Gomez Aparicio Juan Miguel - Gestion Logistica Y Comercial

3 La gestión de las compras

Importante Caso práctico 7 (continuación)

MfY YdlY jglY[af ]f dgk stocks: A_mYde]fl]$ k] kYZ] im]2
 DaealY dY afn]jkaf ]f afn]flYjagk&
 J]\m[] _Yklgk ]f eYfl]faea]flg&  DYk n]flYk \]d YŽg Yfl]jagj Yk[]f\a]jgf Y -((&((( €&
 H]jeal] \akhgf]j \] dYk ”dlaeYk  Dgk [gkl]k kYdYjaYd]k \]d \]hYjlYe]flg \] [gehjYk ^m]jgf \] **&((( €&
 K] `Yf ]eala\g ,+( h]\a\gk&
fgn]\Y\]k \] eYl]jaYd]k&  DYk \]ngdm[agf]k YfmYd]k \] [gehjYk Yk[]f\a]jgf Y *&*(( €&
 Hm]\] Yme]flYj dY j]flYZada\Y\  =d kYd\g e]\ag \] hjgn]]\gj]k ]k \] *&+(( €&

\]d [YhalYd afn]jla\g&

9 hYjlaj \] ]klY af^gjeY[af$ [Yd[mdY dgk \a^]j]fl]k Šf\a[]k \] _]klaf \] [gehjYk&

Solución
 âf\a[] \] [gehjYk2 01&*(( ⋅ )(( = ($)/0,
-((&(((
 âf\a[] \]d [gkl] \]d \]hYjlYe]flg \] [gehjYk2 01&*(( , $ (-

**&(((

 âf\a[] \]d [gkl] \] mf h]\a\g \] [gehjYk2 **&((( -)$).
,+(
 âf\a[] \] jglY[af \] stock:

;gfkmeg \]d YŽg *()* 5 01&*(( € ,)-&+-( )&)+/$1, €
+.-
Stock e]\ag \]d YŽg *()*2
JglY[af \] stock:
1( ˜ )&*(( )(0&((($((
1) ˜ 0-( //&+-($(( 01&*(( /0$+0 n][]k
1* ˜ )&+(( ))1&.(($(( )&)+/$1,
1* ˜ )&*(( ))(&,(($((
,)-&+-($((

Dgk eYl]jaYd]k k] j]fm]nYf /0 n][]k Y dg dYj_g \]d ]b]j[a[ag ][gfea[g$ dg im] aehda[Y im]
k] j]fm]nYf [Y\Y ,$/ \ŠYk +.-'/0 ,$/!&

âf\a[] \]d h]jag\g e]\ag \] hY_g2 +.- 1$,) \ŠYk
01&*((

âf\a[] \] j][`Yrgk2 *&*(( *&+((
01&*(( ($ (*,

Caso práctico 8

DY ]ehj]kY ?YjjY^Yk :gl]ddg$ K&D&$ \]\a[Y\Y Y dY [gehjY%n]flY \] _YjjY^Yk$ la]f] \a^a[md%
lY\]k ]f dY ^afYf[aY[af \] kmk Y[lana\Y\]k& Hgj ]ddg \]k]Y im] ]d h]jag\g e]\ag \] hY_g
k]Y kmh]jagj Yd \] [gZjg - \ŠYk!& 9kŠ$ [geg j]khgfkYZd] \]d \]hYjlYe]flg \] [gehjYk$
l] af\a[Yf im] [Yd[md]k dgk h]jag\gk Y[lmYd]k hYjY hg\]j lgeYj \][akagf]k& DY af^gjeY%
[af ]k dY ka_ma]fl]2

Desde Periodo Días Saldo de Compras
()'()'*()+ proveedores
()'(,'*()+ Hasta
()'(/'*()+ +)'(+'*()+ 1( +&-(($(( /*&((($((
()')('*()+ +('(.'*()+
+('(1'*()+ 1) *&0(($(( -*&((($((
+)')*'*()+
1* 1(($(( +*&((($((

1* )&*(($(( 0*&((($((

365 238.000,00

(Continúa)

72

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3La gestión de las compras

Caso práctico 8 (continuación) Recuerda

Solución Dgk kakl]eYk \] _]klaf \] [Yda\Y\
]klf ZYkY\gk ]f dYk fgjeYk MF=%
Pmp +.- =F AKG$ q ]flj] kmk gZb]langk k]
;gehjYk \]d h]jag\g n ]f[m]fljY ]d \] [gfljgdYj Yim]ddg
im] dY ]ehj]kY [gfka\]jY aehgjlYf%
KYd\g e]\ag \] hjgn]]\gj]k \]d h]jag\g n l]& HYjY ]ddg$ lg\Yk dYk ]ehj]kYk
kge]la\Yk Y ]klYk fgjeYk \]Z]f
 KYd\g \] hjgn]]\gj]k \]d h]jag\g n: ]dYZgjYj mfY k]ja] \] [gfljgd]k hYjY
[Y\Y mfg \] dgk hjg[]kgk im] ]dY%
1( ˜ +&-(( +)-&((($(( Zgj]f&
1) ˜ *&0(( *-,&0(($((
1* ˜ 1(( 0*&0(($((
1* ˜ )&*(( ))(&,(($((
/.+&((($((

 Stock e]\ag \]d YŽg *()+2 /.+&((( *&(1($,) mfa\Y\]k
+.-

 Hjge]\ag \aYjag \] [gehjYk2 *+0&((( .-*$(- €
+.-

 H]jag\g e]\ag \] hY_g2 *&(1($)) +$*( \ŠYk
.-*$(-

=k f][]kYjag YdYj_Yj ]d h]jag\g e]\ag \] hY_g$ hYjY dg [mYd `YZj im] f]_g[aYj [gf dgk
hjgn]]\gj]k mf af[j]e]flg ]f dgk hdYrgk \] hY_g&

C. Otros indicadores de la gestión de compras Importante
9 n][]k$ dY e]bgjY \] Yd_mfgk \]
9\]ek \] dgk \gk af\a[Y\gj]k Yfl]jagj]k dgk kakl]eYk \] _]klaf \] dY [Yda\Y\ af[dmq]f$ ]flj] ] k l g k jY l a g k h m ] \ ] h ] j b m \ a [ Y j Y
gljgk$ dgk ka_ma]fl]k af\a[Y\gj]k hYjY ]d [gfljgd \] dYk [gehjYk2 gljgk& @YZj im] Zmk[Yj mf ]ima%
daZjag&
Financiación de proveedores
Af\a[Y ]d hgj[]flYb] \] dYk ]pakl]f[aYk \] eYl]jaYd]k ^afYf[aY\gk hgj dgk hjgn]]\gj]k& =klY jYlag 73
]k lYflg e]bgj [mYflg ek ]d]nY\Y k]Y$ ka]ehj] q [mYf\g fg k] af[mjjYf ]f _Yklgk ^afYf[a]jgk
hgj YhdYrYea]flgk&

