0&((( 1.200,00 .(($(( +&((($((
. e]k]k * ),,&((( /*&((( )&0(($(( ,(($(( ,&((($((
*&,(($((
+&.(($((

;geg k] n]$ Y e]\a\Y im] Yme]flY ]d f”e]jg \] h]\a\gk$ k] af[j]e]flYf dgk [gkl]k \]d
h]\a\g q ljYfkhgjl]$ h]jg \akeafmq]f dgk \] eYfl]faea]flg \]d stock.

Fgk afl]j]kY eafaearYj dY kmeY \] YeZgk [gkl]k& Ka dY ]ehj]kY \][a\] j]YdarYj kmk h]\a%
\gk e]fkmYde]fl] q fg \aYjaYe]fl]$ kmk _Yklgk k] n]f j]\m[a\gk ]f [Yka --&((($(( €&

=f ]d ]b]ehdg hjghm]klg$ ]d ngdme]f hlaeg \] h]\a\g k] ]f[m]fljY ]f ,0&((( mfa\Y\]k$
dg im] kmhgf] j]YdarYj mf h]\a\g [Y\Y \gk e]k]k&

Fg gZklYfl]$ ]kl] e†lg\g \] lYfl]g j]kmdlY l]\agkg$ q Y n][]k fg hg\j]egk gZl]f]j ]d
eŠfaeg \] dgk [gkl]k lglYd]k hgj ]kl] hjg[]kg$ h]jg fgk `Y k]jna\g hYjY Y^aYfrYj dgk [g%
fg[aea]flgk l]ja[gk ]phda[Y\gk Yfl]jagje]fl]&

b) Por la fórmula del volumen óptimo de pedido

Q = Cg ⋅ D ⋅ * = *&((( ⋅ *00&((( ⋅ * = ,0&((( mfa\Y\]k
Cp ($(-

DY demanda anual ]k2 )&((( Ù *00 *00&((( mfa\Y\]k&

¿Cuántos pedidos efectuará al año, sabiendo que la fábrica mantiene su actividad

durante 288 días al año?

Np D *00&((( . h]\a\gk
Q ,0&(((

Kmhgf_Yegk im] ]d plazo de aprovisionamiento es de 10 días.

Efectuaremos el pedido (Pp) \] ,0&((( mfa\Y\]k [mYf\g ]d fan]d \] stock k]Y \] )(&(((
mfa\Y\]k&

=d hmflg \] h]\a\g \]Z] j]YdarYjk] [mYf\g ]d fan]d \] klg[c k]Y a_mYd Yd consumo de uni-
dades durante el plazo de entrega (Cpe).

Pp Cpe
Cpe = D ⋅ Pe HdYrg \] ]flj]_Y! → )(&((( = *00&((( ⋅ )(

*00 *00

100

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4La gestión de las existencias

B. Variante del volumen óptimo de pedido

=f \]l]jeafY\gk [Ykgk$ ]d ngdme]f hlaeg \] h]\a\g dg hg\]egk gZl]f]j [gehYjYf\g dgk
[gkl]k lglYd]k$ Yhda[Yf\g dY ^jemdY \] Oadkgf$ g Za]f YfYdarYf\g dYk hjghm]klYk ^gjemdY\Yk hgj
]d hjgn]]\gj&

Caso práctico 5

DY ]ehj]kY Af\mkljaYk 9_mYdmr la]f] mfY \]eYf\Y YfmYd \] ,(&-(( mfa\Y\]k j]kh][lg Y
mf \]l]jeafY\g hjg\m[lg& ;Y\Y n]r im] kgda[alY mf h]\a\g Y km hjgn]]\gj k] hjg\m[]f
mfgk _Yklgk \] _]klaf \] *($(( €& =d hj][ag mfalYjag nYjŠY ]f ^mf[af \]d ngdme]f kgda[a%
lY\g hgj h]\a\g$ k]_”f af\a[Y dY lYZdY kmeafakljY\Y hgj ]d hjgn]]\gj& =d [gkl] YfmYd mfa%
lYjag hgj eYfl]faea]flg \] stock kmhgf] *$(( €&

K] fgk ha\] [Yd[mdYj ]d ngdme]f hlaeg \] h]\a\g$ l]fa]f\g ]f [m]flY dY ka_ma]fl] daklY
\] hj][agk2

Unidades pedidas Precio (euros)

<] -(( Y )&((( +$((
<] )&(() Y )&*(( *$1-
<] )&*() Y )&-(( *$1(

Solución
;Yd[mdYegk ]d ngdme]f hlaeg \] h]\a\g k]_”f dY ^jemdY \] Oadkgf2

Q = ,(&-(( ⋅ *( ⋅ * = 1(( mfa\Y\]k Actividades
*
12. DY ]ehj]kY =d :Yj[g$ K&9&$ k]
F&´ \] h]\a\gk YfmYd]k ,(&-(( ,- \]\a[Y Y dY [ge]j[aYdarY[af
1(( \] ZYj[gk ]f eafaYlmjY& La]%
f] mfY \]eYf\Y YfmYd \]
HYjY mf ngdme]f \] 1(( mfa\Y\]k ]d hj][ag ]k +$(( €& *&((( ZYj[gk& ;Y\Y n]r im]
Dgk [gkl]k hYjY ,- h]\a\gk k]jf2 kgda[alY mf h]\a\g Y mf hjg%
n]]\gj la]f] mfgk _Yklgk \]
;gkl] \] Y\imaka[af2 ,(&-(( ˜ +$(( )*)&-(($(( _]klaf \] .$(( €& =d hj][ag
;gkl] \] _]klaf2 ,- ˜ *($(( 1(($(( mfalYjag \] [Y\Y ZYj[g nYjŠY
;gkl] \] eYfl]faea]flg2 1(( ˜ * ]f ^mf[af \]d f”e]jg \]
1(($(( mfa\Y\]k kgda[alY\Yk$ k]_”f
* dY ka_ma]fl] lYZdY2
Coste total 123.300,00

Supongamos que hacemos 30 pedidos. ¿Cuál será el coste total? Unidades Precio
pedidas (euros)
DY [Yfla\Y\ Y kgda[alYj hgj h]\a\g k]j a_mYd Y ,(&-(( )&+-( mfa\Y\]k Y *$1 € k]_”f
+( )(( 1($((
lYZdY!&
)()%*(( 0($((
;gkl] \] Y\imaka[af2 ,(&-(( Ù *$1( ))/&,-($((
;gkl] \] _]klaf2 +( Ù *($(( .(($(( *((%+(( /($((
;gkl] \] eYfl]faea]flg2 )&+-( ˜ *$((
)&+-($(( =d [gkl] YfmYd mfalYjag hgj
* eYfl]faea]flg \] stock ]k
Coste total 119.400,00 \] )$0( €& 9 hYjlaj \] ]klgk
\Ylgk$ j]YdarY ]d [d[mdg \]d
=f dgk [gkl]k lglYd]k ]pakl] mfY j]\m[[af \]d +$). [mYf\g k] j]YdarYf +( h]\a\gk& ngdme]f hlaeg \] h]\a\g&

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4 La gestión de las existencias

Importante 7. El punto de pedido

El VOP: f”e]jg hlaeg \] mfa\Y\]k =f dY j]kgdm[af \]d ;Ykg hj[la[g , fgk `]egk j]^]ja\g Yd hmflg \] h]\a\g Pp!$ Yd hj]_mflYj%
Y kgda[alYj& fgk ]f im† ege]flg \]ZŠY dY ]ehj]kY j]YdarYj ]d h]\a\g hYjY fg [gjj]j ]d ja]k_g \] mfY jglmjY
\] stocks.
El punto de pedido: ege]flg ]f
]d im] j]YdarYj ]d h]\a\g$ ]f ^mf[af =d punto de pedido ]k ]d fan]d \] stock ]f ]d im] k] ]klYZd][] g ]^][l”Y ]d h]\a\g& =k
\]d f”e]jg \] mfa\Y\]k im] im]\Yf \][aj$ ]k dY [Yfla\Y\ \] ]pakl]f[aYk im]$ mfY n]r Yd[YfrY\Y$ gZda_Y Y ]ealaj mf fm]ng h]\a%
]f ]d YdeY[†f& \g \] j]hgka[af&

=f l]gjŠY$ ]kl] fan]d hm]\] ^abYjk] hgj ]d stock [gfka\]jY\g eŠfaeg ek dY [Yfla\Y\ f][]kYjaY
hYjY ]d [gfkmeg \mjYfl] ]d afl]jnYdg \] la]ehg im] e]\aY ]flj] ]d h]\a\g q dY ]flj]_Y \]d
eYl]jaYd hgj ]d hjgn]]\gj&

=d ege]flg \] dY j]hgka[af k] hjg\m[aj ]f ]d ka_ma]fl] [Ykg2

=pakl]f[aYk dª Hmflg \] h]\a\g

Sistemas de reposición de stocks

Dgk lj]k kakl]eYk ek mladarY\gk hYjY dY j]hgka[af \] stocks kgf2
 9 fan]d&
 Hgj [gZ]jlmjY&
 Eaplg&
Dgk ]klm\aYj]egk Y ljYn†k \] mf [Ykg hj[la[g&