>afYf[aY[af \] hjgn]]\gj]k = H]jag\g e]\ag \] hY_g ⋅ JglY[af \] stock ⋅ )((
+.-

Rotación de proveedores
Fgk h]jeal] [gehjgZYj ]d _jY\g \] j]fgnY[af \] dYk ^m]fl]k \] kmeafakljg \] dY ]ehj]kY&
;gf ]ddg$ k] hj]l]f\] ]nalYj dY h]jkakl]f[aY ]f dY Y\bm\a[Y[af Y dgk eakegk hjgn]]\gj]k q e]%
\aj ]d _jY\g \] †palg \]d \]hYjlYe]flg \] [gehjYk ]f dY dg[YdarY[af \] fm]ngk hjgn]]\gj]k
[geh]lalangk&

JglY[af \] hjgn]]\gj]k = ;gehjYk Y hjgn]]\gj]k fm]ngk ⋅ )((
;gehjYk lglYd]k

Plazo medio de entrega
=klaeY$ ]f hjge]\ag$ dgk \ŠYk im] ]ehd]Yf dgk hjgn]]\gj]k ]f k]jnaj dgk h]\a\gk& Afl]j]kY [gf%
l]ehdYj dgk nYdgj]k ]f ]mjgk ]f n]r \] f”e]jg \] h]\a\gk$ hYjY im] ]d [d[mdg j]kmdlYfl] k]Y
ek ka_fa^a[Ylang&

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3 La gestión de las compras

HdYrg e]\ag \] ]flj]_a Vadgj \] dgk h]jag\gk h]f\a]fl]k
Hjge]\ag \aYjag \] [gehjYk

Calidad de las compras
=kl] hgj[]flYb] \]l]jeafY dY hjghgj[af \] dYk [gehjYk im] fg [mehd]f dYk ]kh][a^a[Y[agf]k$
ka]f\g \]k]YZd]$ d_a[Ye]fl]$ im] la]f\Y Y []jg&

Cada\Y\ \] dYk [gehjYk Vadgj \] dYk \]ngdm[agf]k Y hjgn]]\gj]k
Vadgj \] dYk [gehjYk

Carga de trabajo
Af\a[Y ]d nYdgj e]\ag \] dY [gehjY hgj h]jkgfY \] ]kl] \]hYjlYe]flg&

Caj_Y \] ljYZYbg Vadgj \] dYk [gehjYk
HdYfladdY \] [gehjYk

Caso práctico 9

DY ]ehj]kY EY]klj]$ K&D&$ k] \]\a[Y Y dY [gehjY q n]flY \] _mYfYeafgk _mkYfgk im] k] mkYf [geg []Zg ]f dY h]k[Y!& Dgk
\Ylgk hYjY ]d Yfdakak \]d \]hYjlYe]flg \] [gehjYk ]f ]d YŽg *()* kgf dgk ka_ma]fl]k2

=pakl]f[aYk afa[aYd]k \] _mYfYeafgk +((&((($(( €
;gehjYk \] _mYfYeafgk ,((&((($(( €
;gehjYk Y hjgn]]\gj]k fm]ngk af[dma\Yk ]f dYk Yfl]jagj]k! )((&((($(( €
=pakl]f[aYk ^afYd]k \] _mYfYeafgk -((&((($(( €
<]ngdm[agf]k \] [gehjYk \] _mYfYeafgk
KYd\g afa[aYd \] hjgn]]\gj]k -(&((($(( €
KYd\g ^afYd \] hjgn]]\gj]k 0(&((($(( €
NYdgj \] dgk h]\a\gk h]f\a]fl]k \] j][aZaj .(&((($(( €
F”e]jg \] ljYZYbY\gj]k \]d \]hYjlYe]flg .(&((($(( €

)(

;Yd[mdY dgk Šf\a[]k \] [gfljgd \] dY _]klaf \]d \]hYjlYe]flg \] [gehjYk&

1. JglY[af \] stocks
;gfkmeg =pakl]f[aYk afa[aYd]k ;gehjYk =pakl]f[aYk ^afYd]k <]ngdm[agf]k
;gfkmeg +((&((( ,((&((( -((&((( -(&((( )-(&(((

Stock e]\ag YfmYd = +((&((( + -((&((( = ,((&((( €
*

Stock e]\ag \aYjag ,((&((( )&(1-$01 €
+.-

JglY[af \] stocks )-(&((( )+.$00
)&(1-$ 01

Dgk eYl]jaYd]k k] j]fm]nYf )+/ n][]k Y dg dYj_g \]d ]b]j[a[ag ][gfea[g$ dg im] aehda[Y im] k] j]fm]nYf [Y\Y *$.. \ŠYk

+.-')+/ *$.. \ŠYk!& (Continúa)

74

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3La gestión de las compras

Caso práctico 9 (continuación) Cálculo Índice Cálculo
2. J]klg \] af\a[Y\gj]k
HdYrg e]\ag \]
Índice ]flj]_Y

>afYf[aY[af .+$07 ⋅ )+.$07 ⋅ )(( = *&+1- ;Yda\Y\ \] dYk .(&((( -,$/- \ŠYk
Y hjgn]]\gj]k +.- [gehjYk ,((&(((

;Yj_Y \] ljYZYbg +.-

H]jag\g e]\ag +.- .+$0/ \ŠYk -(&((( ⋅ )(( = )*$-
\] hY_g ,((&((( ,(($ (((

JglY[af /(&(((
\] hjgn]]\gj]k
)((&((( ⋅ )(( = *- ,((&((( ,(&(((
,((&((( )(

Caso práctico 10 9 hYjlaj \] ]klgk \Ylgk k] ha\] [Yd[mdYj dgk hgj[]flYb]k \] \]%
ngdm[af \] [Y\Y mfg \] dgk hjgn]]\gj]k&
DY ]ehj]kY EgnadYf\aY$ K&9&$ \]\a[Y\Y dY [gehjY n]flY \] l]d†%
^gfgk enad]k q gj\]fY\gj]k hgjllad]k$ hjghgj[agfY af^gjeY% Solución
[af \] dYk [gehjYk j]YdarY\Yk Y kmk hjgn]]\gj]k$ YkŠ [geg \]
dYk \]ngdm[agf]k hgj [Yda\Y\ ]^][lmY\Yk Y dgk eakegk \mjYfl]
]d YŽg *()+2

Proveedor Importe de Importe de EgnadKlg[c$ K&D& +$)*-
compras devoluciones Gh]f9aj$ K&9& +
EgnadKlg[c$ K&D& L]d];gj$ K&D&
Gh]f9aj$ K&9& 0(&((($(( *&-(($(( Enad ?YdYpaY$ K&9& ,$*)
L]d];gj$ K&D& *((&((($(( .&((($(( /$-
Enad ?YdYpaY$ K&9& ,&((($((
Totales 1-&((($(( +&((($(( N]egk im] Enad ?YdYpaY$ K&9&$ ]k dY ]ehj]kY im] la]f] mf
,(&((($(( 15.500,00 eYqgj Šf\a[] \] \]ngdm[agf]k&
415.000,00

Actividades

9. ;gehd]lY ]f lm [mY\]jfg dY lYZdY ka_ma]fl]2

Ejercicio Existencias Compras Proveedores Rotación P.M. pago
económico (saldo medio) de stocks
Iniciales Finales x )((&((($(( –
) *&)(($(( 0(&((($(( *-
* +&((($(( )&*(($(( *&-(($(( *(&((($(( – **
+ – – )* ,-
, -&((($(( – /-($(( -(&((($(( – )0
-&/(($(( – ,(
)&((($(( -(($((

*&,(($(( +&+(($((

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3 La gestión de las compras

Dinero 5. El periodo medio de maduración
de la empresa
Compras
Cobro El periodo medio de maduración (PMM) es el tiempo que, por término medio, tarda en con-
ProducciónClientesMateriasvertirse en líquida (esto es, en recuperarse) una unidad monetaria invertida en el ciclo de ex-
primas plotación (Fig. 3.10).

Las fases del ciclo de explotación de una empresa se pueden dividir en almacenamiento, fabri-
cación, venta y cobro. Si las encadenamos obtendremos el periodo medio de maduración
económico. Y si a este le restamos el tiempo que la empresa tarda en pagar a sus proveedores,
tendremos otro concepto de gran importancia: el periodo medio de maduración financiero
(Fig. 3.11):

Ventas ALMACENA- FABRICACIÓN VENTAS COBROS

MIENTO

Productos PAGO
terminados

Fig. 3.10. Ciclo de explotación: dinero-
mercancía-dinero.

Periodo medio de maduración financiero

Periodo medio de maduración económico
Fig. 3.11. Periodo de maduración económico y un periodo de maduración financiero.

Importante Bajo la perspectiva financiera, el periodo de maduración financiero (PMMf) consta de
cinco subperiodos:
Cuanto menor sea el periodo medio
de maduración, más ciclos cabrán  ( ) Periodo medio de almacenamiento de materia prima (PMA).
en un año, es decir, mayores rota-  ( ) Periodo medio de fabricacion (PMF).
ciones habrá y, en principio, mayor  ( ) Periodo medio de venta (PMV).
rentabilidad.  ( ) Periodo medio de cobro (PMC).
 ( ) Periodo medio de pago (PMP).

Por su parte, el periodo medio de maduración económico (PMM) no contempla el de
pago.

Importante El periodo medio de almacenamiento (PMA) es el tiempo (normalmente expresado en días)
El cociente entre consumo de ma- que por término medio transcurre desde que entra la materia prima en el almacén de la em-
terias primas y existencias medias presa hasta que sale a la fase de fabricación:
de materias primas es la rotación
de las materias primas. PMA 365
Consumo materias primas
76
Existencias medias de materias primas

El número de días que las materias primas están almacenadas repercuten directamente en la
liquidez de la empresa. En principio, conviene reducir ese periodo al mínimo, aunque siempre
teniendo cuidado de no quedar desabastecidos. De este modo se reducen gastos de manipula-
ción, amortización, obsolescencia, roturas y mermas.

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3La gestión de las compras

=d periodo medio de fabricación (PMF) ]k ]d la]ehg hjge]\ag im] ljYfk[mjj] \]k\] dY ]fljY\Y Importante
\] dgk ^Y[lgj]k ]f hjg\m[[af `YklY im] kYd]f ]f ^gjeY \] hjg\m[lg Y[YZY\g2 =d [g[a]fl] ]flj] nYdgj \] dY hjg\m[%
[af q ]pakl]f[aYk e]\aYk \] hjg%
HE> +.- \m[lgk ]f [mjkg ]k dY jglY[af \] dgk
NYdgj \] dY hjg\m[[af hjg\m[lgk ]f [mjkg&
=pakl]f[aYk e]\aYk \] hjg\m[lgk ]f [mjkg
Importante
9 dY ]ehj]kY d] afl]j]kY mf af[j]e]flg \] dY jglY[af$ \akeafmq]f\g ]kl] h]jag\g& =f mfY =d [g[a]fl] ]flj] [gkl] \] dY hjg%
]ehj]kY [ge]j[aYd fg ]paklaj ]kl] h]jag\g& \m[[af n]f\a\Y q ]pakl]f[aYk e]%
\aYk \] hjg\m[lgk l]jeafY\gk ]k
=d periodo medio de venta (PMV) YZYj[Y \]k\] im] mf hjg\m[lg j][a†f ^YZja[Y\g ]fljY ]f ]d dY jglY[af \] dgk hjg\m[lgk l]j%
YdeY[†f `YklY im] kYd] \]d eakeg [geg [gfk][m]f[aY \] mfY n]flY2 eafY\gk&

HEN +.- Importante
NYdgj \] dY hjg\m[[af n]f\a\Y =d [g[a]fl] ]flj] n]flYk f]lYk q
kYd\g e]\ag \] [da]fl]k ]k dY jglY%
=pakl]f[aYk e]\aYk \] hjg\m[lgk l]jeafY\gk [af ]f n]flYk&

=d la]ehg im] ]kl† ]d hjg\m[lg l]jeafY\g ]f km YdeY[†f h]f\a]fl] \] n]f\]jk] Y^][lY f]_Y%
lanYe]fl] Y dY daima\]r \] dY ]ehj]kY$ hgj dg im] ]k [gfn]fa]fl] \akeafmaj ]kl] h]jag\g lg\g
dg hgkaZd]&

=d periodo medio de cobro (PMC) ]k ]d la]ehg im] ljYfk[mjj] ]flj] dY n]flY q ]d [gZjg2