Caso práctico 6 =pY[lalm\$ K&D&$ ]k mfY ]ehj]kY ]kh][aYdarY\Y ]f dY [gehjY%n]flY \] afkljme]flgk hYjY j]Y%
darYj lg\g lahg \] e]\a\Yk& La]f] mfY \]eYf\Y YfmYd \] *(&((( m\k& q mf stock \] k]_m%
Web ja\Y\ \] )(( m\k& Km hjgn]]\gj lYj\Y - \ŠYk ]f k]jnaj ]d h]\a\g$ Y mf [gkl] \] +* €& =d [gkl]
\] YdeY[]fYea]flg \] [Y\Y mfa\Y\ ]k \] * €&
OafIK: ]k mf hjg_jYeY _jYlma%
lg im] hm]\]k \]k[Yj_Yjl] \] K] fgk ha\] im] [Yd[md]egk dg ka_ma]fl]2
Afl]jf]l& =f dY h_afY \] Kg^lg%
fa[ (www.softonic.com) ]f%  ;Yfla\Y\ kgda[alY\Y ]f [Y\Y h]\a\g&
[gfljYjk mf eg\g k]_mjg \]  ;gfkmeg \mjYfl] ]d hdYrg \] ]flj]_Y&
\]k[Yj_Yjdg$ YkŠ [geg mfY j]k]%  Hmflg \] h]\a\g&
ŽY im] ]phda[Y dg ]k]f[aYd \]
]kl] hjg_jYeY&

Solución Q = *((&((( ⋅ +* ⋅ * = 0(( m\k&
 ;Yfla\Y\ kgda[alY\Y ]f [Y\Y h]\a\g& *

 ;gfkmeg \mjYfl] ]d hdYrg \] ]flj]_Y&

Cpe = *(&((( ⋅ - = */, m\k&
+.-

 Hmflg \] h]\a\g& PP */, )(( +/, m\k&

Fig. 4.6. J]hj]k]flY[af _j^a[Y \]d ngdme]f hlaeg \] h]\a\g gZl]fa\g [gf OafIK:& =f ]d _j^a[g ka_ma]fl] gZl]fa\g [gf dY Yhda[Y[af
af^gjela[Y OafIK:! hg\]egk gZk]jnYj im]2

 = d ngdme]f hlaeg \] h]\a\g k] hjg\m[] [gf
0((Âmfa\Y\]k$ dg [mYd aehda[Y mf [gkl] \] YdeY%
[]fYea]flg )&.(( 0(( ˜ *!&

 H YjY ]k] fan]d dgk [gkl]k \] h]\a\g (setup cost) q
dgk \] eYfl]faea]flg (holding cost) k] a_mYdYf&

9 hYj laj \] ]klgk \Ylgk n]j]egk dY kgdm[af im]
Y\ghlYf dgk \aklaflgk kakl]eYk \] j]hgka[af&

(Continúa)

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4La gestión de las existencias

Caso práctico 6 (continuación) Claves y consejos
a) A nivel
Hgj ]kl] kakl]eY$ Yd fg ]klYj ]k%
DY h]la[af \]d h]\a\g k] ]^][l”Y [mYf\g dYk ]pakl]f[aYk dd]_Yf Y mfY \]l]jeafY\Y [Yfla\Y\$ lYZd][a\g mf [gfkmeg [gfklYf%
Y dY im] `]egk ddYeY\g hmflg \] h]\a\g (Pp). Dgk h]\a\gk kgf \] mfY [Yfla\Y\ [gfklYfl] l]$ dY h]la[af \] 0(( mfa\Y\]k
Q) Q* Q+!& =k ]d kakl]eY ek ]pl]f\a\g hYjY j]hm]klgk \] eYfl]faea]flg (t) z¥ t*!& k] j]YdarY [mYf\g k] dd]_Y Yd
hmflg \] h]\a\g$ im] ]f Yd_mfgk
0((! → Q) Q* Q+ h]jag\gk k] ]^][l”Y ek lYj\] q
+/,! → Pp) Pp* Pp+ ]f gljgk ek l]ehjYfg&

t) z¥ t* z¥ t+

Q

1.100 (800 300)
1.000
(800 250)
900
(800 100)

374 P1 800 P2 800 P3 800 PP
300
250 Fig. 4.7. =f ]d kakl]eY \] j]hgka[af Y fan]d ka]ehj]
Ss 100 k] ha\] dY eakeY [Yfla\Y\ Yd dd]_Yj Yd hmflg \]
h]\a\g&
10 días 5 días 22 días 5 días 8 días 5 días T
27 días
15 días 13 días

b) Por cobertura

:Ybg ]kl] kakl]eY \] j]hgka[af Dgk h]\a\gk k] j]YdarYf ]f ^][`Yk hj]^abY\Yk l) l* l+!$ h]jg
dYk [Yfla\Y\]k h]\a\Yk kgf nYjaYZd]k I) z ¥ I* z I+!$ \] eYf]jY im] ]d fan]d \] ]pakl]f[aYk ]f
dY ^][`Y \] j]YdarYj ]d h]\a\g ek dY [Yfla\Y\ h]\a\Y kme]f mfY [Yfla\Y\ ^abY hYjY [gZ]jlmjY
\]d hjpaeg h]jag\g& <] ]kl] eg\g$ ]d hmflg \] h]\a\g nYjaYj h]jeYf]fl]e]fl] >a_& ,&/!&

Fan]d epaeg \] stock 800 374 1.174 uds.; F&´ h]\a\gk *(&((( *- ;
0((

P) )&)/, +/, 0(( m\k& 3 P* )&)/, /(( ,/, m\k&3 P+ )&)/, +*( 0-, m\k&&

Q (800 300) (854 150) Claves y consejos

1.100 (474 500) =d im] k] `YqY hj]naklg mf [gf%
1.004 kmeg \] */, mfa\Y\]k ]f - \ŠYk
900 fg aehda[Y im] ]f j]Yda\Y\ g[m%
974 jjY ka]ehj]$ hgjim] ]d fan]d \]
]pakl]f[aYk [mYf\g k] j][aZ] ]d
700 P2 474 k]_mf\g h]\a\g ]k *-( mfa\Y%
300 \]k& MfY n]r kmeY\Yk Y dYk
500 800 P3 854 0((Âmfa\Y\]k hj]naYk gZl]f]%
374 P1 egk )&(-(Âmfa\Y\]k&
320

150

10 días 5 días 10 días 5 días 10 días 5 días t Fig. 4.8. =f ]d kakl]eY \]
15 días j]hgka[af hgj [gZ]jlmjY dYk ^][`Yk

kgf [gfklYfl]k q dYk [Yfla\Y\]k

15 días 15 días \]ka_mYd]k& (Continúa)

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4 La gestión de las existencias

Caso práctico 6 (continuación)
c) Mixto

Importante =f ]kl] kakl]eY \] j]hgka[af k] hj]n† dd]_Yj Yd hmflg \] h]\a\g$ h]jg hYjY kYZ]j [mflYk
mfa\Y\]k `Yq im] h]\aj k] \]Z] j]YdarYj mfY hj]nakaf \] dYk mfa\Y\]k im] k] ]kh]jY [gfkm%
=d kakl]eY \] j]hgka[af \] fan]d eaj ]f ]d hdYrg im] ]d hjgn]]\gj lYj\Y ]f k]jnaj dgk eYl]jaYd]k& DY ^afYda\Y\ ]k im] [mYf\g
k] mladarY ]f dY _]klaf \] mf Yd% dd]_m]f q k] kme]f Y dYk ]pakl]f[aYk \]d YdeY[†f fg k] kmh]j] ]d stock epaeg&
eY[†f []fljYd im] kmeafakljY Y
YdeY[]f]k h]ja^†ja[gk& ;Y\Y Yd% =kl] kakl]eY ]k mfY e]r[dY \] dgk \gk Yfl]jagj]k3 dY h]la[af k] `Y[] [mYf\g k] dd]_Y Yd hmf%
eY[†f h]ja^†ja[g hgk]] mfY ¿\g% lg \] h]\a\g (Pp); ]k \][aj$ Pp) Pp* Pp+$ h]jg k] j]YdarY \] lYd ^gjeY im] dY [Yfla\Y\ im]
lY[afÀ ]f stock, q ]d YdeY[†f k] j][aZY Q) z¥ Q* z¥ Q+!$ kmeY\Y Y dYk ]pakl]f[aYk hj]naklYk ]f ]d ege]flg \] dY j][]h[af$
[]fljYd \]Z] j]YdarYj mfY _]klaf k]Yf mfY [Yfla\Y\ ^abY stock epaeg!&
\] stocks ZYkY\Y ]f hj]nakagf]k&
=f fm]kljg [Ykg$ ]d stock epaeg 0(( )(( m\k& ka]ehj] `Yq im] h]\aj `YklY dd]_Yj Y
1((Âm\k&!&

Q

1.018 (800 150) (474 500)
950
(794 + 80)
900
874 851

374 P1 800 P2 718 P3 794
300
150 100 200

9,6 días 5 días 15 días 5 días 12 días 5 días 20 días 5 días t

Fig. 4.9. Kakl]eY 14,6 días 20 días 17 días 25 días
\] j]hgka[af eaplg&

P) «««ª Cm 1(( +/, -,$/1 )(( »º»»
Hj]nakaf 1$.

+/, -,$/1 ˜ -!
¬ ¼ P* 1(( )(( 0((

P* ª««« Cm 1-( +/, +0$,( »º»»
)-

Hj]nakaf +/, +0$, ˜ -! )0*
¬ ¼ P* 1(( )0* /)0

P+ «««ª Cm )&()0 +/, -+$./ º»»»
Hj]nakaf )*

+/, -+$./ ˜ -! )(.
¬ ¼ P+ 1(( )(. /1,

9d [YZg \] *( \ŠYk k] j]YdarY ]d h]\a\g f”e]jg , hgjim] `]egk dd]_Y\g Yd fan]d \] +/, mfa\Y\]k&

;mYf\g k] j][aZ] ]d _†f]jg$ ]d fan]d \] ]pakl]f[aYk k] ]f[m]fljY ]f *(( mfa\Y\]k$ hgj dg im]
]d fan]d \] ]pakl]f[aYk \]khm†k \] dY j]hgka[af k]j \] 0-) mfa\Y\]k&

P, «ª«« Cm 0/, +/, *- »»º»
*(

Hj]nakaf +/, *- ˜ -! *,1
¬ ¼ P, 1(( *,1 .-)

104

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4La gestión de las existencias

Caso práctico 7 Importante
=d kakl]eY \] [gZ]jlmjY \] dY hgka%
DY ]ehj]kY :geZYk DgrYfg$ K&9&$ k] \]\a[Y Y dY [ge]j[aYdarY[af \] ZgeZYk kme]j_a\Yk [af \]d stock k] ]pYeafY ]f ^][`Yk
hYjY ja]_g& @Y j]YdarY\g mf [gfljYlg \] YhjgnakagfYea]flg \] ^gjeY im] dY ]ehj]kY km% hj]^abY\Yk& =d h]jag\g im] nY ]flj]
eafakljY\gjY \]Z] j]ealaj +&.(( mfa\Y\]k$ ]flj]_Yf\g \aYjaYe]fl] ,-( mfa\Y\]k `YklY \gk ^][`Yk k] \]fgeafY ¿h]jag\g
mfY fm]nY h]la[af hgj \a[`Y [Yfla\Y\& 9\]ek$ [gfg[]egk dY ka_ma]fl] af^gjeY[af2 \] j]nakafÀ& QY im] dY ^][`Y ]kl
^abY\Y$ kgdg fgk im]\Y [Yd[mdYj dY
 DYk kYda\Yk \aYjaYk \]d YdeY[†f kgf \] *-( mfa\Y\]k y )-(!& [Yfla\Y\ Y h]\aj ]f ^mf[af \]d fan]d
 =d hdYrg \] YhjgnakagfYea]flg la]ehg im] ljYfk[mjj] \]k\] im] ]d \]hYjlYe]flg \] epaeg \] stock.

^YZja[Y[af kgda[alY dgk eYl]jaYd]k `YklY im] k] dgk kmeafakljY ]d \]hYjlYe]flg \] [ge% 105
hjYk! ]k \] , \ŠYk&
 DY [Yfla\Y\ im] ]fljY ]f YdeY[†f Y \aYjag ]k \] ,-( mfa\Y\]k x ,-(!&

K] \]k]Y kYZ]j ]f im† ege]flg `Yq im] \Yj dY gj\]f \] ^YZja[Y[af hYjY aeh]\aj mfY
jglmjY \] stocks.

Solución

NYegk Y j]YdarYj mf k]_maea]flg \]d hjgZd]eY e]\aYfl] dY ka_ma]fl] lYZdY2

t (días) x (uds.) y (uds.) x y Existencias

) ,-( )-( +(( +((
* ,-( )-( +(( .((
+ ,-( )-( +(( 1((
, ,-( )-( +(( )&*((
- ,-( )-( +(( )&-((
. ,-( )-( +(( )&0((
/ ,-( )-( +(( *&)((
0 ,-( )-( +(( *&,((
1 150 150 *&*-(
)( – 150 150 *&)((
)) – 150 150 )&1-(
)* – 150 150 )&0((
)+ – 150 150 )&.-(
), – 150 150 )&-((
)- – 150 150 )&+-(
). – 150 150 )&*((
)/ – 150 150 )&(-(
)0 – 150 150 1((
)1 – 150 150 /-(
*( – 150 150 .((
*) – 150 150 ,-(
** – 150 150 +((
*+ – 150 150 )-(
*, – 150 150 (
*- – )-( +(( +((
*. ,-( )-( +(( .((
*/ ,-( )-( +(( 1((
– ,-( –
– – –

N]egk im] ]d \ŠY *($ ]f im] ]d stock dd]_Y Y .(( mfa\Y\]k$ `YZj im] \Yj dY gj\]f \] ^Y%

Zja[Y[af hYjY im] dYk hjae]jYk mfa\Y\]k \] YhjgnakagfYea]flg ]flj]f ]f ]d YdeY[†f$ qY

im] ]d hdYrg \] j]YhjgnakagfYea]flg ]k \] [mYljg \ŠYk& (Continúa)

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4 La gestión de las existencias

Importante Caso práctico 7 (continuación)
DY j]hj]k]flY[af _j^a[Y \] dgk fan]d]k \] stock ]k dY ka_ma]fl]2
=f ]d kakl]eY \] j]hgka[af \] af%
n]flYjagk ¿eaplgÀ ]d fan]d \] Yd]jlY 3.000 Stock máximo: 2.400 unidades
\]k]f[Y\]fY ]d h]\a\g$ h]jg dY [Yf% 2.500
la\Y\ ]k [Yd[mdY\Y [Y\Y n]r ]f ^mf%
[af \] dYk af^gjeY[agf]k \]d ]flgj% 2.000
fg$ Za]f k]Yf \] dgk hjg\m[lgk g \] 1.500
dgk [da]fl]k& 1.000

500 Punto de pedido

600 unidades
Agotamiento

stock

0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

Fig. 4.10. =ngdm[af \]d stock.

=f j]kme]f$ dgk stocks kgf mf e]\ag$ fg mfY e]lY& =d gZb]lang \] dgk kakl]eYk \] j]hgka[af ]k
l]f]j dY km^a[a]fl] [Yfla\Y\ \] eYl]jaYd]k ]f ]d afn]flYjag hYjY Yd[YfrYj dY e]lY \] k]jna[ag
hjghm]klY& Mf kakl]eY dg_Škla[g hYjY ]d [d[mdg \] dgk fan]d]k \] stocks g^j][] hgkaZada\Y\]k \]
Yhgqg hYjY dY lgeY \] \][akagf]k$ \] [YjY Y Yd[YfrYj dgk gZb]langk hjghm]klgk& Q [geg `]jjY%
ea]flY hYjY ]d [gfljgd$ Yqm\Y Y ljYlYj \] eYf]jY mfa^gje] q kakl]ela[Y dYk \a^]j]fl]k nYjaY%
Zd]k$ lYd]k [geg dY hj]nakaf \] \]eYf\Y$ lYeYŽg \] dgl]k$ lead-times, ]l[&

Actividades

13. Dgk YjlŠ[mdgk [gehjY\gk Y mf hjgn]]\gj [m]klYf *($(( € [Y\Y mfg q ]d hjgfkla[g \]
dY \]eYf\Y hYjY ]d YŽg ka_ma]fl] ]k \] )&((( mfa\Y\]k& Ka [Y\Y n]r im] k] ]eal] mf
h]\a\g [m]klY -$(( € q ]d [gkl] \] YdeY[]fYb] ]k \] ,$(( € hgj mfa\Y\ Yd YŽg2
a) ¸Im† [Yfla\Y\]k k] \]Z]jŠYf [gehjYj hgj [Y\Y h]\a\g7
b) ¸;md ]k ]d [gklg lglYd \] dgk h]\a\gk hYjY mf YŽg7
c) ¸;md ]k ]d [gklg lglYd \] YdeY[]fYb] hYjY mf YŽg7

14. MfY ]ehj]kY mladarY YfmYde]fl] )*&((( ]fnYk]k hYjY [ge]j[aYdarYj kmk hjg\m[lgk&
;Y\Y ]fnYk] la]f] mf hj][ag \] ($,- € q km [gkl] YfmYd \] eYfl]faea]flg ]k \]
($)(€& J]YdarYj mf h]\a\g [m]klY [geg e]\aY *$-( €$ q lYj\Y ]f k]j k]jna\g 0 \ŠYk&
9 hYjlaj \] dgk \Ylgk Yfl]jagj]k$ [Yd[mdY2
a) =d ngdme]f ][gfea[g \] h]\a\g&
b) =d hmflg \] h]\a\g&

15. MfY ]ehj]kY f][]kalY YfmYde]fl] +((&((( c_ \] eYl]jaY hjaeY hYjY dY hjg\m[[af&
=d [gkl] \] _]klaf \] mf h]\a\g ]k \] )( € q ]d [gkl] \] hgk]kaf mfalYjag YfmYd ]k
\] . €& L]fa]f\g ]f [m]flY im] ]d hj][ag \] [gehjY ]k \] / €'c_$ k] ha\]2
a) ;Yd[mdY ]d h]\a\g hlaeg k]_”f ]d eg\]dg \] Oadkgf&
b) ;Yd[mdY ]d f”e]jg \] h]\a\gk im] \]Z] j]YdarYj YfmYde]fl] l]fa]f\g ]f [m]flY
]d j]kmdlY\g Yfl]jagj&
c) ;Yd[mdY ]d la]ehg im] hYkY ]flj] \gk h]\a\gk&

106

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4La gestión de las existencias

8. El stock de seguridad
y sus costes asociados

=f ]d eg\]dg Yfl]jagj$ ]d fan]d \] kYda\Y \] dYk ]pakl]f[aYk ]jY [gfg[a\g$ h]jg dY j]Yda\Y\ fgk
af\a[Y im] dY \]eYf\Y \] dgk [da]fl]k fg k] [gehgjlY \] Y[m]j\g [gf eg\]dgk \] []jl]rY$ kafg
im] km]d] ^dm[lmYj Y dg dYj_g \]d YŽg& ;mYf\g fg k] [gfg[] [gf []jl]rY ]d jaleg \] kYda\Y \]
dYk mfa\Y\]k YdeY[]fY\Yk$ dY ]ehj]kY \]Z]j ^abYj mf stock \] k]_mja\Y\ hYjY `Y[]j ^j]fl] Y dYk
kYda\Yk im] k] [gfka\]j]f kmh]jagj]k Y dYk fgjeYd]k&