HE; +.-
N]flYk f]lYk
KYd\g e]\ag \] [da]fl]k

9 dY ]ehj]kY d] afl]j]kY \akeafmaj ]d h]jag\g e]\ag \] [gZjg$ hm]klg im] ]ddg Yme]flY km l]%
kgj]jŠY q hm]\]$ hgj lYflg$ \akeafmaj km f][]ka\Y\ \] ]f\]m\Yea]flg q dY [gjj]khgf\a]fl]
[Yj_Y ^afYf[a]jY$ g Za]f gZl]f]j mfY j]flYZada\Y\ e]\aYfl] km _]klaf&

=d periodo medio de pago (PMP), im] qY naegk ]f ]d Yfdakak \] dYk jglY[agf]k$ ]k ]d la]ehg
im] e]\aY ]flj] dY [gehjY Y dgk hjgn]]\gj]k q km [gjj]khgf\a]fl] YZgfg2

HEH +.-
;gehjYk

KYd\g e]\ag \] hjgn]]\gj]k

=f ]kl] [Ykg$ Y dY ]ehj]kY d] afl]j]kYj Yme]flYj ]kl] h]jag\g Yd epaeg hgkaZd]$ ka]ehj]
qÂ[mYf\g fg k] j]fmf[a] hgj ]ddg Y [a]jlYk [gfljYhYjla\Yk [geg \]k[m]flgk hgj hjgflg hY_g!
g aehdaim] [Yj_Yk ^afYf[a]jYk&

;geg kŠfl]kak \] dYk [mYljg ^Yk]k YfYdarY\Yk$ kmj_] ]d [gf[]hlg \] periodo medio de maduración
(PMM). <]k\] im] k] Y\ima]j]f dYk eYl]jaYk hjaeYk ]ehj]kYk af\mkljaYd]k! g dYk e]j[Y\]jŠYk
]ehj]kYk [ge]j[aYd]k! `YklY im] k] [gZjY hgj dYk n]flYk ljYfk[mjj]$ hgj l†jeafg e]\ag$ mf h]%
jag\g im] k] [Yd[mdY e]\aYfl] dY kmeY \] dgk h]jag\gk ka_ma]fl]k2

HEE HE9 HE> HEN HE; Importante

<mjYfl] ]kl] la]ehg dY ]ehj]kY la]f] afegnadarY\g ]f ]d [aj[mdYfl] mfYk hYjla\Yk im] `YZj \] =f dY e]\a\Y ]f im] dY ]ehj]kY
^afYf[aYj& <] Y`Š$ ]d afl]j†k hgj j]\m[aj Yd epaeg km \mjY[af& hm]\Y hY_Yj Y hdYrg Y kmk hjgn]]%
=d h]jag\g e]\ag \] eY\mjY[af ^afYf[a]jg (PMMf) k]j2 \gj]k$ ]d h]jag\g e]\ag \] eY\m%
jY[af ^afYf[a]jg k]j af^]jagj Yd
HEE^ HEE HEH ][gfea[g&

=d h]jag\g e]\ag \] eY\mjY[af$ Yd e]\aj dY \mjY[af \]d [a[dg \] ]phdglY[af$ fgk h]jeal] \]% 77
l]jeafYj fm]kljYk f][]ka\Y\]k \] dY eakeY& <] a_mYd eg\g$ h]jeal] ]nYdmYj dY _]klaf \]d \]hYj%
lYe]flg \] [gehjYk q n]flYk$ ]f dg im] k] j]^a]j] Y dY f]_g[aY[af \] YhdYrYea]flg \]d hY_g \]
dYk [gehjYk q [gZjg \] dYk n]flYk&

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3 La gestión de las compras

Importante =f ]d [Ykg \] ljYlYjk] \] mfY ]ehj]kY [ge]j[aYd fg ]paklaj ]d h]jŠg\g e]\ag \] ^YZja[Y[af hgj
dg$ im] km HE> k] [gfn]jlaj ]f2
=d [gfkmeg k] gZla]f]2
HEE^ +.- +.- +.-
=pakl]f[aYk Afa[aYd]k ;gfkmeg N]flYk ;gfkmeg
[gehjYk
=pakl]f[aYk >afYd]k =pakl]f[aYk e]\aYk KYd\g e]\ag \] [da]fl]k KYd\g e]\ag \] hjgn]]\gj]k
<]ngdm[agf]k \] [gehjYk
Rappels kgZj] [gehjYk

Caso práctico 11

DY ]ehj]kY ;jak%Kgd$ K&9&$ \]\a[Y\Y Y dY [ge]j[aYdarY[af \]d hjg\m[lg \] ¿;jaklYdmfYÀ$
\]k]Y [gfg[]j ]d h]jag\g e]\ag \] eY\mjY[af ^afYf[a]jg \]d ]b]j[a[ag ][gfea[g *()+
]f ^mf[af \] dY af^gjeY[af im] hj]k]flY Y [gflafmY[af2

 =pakl]f[aYk e]\aYk \] hjg\m[lgk )*-&((($(( €
 =pakl]f[aYk e]\aYk \] [da]fl]k +-&((($(( €
 KYd\g e]\ag \] hjgn]]\gj]k +0&((($(( €
 =pakl]f[aYk afa[aYd]k \] hjg\m[lgk
 =pakl]f[aYk ^afYd]k \] hjg\m[lgk )-(&((($(( €
 ;gehjYk \] hjg\m[lgk )((&((($(( €
 <]ngdm[agf]k \] [gehjYk +((&((($(( €
 N]flYk \] hjg\m[lgk
+&((($(( €
-+(&((($(( €

Solución +.- +.- +.-
+,/&((( -+(&((( +((&(((
HEE^ )--$-0 \ŠYk

)*-&((( +-&((( +0&(((

;gfkmeg2 )-(&((( +((&((( )((&((( +&((( +,//&((( €

Caso práctico 12

DY ]ehj]kY =d DY_Yjlg$ K&D&$ \]\a[Y\Y Y dY [ge]j[aYdarY[af \] hj]f\Yk \] n]klaj, `Y hj]nak%
lg im] ]d h]jag\g e]\ag \] [gZjg Y kmk [da]fl]k k]Y a_mYd im] ]d h]jag\g e]\ag \] hY_g Y
kmk hjgn]]\gj]k& Hgj ]ddg$ \] lg\g dg im] [gehjY ka]ehj] \]bY h]f\a]fl] \] hY_g ]d *- $
q n]f\] ]d 0( Yhda[Yf\g mf eYj_]f \]d /( & =d kYd\g e]\ag \] [da]fl]k ]k \] )*&(((€&