El stock de seguridad ]k Yim]ddY hYjl] \]d stock lglYd im] k] eYfla]f] ]f YdeY[†f hgj
]f[aeY \]d stock fgjeYd& =d gZb]lang ]k `Y[]j ^j]fl] Y dYk hgkaZd]k \]egjYk ]f dgk kmea%
fakljgk \] dgk hjgn]]\gj]k q Y dYk \]eYf\Yk YfgjeYde]fl] YdlYk ]f \]l]jeafY\gk \ŠYk g
l]ehgjY\Yk&

=f km [d[mdg \]Z]f afl]jn]faj dgk \an]jkgk \]hYjlYe]flgk \] dY ]ehj]kY$ im] \]Z]jf YhgjlYj
dY af^gjeY[af ka_ma]fl]2

Aprovisionamiento Fabricación Ventas

<Ylgk kgZj] ]d la]ehg f][]kYjag hYjY YdeY[]fYj$ La]ehg eŠfaeg hYjY @Zalg \] dgk [da]fl]k&

ljYfkhgjlYj q ]flj]_Y \] dgk eYl]jaYd]k& ^YZja[Yj dgk hjg\m[lgk&

El coste de rotura fgk na]f] \Y\g hgj dY h†j\a\Y hjgZYZd] ]f im] k] af[mjjaj ka fg k] hm]\] Recuerda
Yl]f\]j Y dY \]eYf\Y hgj ^YdlY \] ]pakl]f[aYk& Ka k] ljYlY \] mfY ]ehj]kY [ge]j[aYd$ ]d `][`g
\] fg Yl]f\]j dY h]la[af \] mf [da]fl] hm]\] ka_fa^a[Yj h]j\]jdg$ hgj km [YhlY[af hgj mf [ge% 9d [gkl] \] jglmjY lYeZa†f k] d]
h]la\gj& =f ]d [Ykg \] ]ehj]kYk af\mkljaYd]k$ dY ^YdlY \] eYl]jaYd]k hm]\] hYjYdarYj ]d hjg[]kg ddYeY stockout.
hjg\m[lang$ q k] la]f]f im] kghgjlYj dgk [gkl]k ^abgk \mjYfl] ]d la]ehg im] k] lYj\] ]f ]d j]Y%
hjgnakagfYea]flg \] \a[`gk eYl]jaYd]k&

=f l†jeafgk _]f]jYd]k$ dY afljg\m[[af \] mf stock \] k]_mja\Y\ kmhgf]2

 9me]flg \]d fan]d e]\ag ]f YdeY[†f q hgj lYflg \]d [gkl] \] YdeY[]fYea]flg&

 9me]flg \] dY [Yfla\Y\ (q) ]pakl]fl] ]f ]d YdeY[†f [mYf\g kgda[alYegk ]d h]\a\g Y dgk
hjgn]]\gj]k&

 9me]flg \] dgk [gkl]k lglYd]k Yd Yme]flYj ]d [gkl] \] YdeY[]fYea]flg!&

=f ]d hdYfl]Yea]flg \] \a[`gk [gkl]k afl]jna]f]f mfY k]ja] \] nYjaYZd]k k] ljYlY \] mfY ^mf[af
\] hjgZYZada\Y\ im] j]khgf\] Y dY ddYeY\Y distribución normal$ im] n]j]egk hgkl]jagje]fl]!$
hgj dg im] ]f ]d ka_ma]fl] [Ykg hj[la[g hjghgj[agfYegk \a[`gk [gkl]k ]f mfY [Yfla\Y\ qY
hj]\]l]jeafY\Y&

Actividades 107

16. DY ]ehj]kY 9N9L9J$ K&9&$ \]\a[Y\Y Y dY ^YZja[Y[af \] gj\]fY\gj]k$ la]f] Y[lmYde]fl]
mf stock \] k]_mja\Y\ \] .&((( mfa\Y\]k& 9fl] dY dd]_Y\Y \] dY [YehYŽY \] FYna\Y\$
\]k]Y af[j]e]flYj ]d stock \] k]_mja\Y\ Y 0&((( gj\]fY\gj]k& =kl] kgZj]%stock k]
eYfl]f\j \mjYfl] +( \ŠYk& K] [m]flY$ Y\]ek$ [gf ]klY af^gjeY[af2
 =d [gkl] \] ^YZja[Y[af \] [Y\Y gj\]fY\gj ]k \] +.( €&
 =d [gkl] \] _]klaf \] dgk eYl]jaYd]k ]k \] )* € hgj gj\]fY\gj&
 =d [gkl] \]d ljYfkhgjl] \] dgk eYl]jaYd]k \] [Y\Y gj\]fY\gj ]k \] + €&
 Dgk [gkl]k ^abgk \] dY ]ehj]kY Yk[a]f\]f Y +((&((( €&

9 hYjlaj \] dY af^gjeY[af Yfl]jagj$ [Yd[mdY ]f [mflg k] af[j]e]flY ]d [gkl] lglYd \]
dY ]ehj]kY hgj Yme]flYj ]d stock \] k]_mja\Y\&

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4 La gestión de las existencias

Caso práctico 8 DY ]ehj]kY ;Yj]lgk$ K&9&$ k] \]\a[Y Y dY ^YZja[Y[af \] [Yj]lYk \] [Ym[`g hYjY ^a]klYk q
[YjfYnYd]k& K]_”f ]klm\agk j]YdarY\gk$ la]f] hj]naklY mfY \]eYf\Y YfmYd \] +(&((( c_
Web \] [Ym[`g$ im] ]k hj[la[Ye]fl] [gfklYfl] \mjYfl] lg\g ]d YŽg& =d [gkl] mfalYjag ]k \]
=f hjg_jYeY OafIK: ]k _jYlmalg q /$((€'c_& =d [gkl] \] j]YdarYj mf h]\a\g \] [Ym[`g Yk[a]f\] Y )-( €$ q ]d [gkl] \] eYf%
\akhgf] \] ]b]ehdgk q eYfmYd]k& Dg l]faea]flg ]k \] ($-( € YfmYd]k hgj c_& =d hdYrg \] YhjgnakagfYea]flg q ]flj]_Y \]d
hm]\]k gZl]f]j ]f Afl]jf]l$ ]f dY hjgn]]\gj (t) ]k \] lj]k \ŠYk& =d [gfkmeg epaeg \aYjag ]k \] )1( c_$ q ]d [gfkmeg e]\ag
h_afY \]d \]kYjjgddY\gj q ]f ]d hgj% \aYjag \] )(( c_& 9 hYjlaj \] ]klgk \Ylgk k] fgk ha\] im] [Yd[md]egk2
lYd Kg^lgfa[2
http://winqsb.softonic.com a) =d ngdme]f hlaeg \] h]\a\g&
b) =d f”e]jg \] h]\a\gk YfmYd]k q ]d h]jag\g \] j]nakaf&
c) =d stock \] k]_mja\Y\ q ]d hmflg \] h]\a\g&
d) DY [Yfla\Y\ Y kgda[alYj ka ]f ]d ege]flg \] j]nakaf \]d fan]d \] ]pakl]f[aYk k] ]f[m]f%

ljY ]f .(( c_&

Solución

a) 9hda[Yegk dY ^jemdY \] Oadkgf hYjY \]l]jeafYj ]d ngdme]f hlaeg \] h]\a\g2

VOP = +(&((( ⋅ )-($(( ⋅ * = ,&*,+
($-

b) F”e]jg \] h]\a\gk YfmYd]k +(&((( / h]\a\gk
,&*,+

H]jag\g \] j]nakaf +.- -* \ŠYk
/

c) Stock \] k]_mja\Y\ CM È Cm! Ù Pe )1( )((! Ù + */( c_

Hmflg \] h]\a\g2 Pp! ;gfkmeg ]f hdYrg \] ]flj]_Y Cpe! Ss2

(Pp) +(&((( ⋅ + + */( = -). c_
+.-

d) Fan]d epaeg \] stock: NMs! Pp VOP = -). ,&*,+ ,&/-1 c_

;geg ]d fan]d \] ]pakl]f[aYk k] ]f[m]fljY ]f .(( c_$ `YZj im] kgda[alYj `YklY [gehd]lYj
]d fan]d epaeg \] stock, ]k \][aj$ ,&/-1 .(( ,&)-1 c_&

9d k]j dY revisión periódica, ]f ]d ege]flg \] kgda[alYj ]d h]\a\g fgk ]f[gfljYegk hgj \]%
ZYbg \]d hmflg \] h]\a\g ^abY\g$ ]f +. mfa\Y\]k$ im] `]egk \] kmeYj ]f ]kl] [Ykg Yd VOP&

Ngdn]egk Y mladarYj ]d hjg_jYeY af^gjela[g OafIK:$ Y ljYn†k \] dY gh[af Inventory
Theory and System, hYjY gZl]f]j ]d [d[mdg \]d ¿dgl] ][gfea[g \] [gehjYÀ& @] YimŠ dY
_j^a[Y im] fgk g^j][] [gf dY kgdm[af \]d hjgZd]eY2

Fig. 4.11. Ngdme]f hlaeg \] h]\a\g
\] dY ]ehj]kY ;Yj]lg$ K&9&

108

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4La gestión de las existencias

Caso práctico 9

DY ]ehj]kY Gj]bYk$ K&9&$ \]\a[Y\Y Y dY [ge]j[aYdarY[af ] afklYdY[af \] Yfl]fYk hYjYZ%
da[Yk$ \]k]Y [gfg[]j \an]jkgk \Ylgk ][gfea[gk j]dYlangk Y km YdeY[†f$ q k] hdYfl]Y ]f
hjae]j dm_Yj \]l]jeafYj [md ]k ]d stock \] k]_mja\Y\& ;m]flY [gf dgk \Ylgk ka_ma]fl]k
kgZj] dY ]ngdm[af `aklja[Y \] km fan]d \] stocks:

Enero Año 1 Año 2 Año 3 Año 4
Febrero
Marzo **( )*( **( ),(
Abril 0( ).( *,( )0(
Mayo *(( )0( *(( ),(
Junio )(( )*( )(( )0(
Julio )0( ).( *,( )*(
Agosto +(( **( ).( ).(
Septiembre )(( )0( 0( )0(
Octubre ).( ),( ),( *((
Noviembre **( ).( *0( *,(
Diciembre +*( +0( *(( **(
),( )0( *.( )*(
*.( *(( ),( )((

<]Z]egk [Yd[mdYj ]d stock \] k]_mja\Y\$ kYZa]f\g im]2 Importante
MladarY dY `gbY \] [d[mdg hYjY
 =d j]YhjgnakagfYea]flg \]d YdeY[†f k] ]^][l”Y e]fkmYde]fl]& gZl]f]j dgk \Ylgk \] dY lYZdY2 YkŠ
 =d [gkl] \] jglmjY k] `Y ]klaeY\g ]f )-$(( €& hg\jk mladarYj ^mf[agf]k im]
 DY lYkY \] hgk]kaf ]k \]d )( & Y`gjjYf la]ehg q ]jjgj]k&
 =d [gkl] mfalYjag ]k \] 1($(( €&
 DY hj]nakaf \] n]flYk ]k \] ),. mfa\Y\]k e]fkmYd]k& (Continúa)
109
Solución

=f hjae]j dm_Yj$ `]egk \] ]klaeYj ]f im† _jY\g hm]\]f \]knaYjk] \] km nYdgj e]\ag dYk
kYda\Yk j]Yd]k$ q [gehYjYj dY ^j][m]f[aY \] dYk \an]jkYk \]knaY[agf]k hgkalanYk q f]_YlanYk
im] ]d [gfkmeg j]Yd j]hj]k]flY kgZj] ]d hj]kmhm]klY\g&

HYjY mf e]bgj k]_maea]flg$ nYegk Y hdYfl]Yj ]d ]b]j[a[ag Yqm\f\gfgk \] dY `gbY \] [d%
[mdg hYjY [gfkljmaj mfY lYZdY ]f dY im] k] em]klj]f dgk \Ylgk ka_ma]fl]k2

 Salidas mensuales. K] [gdg[Yf \] eYqgj Y e]fgj dYk kYda\Yk \] YdeY[†f&

 Frecuencia. =k ]d f”e]jg \] n][]k im] k] j]hal] [Y\Y mfY \] dYk kYda\Yk& Hgj ]b]ehdg$
]d nYdgj +(( kgdg YhYj][] mfY n]r ]f dgk [mYljg YŽgk$ ]f [YeZag$ ]d nYdgj *,( YhYj][]
, n][]k&

 Frecuencia acumulada. =k dY kmeY Y[memdY\Y \] dYk ^j][m]f[aYk \] dYk kYda\Yk&

 Frecuencia acumulada en porcentaje. =k mf lYflg hgj [a]flg im] j]hj]k]flY [Y\Y mfY
\] dYk ^j][m]f[aYk kgZj] ]d lglYd \] dY Y[memdY\Y& 9kŠ$ dY kmeY \] dYk ^j][m]f[aYk \] dYk
kYda\Yk ]k \] ,0& 9 dY ^j][m]f[aY * d] [gjj]khgf\] ]d ,$)/ \]d lglYd& 9d nYdgj , d] [g%
jj]khgf\]j ]d 0$++ $ q YkŠ km[]kanYe]fl]&

 Desviaciones de las salidas. DY kmeY \] dYk kYda\Yk \] dgk [mYljg YŽgk ]k \] 0&/*(& Km
e]\aY k]j 0&/*(',0 )0)$./& Dm]_g dY hjae]jY \]knaY[af \] dYk kYda\Yk fgk na]f]
\Y\Y hgj ]d ka_ma]fl] [ehmlg2 +0( )0)$./ )10$++$ q YkŠ km[]kanYe]fl]&

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4 La gestión de las existencias

Caso práctico 9 (continuación)

DY lYZdY im] j]kmdlY \] j]YdarYj ]klYk gh]jY[agf]k ]k dY ka_ma]fl]2

Salidas Frecuencia Frec. Frec. acumulada Desviación de Xi Cp Coste total
mensuales acumulada en % F(S) las salidas Xi Cp
)$0/- )&/0-
+0( ) ) *$(0 )10$++ +$/- )&*,- )&/0.$0/-
,$)/ )+0$++ -$.*- )&(.- )&*,0$/-
+*( ) * .$*- ))0$++ /$- 00- )&(/($.*-
0$++ 10$++ ))$*- /(- 01*$-
+(( ) + )*$-( /0$++ ).$0/- -*- /).$*-
)0$/- -0$++ *.$*- +,- -,)$0/-
*0( ) , *1$)/ +0$++ +-$.*- ).- +/)$*-
+1$-0 )0$++ ,0$/- *(($.*-
*.( * . -,$)/ )$./ .( * ,0$/-
..$./ *)$./ /)$*- *
*,( + 1 /1$)/ ,)$./ /0$/- * .(
0/$-( .)$./ 0.$*- * /)$*-
**( - ), 1-$0+ 0)$./ 1( * /0$/-
)(( )()$./ * 0.$*-
*(( - )1
1(
)0( / *.

).( . +*

),( . +0

)*( , ,*

)(( , ,.

0( * ,0

Claves y consejos =d ja]k_g \] jglmjYk hgj [Y\Y e]k ]da_a]f\g mf stock \] k]_mja\Y\ [mqg nYdgj k]Y (Ss), fgk
n]f\j \Y\g hgj2
<]k\] mf hmflg \] naklY ][gf%
ea[g fg la]f] k]fla\g ]klm\aYj F Ss! )*
dYk \]knaY[agf]k f]_YlanYk& P

=k \][aj$ ]klYj ]f ^mf[af \] dY [Yfla\Y\ \] stock \] k]_mja\Y\ (Ss) im] l]f_Yegk q \]d
f”e]jg \] n][]k im] j]Yhjgnakagf]egk ]d YdeY[†f ]f fm]kljg [Ykg )* n][]k ]f ]d YŽg
Yd k]j e]fkmYd ]d j]YhjgnakagfYea]flg!&

=d [gkl] YfmYd \] jglmjYk k] [Yd[mdY [gf dY ][mY[af2

X) = )*R ⋅F Ss!
P

\gf\] R ]k ]d [gkl] mfalYjag \] jglmjY hjgZYZd]! e]fkmYd&

=d [gkl] \] hgk]kaf [gf ]klY gljY ][mY[af2

Cp T Ù Pu Ù Ss

\gf\]2

T LYkY mfalYjaY \] hgk]kaf&
Pu ;gkl] mfalYjag \] mf hjg\m[lg&
Ss Stock \] k]_mja\Y\ \]knaY[af!&

(Continúa)

110

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4La gestión de las existencias

Caso práctico 9 (continuación)

Ka j]hj]k]flYegk _j^a[Ye]fl] YeZgk [gkl]k$ n]egk [eg nYjŠYf mfg q gljg ]f ^mf[af
\]d fan]d \] \a[`g stock.

40 2.000 Importante
35 1.800
30 1.600 =d stock \] k]_mja\Y\ ]kl j]dY[agfY%
25 1.400 \g [gf ]d fan]d \] k]jna[ag im] k]
20 1.200 \]k]Y j]YdarYj& =d af[j]e]flg \]d fa%
15 1.000 n]d \] k]_mja\Y\ af[j]e]flY ]d fan]d
10 \] k]jna[ag$ h]jg lYeZa†f ]d [gkl] \]d
800 YdeY[†f&
5 600
0 400 200 220 240 260 280 300 320 380
200 Salidas mensuales
200 220 240 260 280 300 320 380
Salidas mensuales 0

Fig. 4.12. ;gehYjY[af ]flj] YeZgk lahgk \] [gkl]k \] dY ]ehj]kY Gj]bYk$ K&9&

K] ljYlY$ hgj lYflg$ \] \]l]jeafYj ]d nYdgj \] Ss! im] `Y_Y eŠfaeY dY kmeY \] ]klgk [gk%
l]k ]phj]kY\Y ]f dgk ka_ma]fl]k l†jeafgk2

X) + Cp = )*R ⋅F Ss! + T ⋅ P ⋅ Ss
P

<gf\] hYjY ]d hjae]j nYdgj l]f\jŠYegk2

X) = )* ⋅ )- ⋅ ($(*(0 = ))&0/-
*

Cp ($)( ˜ 1( ˜ )10$++ )&/0-

DY lYZdY Yfl]jagj fgk em]kljY im] ]d [gkl] lglYd YfmYd hj]k]flY mf eŠfaeg hYjY ]d nYdgj
Ss -0$++& H]jg ]kl] nYdgj aehda[Y mf ja]k_g \] jglmjY \]d )0$/- \] dYk n][]k$ ]k \][aj$
im] [geg hjge]\ag k] j]_akljYjf [Y\Y e]k ($)0/- jglmjYk 1',0!$ g k]Y2

($)0/- ˜ )* *$*- jglmjYk Yd YŽg

Hgj lYflg$ ]d ngdme]f hlaeg \] h]\a\g k]jŠY \] *,( mfa\Y\]k$ \] dYk [mYd]k$ )0* ]k dY
[Yfla\Y\ hj]naklY \] n]flYk q +0 [geg stock \] k]_mja\Y\&

=k ]na\]fl] im] hYjY km[]kangk h]\a\gk ]klY [Yfla\Y\ k] j]YbmklYjŠY ]f ^mf[af \] dYk
]pakl]f[aYk j]Yd]k&

Otra forma \] \]l]jeafYj ]d stock \] k]_mja\Y\ k]jŠY ZYkf\gfgk ]f dgk ka_ma]fl]k \Ylgk2