<]l]jeafY ]d h]jag\g e]\ag \] [gZjg$ ]d \] eY\mjY[af q dYk [gehjYk \]d h]jag\g$ kY%
Za]f\g im] dYk ]pakl]f[aYk e]\aYk [gaf[a\]f [gf dYk ^afYd]k ]d *( \] dg [gehjY\g im]
fg k] `Y [gfkmea\g!$ q im] dYk ]pakl]f[aYk afa[aYd]k kgf []jg&

Solución

Ka im]j]egk a_mYdYj dgk h]jag\gk e]\agk \] [gehjY q hjg\m[[af$ ]k \][aj$ HE; HEH$
l]f\j]egk im] a_mYdYj2

+.- +.-
N]flYk ;gehjYk

KYd\g e]\ag \] [da]fl]k KYd\g e]\ag \] hjgn]]\gj]k

;gfkmeg2 ($0 ˜ ;gehjYk

N]flYk2 )$/ ˜ ($0 ˜ ;gehjYk +.- +.-
;gehjYk
)$/ ˜ ($0! ˜ ;gehjYk
)(( ($*- ˜ ;gehjYk

9d k]j dgk \gk ]d]e]flgk a_mYd]k$ ka kmhjaeaegk ¿;gehjYkÀ ]f ]d k]_mf\g ea]eZjg \] dY

][mY[af gZl]f]egk 1)$*-& Hgj dg lYflg$ ]kl] nYdgj ]k ]d HEH q ]d HE;& (Continúa)

78

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Caso práctico 12 (continuación) 3La gestión de las compras
Gh]jYegk ]f ]d hjae]j ea]eZjg hYjY gZl]f]j ]d nYdgj \] dYk [gehjYk2
Importante
+.- +&**)&-+-$0( DYk ]ehj]kYk af\mkljaYd]k l]f\jf
)$/ ˜ ($0 dYk [mYljg ^Yk]k \]d h]jag\g e]\ag
)*&((( \] eY\mjY[af$ ea]fljYk im] dYk
[ge]j[aYd]k fg l]f\jf dY [gjj]k%
;gfkmeg2 ) ($*! ˜ +&**)&-+-$0( *&-//&**0$.( € hgf\a]fl] Yd h]jag\g \] ^YZja[Y[af&

KYd\g e]\ag \] hjgn]]\gj]k2 ($*- ˜ +&**)&-+-$0( 0(-&+0+$1- €

N]flYk2 +&**)&-+-$0( ˜ ($0 ˜ )$/ ,&+0)&*00$/( €
HEN +.- ,-.$*- \ŠYk
*&-//&**0
+&**)&-+-$0(

Hgj lYflg$ ]d h]jag\g e]\ag \] eY\mjY[af k]j a_mYd Y2
HHE HEN HE; HEH ,-.$*- 1)$*- 1)$*- .+0$/- \ŠYk

Actividades

10. DY ]ehj]kY KaddYk Egdaf]jg$ K&9&$ k] \]\a[Y Y dY ^YZja[Y[af \] kaddYk eg\]dg Funciona-
rio. ;gfka\]jY dY af^gjeY[af ka_ma]fl]2

È 9d hjaf[ahag \]d YŽg *()* dYk ]pakl]f[aYk \] eYl]jaYk hjaeYk ]f YdeY[†f ]jYf \]2

EY\]jY ,(&((($(( €
:Yjfar -&((($(( €
;gdY *&,(($(( €

È D Yk ]pakl]f[aYk ]f kaddYk ]klYZYf nYdgjY\Yk ]f /+&((( ]mjgk&
È < mjYfl] ]d YŽg *()* k] ]^][lmYjgf dYk ka_ma]fl]k gh]jY[agf]k2

;gehjYk \] eY\]jY )*/&((($(( €
;gehjYk \] ZYjfar )+&((($(( €
;gehjYk \] [gdY 0&((($(( €

È D Yk ]pakl]f[aYk e]\aYk \] eYl]jaYk hjaeYk `Yf kmhm]klg *(&((( €& =d [gfkmeg \]
eYl]jaYk hjaeYk j]hj]k]flY ]d 1( \] dYk [gehjYk&

È K ] ^YZja[Yjgf kaddYk hgj aehgjl] \] ).(&((( €$ \] dYk [mYd]k k] n]f\a]jgf ]d /-
Yhda[Yf\g mf eYj_]f [ge]j[aYd \]d .( &

È DYk ]pakl]f[aYk e]\aYk \] kaddYk `Yf kmhm]klg )-&(((€&

È 9 d ^afYdarYj ]d YŽg k] gZk]jnY im] dYk ]pakl]f[aYk e]\aYk \] hjg\m[lgk ]f [mjkg \]
^YZja[Y[af ^m]jgf +.&((( €&

È = d kYd\g e]\ag \] [da]fl]k `Y kmhm]klg mf nYdgj e]\ag \]d *- \] dYk n]flYk$ YkŠ
[geg ]d +- \] dYk [gehjYk$ ]d nYdgj e]\ag \]d kYd\g \] hjgn]]\gj]k&

;Yd[mdY ]d h]jag\g e]\ag \] eY\mjY[af&

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3 La gestión de las compras

Síntesis

LA GESTIÓN DE COMPRAS
A través de la función de aprovisionamiento

Con el objetivo de Dividida en

Minimizar costes Maximizar el servicio

Modelos Compras Almacén

Horizontal Vertical Con el objetivo de

t % BS DPOUJOVJEBE FO FM BCBTUFDJNJFOUP t $ ÈMDVMP EFM DPTUF EF DPNQSB
t $ POUSPM QSFTVQVFTUPT
t " TFHVSBS MB DBMJEBE Z DBOUJEBE EF MPT t * OEJDBEPSFT EF DPNQSB
suministros

t % FGJOJS FM OJWFM EF JOWFOUBSJPT
evitando roturas de stock y mermas
por obsolescencia y deterioro

t & TUVEJBS OVFWBT GVFOUFT EF
suministros

t . BOUFOFS MPT DPTUFT EF BERVJTJDJØO
y mantenimiento de stocks a niveles
adecuados

Periodo Medio de Maduración económico

Almacén Fabricación Venta Cobro Pago

Reducir el Reducir Reducir el Reducir el Aumentar el

tiempo de stock el tiempo tiempo de tiempo en cobrar tiempo en

de las materias producción los P.T. en el a los clientes pagar a los

primas almacén proveedores

Periodo Medio de Maduración financiero

80

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3La gestión de las compras

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

Test de repaso

1. La función de aprovisionamiento consiste en: 6. El periodo medio de pago nos indica:
a) Almacenar al precio más bajo posible. a) El número de veces al año que pagamos al proveedor.
b) Comprar lo más barato posible. b) El número de días que por término medio tardamos en
c) Contribuir a los objetivos comunes de la empresa, a tra- pagar a los proveedores.
vés de la adquisición, recepción y almacenamiento de c) El número de días que por término medio tardan en ser-
los materiales que esta necesita para la elaboración de virnos la mercancía el proveedor.
sus productos. d) Ninguna de las anteriores es correcta.
d) Ninguna de las anteriores es correcta.
7. En el modelo horizontal de compras:
2. El departamento encargado de recibir las solicitudes de a) Cada departamento realiza la función de compras.
materiales necesarios, así como de buscar los proveedores b) No existe un departamento de compras propiamente.
adecuados, es el de: c) Todas las anteriores son correctas.
a) Aprovisionamiento. d) Ninguna de las anteriores es correcta.
b) Almacén.
c) Compras. 8. Los materiales cuello de botella:
d) Ninguna de las anteriores es correcta. a) Son productos de elevado valor unitario.
b) Son productos de reducido valor unitario.
3. Si, al efectuar una compra, el coste total de la factura es c) Son productos con pocos proveedores.
mayor que el importe bruto de la misma, en este caso el d) Ninguna de las anteriores es correcta.
coste unitario de uno de los productos será:
a) Menor que el precio de compra. 9. Según el Plan General Contable, el precio de adquisición
b) Mayor que el precio de compra. está formado por:
c) No se puede calcular el precio de compra. a) El precio de compra.
d) Ninguna de las anteriores es correcta. b) El precio de compra más los gastos de transporte.
c) El precio de compra más todos los gastos necesarios
4. Si, al calcular el coste unitario de un artículo, una vez efec- para que el producto se encuentre en el almacén de la
tuado el prorrateo de la factura, la constante de proporcio- empresa.
nalidad es menor que la unidad, esto implica: d) Ninguna de las anteriores es correcta.
a) Que el precio de compra es menor que el precio de
coste. 10. El ratio de rotación de proveedores nos permite:
b) Que el precio de compra es mayor que el precio de a) Comprobar el grado de renovación de las fuentes de
coste. suministro de la empresa.
c) Que el precio de compra y el de coste coinciden. b) Comprobar la calidad de las compras.
d) Ninguna de las anteriores es correcta. c) Comprobar el grado de adecuación de los proveedores.
d) Ninguna de las anteriores es correcta.
5. Si en una empresa la rotación de stocks es igual a 12, esto
significa: 11. Entre los objetivos de la función de aprovisionamiento se
a) Que se renueva una vez cada mes. encuentra:
b) Que se renueva cada 12 días. a) Maximizar el beneficio de la empresa.
c) Que se renueva cada 12 meses. b) Minimizar los costes de los inventarios.
d) Ninguna de las anteriores es correcta. c) Minimizar los costes y maximizar el servicio.
d) Ninguna de las anteriores es correcta.

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3 La gestión de las compras

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Comprueba tu aprendizaje

Definir las fases que componen un programa de aprovisiona- DYk hj]nakagf]k hYjY ]d hjpaeg YŽg kgf kaeadYj]k Y dYk \]d
miento desde la detección de necesidades hasta la recepción hj]k]fl] ]b]j[a[ag$ h]jg hj]l]f\]egk im] ]f ]d h]jag\g ka%
de la mercancía. _ma]fl] ]d HEE k]Y )( \ŠYk af^]jagj& Hgj ]ddg$ ]d \]hYjlYe]f%
lg \] [gehjYk `Y \] f]_g[aYj ]d YhdYrYea]flg ]f ]d hY_g Y
1. ¸=f im† ^Yk]k g Y[lana\Y\]k \] dYk ka_ma]fl]k hm]\] afl]_jYj% hjgn]]\gj]k& L]fa]f\g ]klg ]f [m]flY$ \]l]jeafY ]d kYd\g
k] `Y[aY Yljk q `Y[aY \]dYfl] mfY ]ehj]kY im] k] \]\aim] Y e]\ag \] hjgn]]\gj]k hYjY ]d hjpaeg ]b]j[a[ag [gf ^afYda\Y\
dY ^YZja[Y[af \] `YjafY7 \] [gfk]_maj ]d gZb]lang hjghm]klg&

a) Ka]eZjY \]d lja_g 6. 9 [gflafmY[af k] hjghgj[agfY af^gjeY[af \] nYjagk ]b]j[a%
b) ;gk][`Y [agk ][gfea[gk [gjj]khgf\a]fl]k Y dY ]ehj]kY ;ge]j[aYd
c) Egda]f\Y Dh]r ;Yd]jg&

d) >YZja[Y[af \] `YjafY Ejercicio Iniciales Existencias x
e) =dYZgjY[af \] hYf económico *&-(($(( *&((($((
f) N]flY Yd hgj e]fgj Finales
) )&-(($((

2. Af\a[Y dYk ^Yk]k \] Y[lana\Y\ \] mf \]hYjlYe]flg \] [ge% * +&((($(( – )&0(($((
hjYk gj_YfarY\g `gjargflYde]fl]& ¸;md]k k]jŠYf dYk \a^]j]f%
[aYk [gf mf eg\]dg n]jla[Yd7 + 0(($(( +(($(( )&**($((

, )&-(($(( *&((($(( –

Prever con tiempo suficiente el reaprovisionamiento de la Compras Proveed. Rotación P.M. Pago
cadena de suministro para ajustar los volúmenes de stock al (Saldo de stocks
nivel de servicio, evitando los desabastecimientos. medio)

3. DY ]ehj]kY <>9E 9[[agf]k$ K&D&$ j]Ydar \mjYfl] ]d YŽg *()* 0(&((($(( -&*(($(( – –
[gehjYk hgj mf aehgjl] \] )((&((( €& DYk ]pakl]f[aYk afa% -(&((($(( – )( *)$1
[aYd]k ]jYf )(&((( € q dYk ^afYd]k ,&((( €& – *- +-
– – -( ,(
<]l]jeafY dY jglY[af \] stocks, kYZa]f\g im] dYk ]pakl]f% /(&((($((
[aYk e]\aYk \mjYfl] ]d h]jag\g ^m]jgf \] )*&-(( €&