 CM ;gfkmeg epaeg \aYjag&
 Cm ;gfkmeg e]\ag \aYjag&
 Pe HdYrg \] ]flj]_Y g YhjgnakagfYea]flg \]d hjgn]]\gj&
 Ss CM Cm! Ù Pe&

Actividades a) =d lYeYŽg \]d dgl] hlaeg \] [gehjY&
b) =d f”e]jg \] h]\a\gk YfmYd]k&
17. DY ]ehj]kY :Yjjad]jg$ K&9&$ ]kh][aYdarY\Y ]f dY [ge]j[aYdarY% c) =d h]jag\g \] j]nakaf&
[af \] ZYjjad]k hYjY []jn]rY$ ljYZYbY **( \ŠYk Yd YŽg& =d [gklg d) =d hmflg \] h]\a\g&
\] ]eakaf \] mf h]\a\g m gj\]f ]k \] +($(( € q ]d [gkl] \]
YdeY[]fYea]flg mfalYjag \] dgk ZYjjad]k ]k \] *$-(Â €& =d
la]ehg \] hjgnakaf j]im]ja\g hYjY j][aZaj mf h]\a\g \] ZYjja%
d]k \] []jn]rY \]k\] ]d \akljaZma\gj ]k \] +Â\ŠYk& <]l]jeafY2

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4 La gestión de las existencias

9. Cálculo del punto de pedido y del
stock de seguridad cuando la demanda
sigue una distribución normal

Importante ;mYf\g mf ^]fe]fg k] j]hal] emq Y e]fm\g$ q hgj dg lYflg kmk \Ylgk kgf [gfg[a\gk ]f l†j%
HYjY kYZ]j ek \] dY \akljaZm[af eafgk \] hjgZYZada\Y\$ hYjY gZl]f]j mf e]bgj [gfg[aea]flg \] †d ]f ]d ^mlmjg$ hg\]egk Yhda[Yj
fgjeYd hm]\]k [gfkmdlYj dY ka_ma]f% dY \]fgeafY\Y \akljaZm[af fgjeYd&
l] h_afY o]Z2 http://www.uoc.
edu/in3/emath/docs/Distrib_Nor DY jglmjY \] stocks k] hjg\m[] [mYf\g dY \]eYf\Y ]f ]d hdYrg \] ]flj]_Y ]k ek ]d]nY\Y im]
mal.pdf dYk ]pakl]f[aYk ]f ]d YdeY[†f$ h]jg dY \]eYf\Y ]k \a^Š[ad \] [Yd[mdYj [gf hj][akaf$ hm]k \]h]f%
\] \] dY Yehdalm\ \]d hdYrg \] ]flj]_Y q \] dY \]eYf\Y \] hjg\m[lgk \] dgk [da]fl]k& =k \][aj$
1 P 0, V2 0,2 dg ”fa[g im] hg\]egk `Y[]j ]k e]\ajdY ]f l†jeafgk \] hjgZYZada\Y\$ q ]k YimŠ \gf\] nYegk Y
0,9 P 0, V2 5,0 kmhgf]j im] \a[`Y \]eYf\Y k] [gehgjlY k]_”f dgk hYje]ljgk \] dY \akljaZm[af fgjeYd
0,8 P 0, V2 0,5
0,7 DY \akljaZm[af fgjeYd k] hm]\] Yhda[Yj Y fme]jgkgk ^]fe]fgk im] g[mjj]f ]f dY fYlmjYd]rY$
0,6 q k] [YjY[l]jarY hgj im] dgk nYdgj]k k] \akljaZmq]f \] eYf]jY mfa^gje] Y ljYn†k \] dY \]fgea%
0,5 fY\Y [YehYfY \] ?Ymkk$ \] ^gjeY im] km nYdgj e]\ag k] ]f[m]fljY ]f ]d nYdgj ek Ydlg \] dY
0,4 [YehYfY q Y km arima]j\Y q \]j][`Y \]bY ]d eakeg f”e]jg \] nYdgj]k -( !&
0,3
0,2 MfY [mjnY fgjeYd na]f] \]^afa\Y hgj dY e]\aY q dY \]knaY[af lŠha[Y & MfY n]r [Yd[mdY\Yk \a[`Yk
0,1 nYjaYZd]k k] hm]\] ]klaeYj im] dY hjgZYZada\Y\ \] dY nYjaYZd] k]Y kmh]jagj g af^]jagj Y mf \]l]j%
5 4 3 2 1 0 1 2 3 4 5 eafY\g f”e]jg&
Fig. 4.13. NYjaYk \akljaZm[agf]k fgjeYd]k&
LYflg P [geg V hm]\]f Ykmeaj infinitos valores, dg im] `Y[] aehjY[la[YZd] `Y[]j lYZdYk \]
hjgZYZada\Y\]k hYjY lg\Yk dYk hgkaZd]k \akljaZm[agf]k fgjeYd]k& Hgj ]ddg$ k] mladarY dY distribu-
ción normal reducida o tipificada, ]f dY [mYd P ( q V )& ;mYdima]j \akljaZm[af fgjeYd$ kaf
aehgjlYj [md k]Y km e]\aY q km \]knaY[af lŠha[Y$ hm]\] [gfn]jlajk] ]f mfY fgjeYd laha^a[Y\Y
j]YdarYf\g dY ljYfk^gjeY[af ka_ma]fl]2

Z X P
V

rV 68 %
r2V 95 %
r3V 99 %

68 %

Importante 3 2 1 95 % 1 2 Z
99 % 3
DY \]knaY[af lŠha[Y fgk ea\] dY j]%
hj]k]flYlana\Y\ \] dY e]\aY& 0

Fig. 4.14. <akljaZm[af fgjeYd laha^a[Y\Y&

Web =d [d[mdg \] hjgZYZada\Y\]k mladarYf\g dY \akljaZm[af fgjeYd laha^a[Y\Y dg hg\]egk j]kgdn]j \]
\gk ^gjeYk2
Ka \]k]Yk n]j mf ]b]ehdg \] [eg k]
Yhda[Y dY \akljaZm[af fgjeYd [gf dY  9 ljYn†k \] dY `gbY \] [d[mdg =p[]d$ [gf dY ^mf[af ]klY\Škla[Y DISTRIB.NORM.ESTAND.INV&
`gbY \] [d[mdg hm]\]k$ Zmk[Yj ]f Lg\gk dgk hjg_jYeYk \] `gbY \] [d[mdg km]d]f l]f]j mfY ^mf[af kaeadYj&
QgmLmZ] ]d nŠ\]g «Ejemplo de uso de
la distribucion normal EJEMPLO 1»  E]\aYfl] lYZdYk&

112 DYk hjgZYZada\Y\]k \] dY nYjaYZd] laha^a[Y\Y z! ]klf lYZmdY\Yk hYjY dgk \a^]j]fl]k nYdgj]k \]
dY nYjaYZd]& =f[gfljYjk dY lYZdY \] ]klgk nYdgj]k Yd ^afYd \] ]kl] daZjg& MfY n]r ljYfk^gjeY\Y dY
nYjaYZd] Y nYdgj]k \] z k] Zmk[Y ]f dY lYZdY ]d j]Y [gjj]khgf\a]fl]&

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4La gestión de las existencias

Caso práctico 10 Importante

Kmhgf_Yegk im] k] [Yd[md ]d nYdgj z q ]d j]kmdlY\g ]k )$1)& ¸;md ]k ]d j]Y ZYbg dY [mjnY ;mYflg eYqgj k]Y ]d fan]d \] k]jna%
fgjeYd ]flj] P q x7 [ag$ e]fgj k]j dY hjgZYZada\Y\ \]
jglmjYk g \]kYZYkl][aea]flg ]f ]d
Solución YdeY[†f

<]k[]f\]j]egk hgj dY [gdmefY \] dY lYZdY ]f[YZ]rY\Y [gf dY d]ljY z `YklY dd]_Yj Y ¿)&1À
Dm]_g fgk egn]j]egk ]f \aj][[af `gjargflYd Y dY \]j][`Y q d]]j]egk dY hjgZYZada\Y\ ]f
dY [gdmefY [gf ]d ]f[YZ]rY\g )& =d j]kmdlY\g ]k ($,/)1&

Caso práctico 11

Dgk \Ylgk `aklja[gk \] \]eYf\Y \] mfY ]ehj]kY hYjY dgk ”dlaegk )( h]jag\gk kgf dgk Periodo Demanda Xi2
im] ^a_mjYf ]f dY lYZdY \]d eYj_]f& Ka ]d hmflg \] h]\a\g ]k \] )1( mfa\Y\]k$ [Yd[mdY dY (xi)
hjgZYZada\Y\ \] im] k] hjg\mr[Y mfY jmhlmjY \] stocks kmhgfa]f\g im] dY \]eYf\Y ka% ) ,(&(((
_m] mfY \akljaZm[af fgjeYd& ¸;md ]k ]d fan]d \] k]jna[ag7 ¸;md k]j dY hjgZYZada\Y\ \] * *(( +*&,((
im] dY \]eYf\Y k]Y af^]jagj Y ).( mfa\Y\]k7 + )0( *-&.((
, ).( ,0&,((
Solución - **( ).&1((
. )+( **&-((
1.º ;Yd[mdYegk dY e]\aY q dY \]knaY[af lŠha[Y \] dY \]eYf\Y / )-( ).&1((
X = Σin=)Xi = )&./( = )./ 0 )+( *0&1((
n )( 1 )/( +*&,((
)( )0( **&-((
σ= Σni=) X * − X*! = *0.&-(( − )./* ! = */$-0 LglYd )-( *0.&-((
i )&./(

n )(

2.º K] hjg\m[aj mfY jglmjY \] stocks ka dY \]eYf\Y \mjYfl] ]d hdYrg \] ]flj]_Y kmh]jY
]d hmflg \] h]\a\g$ ]k \][aj$ im] x $ ka]f\g R dY \akljaZm[af fgjeYd&