4. EY\]jYk EY\]jg$ K&9&$ ]^][lm \mjYfl] ]d ]b]j[a[ag *()* ;gehd]lY dY lYZdY ]f lm [mY\]jfg& HYjY ]ddg \]Z]k Yhda[Yj dgk
[gehjYk hgj mf aehgjl] \] +*)&((( €$ q ]d kYd\g e]\ag \] [gfl]fa\gk hjghgj[agfY\gk ]f dY mfa\Y\ j]kh][lg Yd [d[mdg
hjgn]]\gj]k \mjYfl] ]d h]jag\g ^m] \] ,-&((( €& HYjY ]d \] ]pakl]f[aYk$ [gehjYk$ kYd\g e]\ag \] hjgn]]\gj]k$ jglY%
]b]j[a[ag ka_ma]fl]$ dYk hj]nakagf]k \] YhjgnakagfYea]flg ]p% [af \] stock, ]l[&
h]jae]flYf mf af[j]e]flg \]d )( [gf j]kh][lg Yd YŽg
Yfl]jagj$ q hj]l]f\]egk im] ]d h]jag\g e]\ag \] hY_g Ym% Obtener el periodo medio de maduración de una empresa
e]fl] ]f 0 \ŠYk& comercial.

L]fa]f\g ]klg ]f [m]flY$ \]l]jeafY [md k]j ]d kYd\g e]\ag 7. DY ]ehj]kY Dg_aL][fg$ \]\a[Y\Y Y dY [gehjY%n]flY \] gj\]%
\] dY [m]flY \] hjgn]]\gj]k hYjY ]d ]b]j[a[ag ka_ma]fl]& fY\gj]k$ fgk hj]k]flY dY ka_ma]fl] af^gjeY[af2
È ;gehjY \] gj\]fY\gj]k2 )&*((&((( €
5. DY ]ehj]kY Haklgf]k Jg\Yfl]k$ K&9&$ fgk hj]k]flY dY ka_ma]f% È =pakl]f[aYk afa[aYd]k \] gj\]fY\gj]k2 0(&((( €
l] af^gjeY[af [gjj]khgf\a]fl] Yd ]b]j[a[ag *()*2 È =pakl]f[aYk ^afYd]k \] gj\]fY\gj]k2 -(&((( €
È KYd\g e]\ag \] [da]fl]k2 )- \] n]flYk
È ;gehjYk2 **(&((( € È KYd\g e]\ag \] hjgn]]\gj]k2 )* \] [gehjYk
È =d eYj_]f [ge]j[aYd Yhda[Y\g ]f dYk n]flYk ]k ]d .( &
È N]flYk2 *0(&((( €
;Yd[mdY ]d h]jag\g e]\ag \] n]flY$ ]d \] [gZjg q ]d \] hY_g&
È ;gkl] \] n]flYk2 *+(&((( €

È KYd\g e]\ag [da]fl]k2 *+&((( €

È KYd\g e]\ag hjgn]]\gj]k2 )1&((( €

È =pakl]f[aYk e]\aYk2 ),&((( €

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3La gestión de las compras

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

Comprueba tu aprendizaje

8. DY ]ehj]kY AeY_afY[agf]k$ K&9&$ Y\imaja q [gfkmea \m% 11. =f mf k][lgj [ge]j[aYd$ ]d h]jag\g e]\ag \] n]flY \] dYk
jYfl] ]d ]b]j[a[ag ][gfea[g hYkY\g +(&((( € \] eYl]jaY ]ehj]kYk 9 q : ]k ]d eakeg$ h]jg ]d h]jag\g e]\ag \] [g%
hjaeY Virtual hYjY dY ^YZja[Y[af \] km hjg\m[lg Entelequia& Zjg \] : ]k ]d \gZd] im] ]f 9& =d HEE^ ]f YeZYk ]ehj]kYk
Hgj l†jeafg e]\ag$ eYflmng mf fan]d \] ]pakl]f[aYk \] dYk ]k \] +( \ŠYk$ q dYk \gk Yhda[Yf mf eYj_]f [ge]j[aYd \]
eakeYk ]f ]d YdeY[†f \] +&((( €& =d nYdgj \] dY hjg\m[% n]flY \]d ,( &
[af ]k \] -(&((( € q ]d nYdgj \]d fan]d e]\ag \] hjg\m[%
lgk ]f [mjkg \] ]dYZgjY[af \] *&-(( €& =d [gkl] \] dY hjg% <akhgf]egk Y\]ek \] dY ka_ma]fl] af^gjeY[af2
\m[[af n]f\a\Y Yk[]f\a Y .(&((( €& =d nYdgj e]\ag \]
]pakl]f[aYk ]f ]d YdeY[†f \] hjg\m[lgk l]jeafY\gk Yk[]f% =pakl]f[aY afa[aYd Empresa A Empresa B
\a Y -&-((€& N]f\a km hjg\m[[af hgj mf aehgjl] \] \] ;gfkmeg
/(&((( €$ q kmk [da]fl]k lmna]jgf mfYk \]m\Yk e]\aYk Y dg =pakl]f[aYk ^afYd]k *(&((($(( )/&((($((
dYj_g \]d ]b]j[a[ag \] +&*(( €& =d kYd\g e]\ag \] hjgn]]\g% /-&((($(( *-&((($((
j]k Yk[]f\a Y ,&((( €& +(&((($(( ,&((($((

;Yd[mdY ]d h]jag\g e]\ag \] eY\mjY[af ][gfea[g q ^a%
fYf[a]jg \] AeY_afY[agf]k$ K&9&

9. MfY ]ehj]kY `Y j]YdarY\g ]f ]d ]b]j[a[ag [gehjYk Y [j†% =pakl]f[aYk e]\aYk 0&-(($(( –
\alg Y hjgn]]\gj]k hgj nYdgj \] ))&((( €$ eYfl]fa]f\g KYd\g e]\ag \] [da]fl]k – /(($((
mf kYd\g e]\ag \] *&((( €& DY eakeY ]ehj]kY `Y ]^][% KYd\g e]\ag hjgn]]\gj –
lmY\g n]flYk Y [j†\alg hgj )--&((( € [gf mf kYd\g e]\ag –
\] )+&((( €& L]fa]f\g ]f [m]flY dgk \Ylgk Yfl]jagj]k$
[Yd[mdYj ]d h]jag\g e]\ag \] eY\mjY[af \] [da]fl]k q 12. DY Lgjladd]jŠY$ K&D&$ ]k mfY ]ehj]kY \]\a[Y\Y Y dY [ge]j[aYda%
hjgn]]\gj]k& rY[af \] lgjladdYk& La]f] mf HEE^ \] *)Â\ŠYk$ ]d HEN ]k \]
,( \ŠYk$ ]d HE; )1 \ŠYk q dgk kYd\gk e]\agk \] hjgn]]\gj]k$
10. DY ]ehj]kY C%QY%L$ K&D&$ [m]flY [gf dgk ka_ma]fl]k \Ylgk2 [da]fl]k q ]pakl]f[aYk Yk[a]f\] Y ,(&((( €$ +(&((( € q
*(&(((€ j]kh][lanYe]fl]& L]fa]f\g ]f [m]flY ]klY af^gj%
=pakl]f[aYk afa[aYd]k \] eYl]jaYk hjaeYk )+(&((($(( eY[af$ [Yd[mdY2