P X! ! )1( P Z ! )1( )./ P Z ! ($0*!
*/$-0
3.º :mk[Yegk ]f dY lYZdY&

;geg dY lYZdY fgk g^j][] P Z ($0*!$ j]YdarYegk ]d ka_ma]fl] [d[mdg2
P Z ! ($0*! ) P(Z ($0*! ) ($/1)( ($*(1$ ]k \][aj$ ]d *($1

=d nivel de servicio s]j ]d [gfljYjag \] dY hjgZYZada\Y\ \] jglmjY \] stock, ]k \][aj$ ) ($*1)( /($1 & =kl] j]kmdlY\g
j]hj]k]flY mf lgim] \] Yl]f[af aehgjlYfl]$ hm]k \] [Y\Y )(( h]\a\gk \]bYegk \] Yl]f\]j *1 ) ($/(1!&

La probabilidad \] im] dY demanda k]Y inferior a 160 mfa\Y\]k k]j a_mYd Y2

P X! ! ).( P Z ! )1( )./ P Z ($*-!
*/$-0
=d j]kmdlY\g ]k f]_Ylang$ q ]f dY lYZdY kdg k] lYZmdYf nYdgj]k hgkalangk& 9kŠ im] hjg[]\]j]egk \] ]kl] eg\g2

P(Z ($*-! P(Z ! ($*-! ) P(Z ($*-! ) ($-10/ ($,()+ → ,($)+

Actividades a) ;Yd[mdY dY hjgZYZada\Y\ \] im] dY \]eYf\Y k]Y kmh]jagj
Y ,( mfa\Y\]k$ YkŠ [geg ]d stock \] k]_mja\Y\ q ]d hmflg
18. DY hla[Y N=%N=G$ K&D&$ [ge]j[aYdarY dYk ^YegkYk _Y^Yk Rom- \] h]\a\g hYjY mf fan]d \] k]jna[ag \]d 1. &
petechok. DY \]eYf\Y \] ]kl] YjlŠ[mdg ka_m] mfY \akljaZm%
[af fgjeYd$ [gf dY ka_ma]fl] hj]nakaf \] n]flYk Y dg dYj_g b) J]hj]k]flY _j^a[Ye]fl] dY _]klaf \] stock k]_ma\Y hgj
\]d ]b]j[a[ag *()+2 dY ]ehj]kY&

E F MAM J J A S OND

-( +- ,( *+ *- -( ,- +0 ,- -. ./ +(

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5 El almacén dentro de la red logística

Síntesis &- "-."$²/ Almacenes de entrada

Almacenes de salida

TIPOS DE ALMACENES

Según la Según Según Según
naturaleza del la la función la
logística
producto localización propiedad
Consolidación
Materias Central Propio
primas Ruptura
Regional En alquiler
Productos Combinado
en curso De plataforma Leasing

Productos
terminados

Material
auxiliar

Con las funciones

Recepción Almacenaje .BOUFOJNJFOUP Picking Expedición
Con la distribución

Interna (lay-out) Externa (localización)
t «SFB EF BMNBDFOBKF
t «SFB EF NBOJQVMBDJØO A través de modelos
t «SFB EF DBSHB EFTDBSHB
t «SFB EF TFSWJDJPT JOUFSOPT t .FDÈOJDPT
t «SFB EF TFSWJDJPT FYUFSOPT t "EJUJWPT
t .VMUJQMJDBUJWPT
144 t $FOUSP EF HSBWFEBE

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5El almacén dentro de la red logística

Nota: Todas las actividades de esta página deben hacerse en un cuaderno aparte.

Test de repaso

J]khgf\] ]d l]kl ]f lm [mY\]jfg2 8. =d lay-out [gfkakl] ]f2
a) L]f]j ]f [m]flY dY d]_akdY[af kgZj] YdeY[]f]k&
1. =d «Just In Time» ]k mfY l]gjŠY im] YZg_Y hgj2 b) =d \ak]Žg \] dgk YdeY[]f]k&
a) K]jnaj dgk hjg\m[lgk Y dgk [da]fl]k kaf j]ljYkgk& c) =d hjg[]kg \] ]fljY\Y q kYda\Y \] dgk eYl]jaYd]k&
b) MladarYj dgk k]jna[agk \] ljYfkhgjl] ek jha\gk& d) Faf_mfY \] dYk Yfl]jagj]k ]k [gjj][lY&
c) Afl]flYj j]\m[aj Yd epaeg ]d fan]d \] stocks ]f ]d Yd%
eY[†f& 9. =d j]Y \] YdeY[]fYb] ]kl [gehj]f\a\Y hgj2
d) Faf_mfY \] dYk Yfl]jagj]k ]k [gjj][lY& a) ßj]Y ”lad q j]Y \] j][]h[af&
b) ßj]Y \] hYkaddg q j]Y \] \]khY[`g&
2. DY dg_Škla[Y$ ]f dg j]^]j]fl] Y dgk YdeY[]f]k$ k] ]f[Yj_Y \]2 c) ßj]Y ”lad q j]Y \] hYkaddg&
a) >gjeYj Yd h]jkgfYd \] dgk YdeY[]f]k& d) Faf_mfY \] dYk Yfl]jagj]k ]k [gjj][lY&
b) =d egnaea]flg afl]jfg \] dgk YdeY[]f]k&
c) <ak]ŽYj dY [Y\]fY \]k\] im] ]fljYf dgk eYl]jaYd]k ]f ]d 10. Dgk eg\]dgk e][fa[gk \] dg[YdarY[af \] YdeY[]f]k la]%
k]fg \] dY ]ehj]kY `YklY im] k] hgf]f dgk hjg\m[lgk Y f]f ]f [m]flY2
\akhgka[af \] dY \akljaZm[af& a) Lg\gk dgk hYje]ljgk ka_fa^a[Ylangk&
d) Faf_mfY \] dYk Yfl]jagj]k ]k [gjj][lY& b) Kgdg ]d [gkl] \]d ljYfkhgjl]&
c) =d [gkl] \] ljYfkhgjl] q ]d l]jj]fg&
3. MfY \] dYk jYrgf]k hYjY dY ]pakl]f[aY \] dgk YdeY[]f]k ]k2 d) Faf_mfY \] dYk Yfl]jagj]k ]k [gjj][lY&
a) ?mYj\Yj hYjY ]kh][mdYj ]f ]d ^mlmjg&
b) =nalYj \]k]imadaZjagk ]flj] dY \]eYf\Y q dY g^]jlY \] 11. =d YdeY[†f \] hdYlY^gjeY h]jl]f][] Y dY [dYka^a[Y[af \]
hjg\m[lgk& YdeY[]f]k j]YdarY\Y hgj2
c) 9[YhYjYj eYl]jaYd]k ] aeh]\aj im] l]f_Y Y[[]kg Y ]ddgk a) FYlmjYd]rY \]d hjg\m[lg&
dY [geh]l]f[aY& b) >mf[af dg_Škla[Y&
d) Faf_mfY \] dYk Yfl]jagj]k ]k [gjj][lY& c) Hjgha]\Y\&
d) Faf_mfY \] dYk Yfl]jagj]k ]k [gjj][lY&
4. =d YdeY[†f \] [gfkgda\Y[af la]f] [geg ^mf[af2
a) <ana\aj mf h]\a\g \] _jYf ngdme]f ]f nYjagk ]fnŠgk& 12. =d [\a_g =9F )+ ]k2
b) J]mfaj ]f mf kgdg YdeY[†f lg\gk dgk eYl]jaYd]k \] dY a) Mf [\a_g Yd^Yfme†ja[g&
]ehj]kY& b) Mf [\a_g ]d][ljfa[g&
c) 9_jmhYj ]f mf kgdg ]fnŠg nYjagk h]\a\gk& c) Mf [\a_g \] ZYjjYk&
d) Faf_mfY \] dYk Yfl]jagj]k ]k [gjj][lY& d) Faf_mfY \] dYk Yfl]jagj]k ]k [gjj][lY&

5. =d YdeY[†f \] jmhlmjY la]f] [geg ^mf[af2 13. =d lay-out `Y[] j]^]j]f[aY Y2
a) <ana\aj mf h]\a\g \] _jYf ngdme]f ]f nYjagk ]fnŠgk& a) DY kYda\Y \] dYk e]j[Yf[ŠYk \]d YdeY[†f&
b) J]mfaj ]f nYjagk YdeY[]f]k dgk eYl]jaYd]k \] dY ]ehj]kY& b) =d \ak]Žg \] dgk ]khY[agk \] dgk YdeY[]f]k&
c) 9_jmhYj ]f mf kgdg ]fnŠg nYjagk h]\a\gk& c) DYk j]_dYk im] `Yq im] gZk]jnYj hYjY eYfl]f]j dgk YdeY%
d) Faf_mfY \] dYk Yfl]jagj]k ]k [gjj][lY& []f]k&
d) Faf_mfY \] dYk Yfl]jagj]k ]k [gjj][lY&
6. =f =khYŽY$ ]d gj_Yfakeg ]f[Yj_Y\g \] [ggj\afYj dY [g\a^a%
[Y[af \] ZYjjYk ]k2 14. =d ^Y[lgj \] dg[YdarY[af \] dgk YdeY[]f]k `Y[] j]^]j]f[aY Y2
a) 9=;G;& a) Dgk eglangk hgj dgk im] mf ^Y[lgj ]k l]fa\g ]f [m]flY Y
b) =9F& dY `gjY \] \][a\aj dY mZa[Y[af \] mf YdeY[†f&
c) 9D=;GH& b) DY [Yfla\Y\ \] YljaZmlgk \] dY dg[Yda\Y\ \gf\] ]kl ^abY%
d) Faf_mfY \] dYk Yfl]jagj]k ]k [gjj][lY& \g ]d YdeY[†f&
c) DY [mYda\Y\ im] hgk]] mf \]l]jeafY\g ^Y[lgj _]g_j^a[g&
7. =d picking [gfkakl] ]f2 d) Faf_mfY \] dYk Yfl]jagj]k ]k [gjj][lY&
a) ;gehjgZYj dY e]j[Yf[ŠY j][aZa\Y&
b) =ealaj dY ^Y[lmjY&
c) Hj]hYjYj ]d h]\a\g&
d) Faf_mfY \] dYk Yfl]jagj]k ]k [gjj][lY&

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5 El almacén dentro de la red logística

Nota: Todas las actividades de esta página deben hacerse en un cuaderno aparte.

Comprueba tu aprendizaje

Conocer los factores que pueden influir en la localización. Conocer los métodos de localización de almacenes.

1. DY dg[YdarY[af \] dgk YdeY[]f]k$ ¸hm]\] Y^][lYj Y dgk [gk% 13. DY ]ehj]kY Lgjim]eY\Y$ K&9&$ k] \]\a[Y Y dY ^YZja[Y[af \]
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Conocer los sistemas de codificación de almacenes. p
q Ponderación (Fi)
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ka [gfg[]k mf f]_g[ag ek hjg^mf\Ye]fl]$ hm]\]k ghlYj DYk hmflmY[agf]k ]f [Y\Y dg[YdarY[af kgf dYk ka_ma]fl]k2
hgj j]YdarYj dY [g\a^a[Y[af \] \a[`Y ]ehj]kY&
Factor Factores y su puntuación RR
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p Localización -
12. DY ]ehj]kY EY[jg[`YhY\g$ K&D&$ hgk]] mf YdeY[†f [gf dYk q R /
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.
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 =d j]Y \] j][]h[af j][aZ] mfY [Yj_Y YfmYd \] +((&(((ÂC_ [af& =klY ]phYfkaf k] \]Z] Y dY [YhY[a\Y\ daealY\Y \]d
YdeY[†f ]pakl]fl]& DY ka_ma]fl] lYZdY em]kljY mfY k]ja] \]
Y dg dYj_g \] dgk **( \ŠYk im] gh]jY ]d YdeY[†f& ^Y[lgj]k j]d]nYfl]k hjghm]klgk hgj dY Y\eafakljY[af \] dY
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9 hYjlaj \] dY af^gjeY[af Yfl]jagj$ [Yd[mdY2

a) =d j]Y lglYd \]d YdeY[†f&

b) =d j]Y \] YdeY[]fYea]flg&

c) =d j]Y \] j][]h[af q \]khY[`g&

146

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5El almacén dentro de la red logística

Nota: Todas las actividades de esta página deben hacerse en un cuaderno aparte.

Comprueba tu aprendizaje

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[geg km aehgjlYf[aY j]dYlanY q dYk [Yda^a[Y[agf]k \Y\Yk hgj e]f\YjŠYk mladarYf\g ]d e†lg\g emdlahda[Ylang7
]d _jmhg \] ]ph]jlgk hYjY \gk [am\Y\]k \] afl]j†k&
17. <]l]jeafY dY dg[YdarY[af im] _YjYfla[] dgk e]fgj]k [gkl]k
Factor de Importancia Calificación \] gh]jY[af \] mf YdeY[†f \] kmeafakljgk$ hYjY []fljgk
localización relativa (escala 1-100) _Ykljgfea[gk \] mfY aehgjlYfl] rgfY lmjŠkla[Y \]d hYŠk&
HYjY ]ddg k] [m]flY [gf dgk ka_ma]fl]k \Ylgk2
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;gkl]k ($*- /( .( Centros Localización Carga
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),

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lang7 > -30! )-

16. MfY ]ehj]kY [mqY Y[lana\Y\ ^mf\Ye]flYd ]kl j]dY[agfY\Y HYjY gZl]f]j km kgdm[af mladarY dY `gbY \] [d[mdg \] =p[]d
[gf ]d hjg[]kYea]flg \] h]ljd]g \]Z] \][a\aj ]flj] lj]k im] ]f[gfljYjYk ]f ]d ;=G&
dg[Yda\Y\]k hYjY dY [gfkljm[[af \] mf YdeY[†f \] h]lj%
d]g& DY ]ehj]kY `Y k]d][[agfY\g [af[g ^Y[lgj]k [geg ZYk] Conocer los principales índices de control de los almacenes.
hYjY dY ]nYdmY[af$ q d]k `Y Yka_fY\g mf nYdgj ]f h]kg \]
mfg Y [af[g hYjY [Y\Y ^Y[lgj& 18. DY ]ehj]kY RYeYjZm\Y$ K&D&$ kmeafakljY dY ka_ma]fl] af^gj%
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kgZj] mfY ZYk] \] ) Y )(( hmflgk$ lYd q [geg k] em]kljY Y  =d YdeY[†f la]f] mfYk \ae]fkagf]k \] 0( e \] dYj_g$
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Localidad

Factor A B C

) )(( 0( )((

* -( /( /(

+ +( 0( .(

, )( .( 0(

- 1( .( -(

www.FreeLibros.me 147

5 El almacén dentro de la red logística

Práctica final

Localización y gestión de un almacén

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hdY[Yk ]d][ljfa[Yk \] dYk ]klm^Yk ]f mfY afklYdY[af af%
\]h]f\a]fl]$ \]\a[Y\Y ]p[dmkanYe]fl] Y ]ddg& =f ]d eYhY
Y\bmflg YhYj][]f dYk [ggj\]fY\Yk \] dY mZa[Y[af \] dYk
^Zja[Yk Y[lmYd]k&

=d [gfkmeg nYdgjY\g [gkl]! \] dYk hdY[Yk ]d][ljfa[Yk
hYjY [Y\Y mfY \] dYk ^Zja[Yk Y[lmYd]k ]k ]d ka_ma]fl]2

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Eklgd]k *+2)( *+(&((( €
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>m]fdYZjY\Y )02)+ 0(&((( €

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f]fl]k \] hdY[Yk ]d][ljfa[Yk ]f ]d fm]ng YdeY[†f& HYjY ]ddg k] kYZ] im] k] mladarYjf dgk ka_ma]fl]k [gehgf]fl]k ]d][%
ljfa[gk2

Familia Productos

9akdY\gj]k 9AK%+((3 9AK%*((3 9AK%-((

;gf][lgj]k ;GF%+-(3 ;GF%**($ ;GF%)((

HdY[Yk ZYk]k HD:%)3 HD:%*

J]d†k J=D%93 J=D%:

<akahY\gj]k <AK%01(3 <AK%*(((

DYk fm]nYk afklYdY[agf]k [gflYjf [gf2

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Ydlg&

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 Mf j]Y \] j][]h[af im] j][aZaj mfY [Yj_Y YfmYd \] *(&((( C_ Y dg dYj_g \] dgk **( \ŠYk im] gh]jYj ]d YdeY[†f&
 MfY e]\aY \] ($((* \ŠYk \] hdYrg hjge]\ag hYjY j][aZaj dYk e]j[Y\]jŠYk&
 Mf [g]^a[a]fl] \] af]klYZada\Y\ \] j][]h[af \] )$*&
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 ;Y\Y [Yj_Y g[mhY ($(+ e* \]d j]Y \] j][]h[af&

Hgj gljY hYjl]$ dY \akljaZm[af ^afYd \] dYk ]klm^Yk Y dgk [da]fl]k k] `Y j]YdarY\g Y ljYn†k \] mf []fljg \] [gfkgda\Y[af mZa%
[Y\g ]f >m]fdYZjY\Y$ h]jg k] ]kl hdYfl]Yf\g [gfn]jlaj \a[`g []fljg ]f mfg \] jmhlmjY&

Cuestiones:

1. Af\a[Y ]d dm_Yj a\f]g \] [gfkljm[[af \] dY fm]nY ^Zja[Y Y ljYn†k \]d e†lg\g \]d []fljg \] _jYn]\Y\&
2. <ak]ŽY mf kakl]eY \] [g\a^a[Y[af Yd^Yfme†ja[g hYjY ]d YdeY[†f \] dY fm]nY ^Zja[Y$ [gf ZYk] ]f dY af^gjeY[af ^Y[ada%

lY\Y&
3. ;Yd[mdY dgk af\a[Y\gj]k \]d [gfljgd \]d YdeY[†f&
4. Af\a[Y dYk n]flYbYk q \]kn]flYbYk im] hj]k]flYj ]d [YeZag \] kakl]eY \] \akljaZm[af \] dgk hjg\m[lgk Y dgk [da]fl]k&

148

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6Unidad

La gestión del transporte

En esta unidad aprenderemos a:
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\]ÂljYfkhgjl]&
 ;dYka^a[Yj dgk hjaf[ahYd]k e]\agk

\] ljYfkhgjl] q k]d][[agfYj ]d ek
Y\][mY\g&
 <a^]j]f[aYj q ]d]_aj dYk hjaf[ahYd]k
Af[gl]jek hYjY j]YdarYj ]d ljYfkhgjl]&
 HdYfa^a[Yj dYk jmlYk \] ljYfkhgjl]&

Y estudiaremos:
 Dgk gZb]langk \] dY ^mf[af

\]ÂljYfkhgjl]&
 Dgk \aklaflgk eg\gk \] ljYfkhgjl]&
 DYk [dmkmdYk Af[gl]jek mladarY\Yk

]f ]d [ge]j[ag afl]jfY[agfYd&
 DY eafaearY[af \] dgk [gkl]k

\]dÂljYfkhgjl]&

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