=pakl]f[aYk ^afYd]k \] eYl]jaYk hjaeYk *)(&((($(( a) DYk [gehjYk YfmYd]k ]^][lmY\Yk&

=pakl]f[aYk e]\aYk \] hjg\m[lgk ]f [mjkg )),&((($(( b) =d hgj[]flYb] \] eYj_]f [ge]j[aYd e]\ag Yhda[Y\g ]f
NYdgj \] dgk hjg\m[lgk l]jeafY\gk ,((&((($(( n]flYk&
KYd\g e]\ag \] hjgn]]\gj]k ))*& ((($((
c) DYk ]pakl]f[aYk ^afYd]k \] hjg\m[lgk l]jeafY\gk$ kYZa]f%
\g im] dYk afa[aYd]k kgf \] *-&((( €

;gehjYk \] eYl]jaYk hjaeYk *,(&((($(( 13. MfY ]ehj]kY j]Ydar ]f ]d ]b]j[a[ag [gehjYk Yd [gflY\g hgj
N]flYk \] hjg\m[lgk l]jeafY\gk *&)((&((($(( nYdgj \] *( (&( ( ( €$ eYfl]fa]f\g mf kYd\g e]\ag \]
KYd\g e]\ag \] [da]fl]k )-&((( €& =d [gkl] lglYd \] dY hjg\m[[af j]YdarY\Y ]f ]k]
=pakl]f[aYk e]\aYk \] hjg\m[lgk l]jeafY\gk ,/&((($(( YŽg ^m] \] +-(&((( €$ q dY e]\aY \]d stock \] hjg\m[lgk
;gkl] \] dY hjg\m[[af n]f\a\Y ,0&((($(( ]f [mjkg \] ^YZja[Y[af ^m] \] *(&((( €& <mjYfl] ]k] YŽg
0((&((($(( n]f\a lg\Y dY hjg\m[[af im] ^YZja[ q ]d fan]d e]\ag \]
9 hYjlaj \] ]klgk \Ylgk$ [Yd[mdY2 ]pakl]f[aYk im] eYflmng ^m] \] ),&((( €& Dgk af_j]kgk lg%
a) =d h]jag\g \] eY\mjY[af ][gfea[g& lYd]k hgj n]flYk im] gZlmng ^m]jgf \] .((&((( €$ q ]d kYd%
b) =d h]jag\g \] eY\mjY[af ^afYf[a]jg& \g \] [da]fl]k ^m] \] )+(&((( €& L]fa]f\g ]f [m]flY dgk
\Ylgk Yfl]jagj]k2

a) ;Yd[mdY ]d h]jag\g e]\ag \] eY\mjY[af \] dY ]ehj]kY&

b) Ka dY hgdŠla[Y \] dY ]ehj]kY ]jY [gf[]\]j Y kmk [da]fl]k
mf hdYrg e]\ag \] hY_g \] )( \ŠYk$ ]phda[Y ka dY `Y eYf%
l]fa\g&

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3 La gestión de las compras

Práctica final

El periodo medio de maduración

9DM;9K9 ]k mfY ]ehj]kY im] k] \]\a[Y Y dY ljYfk^gjeY[af q hgkl]jagj [ge]j[aYdarY[af \] Ydmeafag$ im] \]Z] k]j egd%
\]Y\g q dY[Y\g hYjY gZl]f]j ]d hjg\m[lg ^afYd& DY ]ehj]kY \]k]Y [gfg[]j [md ]k ]d h]jag\g e]\ag \] eY\mjY[af \]d [a[dg
\] ]phdglY[af$ hYjY dg [mYd kmeafakljY dY ka_ma]fl] af^gjeY[af2

Cuenta de pérdidas y ganancias Ejercicio 2013

N]flYk +(&((($((!
;gfkmeg \] eYl]jaYk hjaeYk )-&((($((!
NYjaY[af \] ]pakl]f[aYk \] hjg\m[lgk l]jeafY\gk
Gljgk _Yklgk \] ]phdglY[af ,(($((!
?Yklgk ]p[]h[agfYd]k )(&((($((!
J]kmdlY\g \]d ]b]j[a[ag
+&((($((!
*&,(($((!

Dgk kYd\gk \]d ZYdYf[] im] Y^][lYf Yd [d[mdg \]d HEE kgf2

EYl]jaYk hjaeYk Ejercicio 2013 Ejercicio 2012
Hjg\m[lgk ]f [mjkg
Hjg\m[lgk l]jeafY\gk /(($(( .(($((
;da]fl]k -$(( -$((
Hjgn]]\gj]k
)&0(($(( )&,(($((
*&1(($(( *&-(($((
*&0(($(( *&1(($((

Cuestiones:
1. 9qm\Y Y ]klY ]ehj]kY Y [Yd[mdYj ]d h]jag\g e]\ag \] eY\mjY[af ][gfea[g q ^afYf[a]jg \]d ]b]j[a[ag *()+$ q ]eal] mf

af^gje] kgZj] dgk j]kmdlY\gk gZl]fa\gk&

2. ;ge]flY q jYrgfY2 ¸[eg Y^][lYjŠYf Yd [YhalYd [aj[mdYfl] \] ]klY ]ehj]kY dYk ka_ma]fl]k gh]jY[agf]k7
a) Im] dYk ]pakl]f[aYk \] hjg\m[lgk l]jeafY\gk `mZa]jYf ka\g []jg&
b) DY Y\imaka[af \] ek eYl]jaYk hjaeYk ^afYf[aY\Yk hgj dgk hjgn]]\gj]k&
c) DY \glY[af \] mfY hjgnakaf hgj \]l]jagjg \] dYk [m]flYk \] [da]fl]k q \]m\gj]k&
d) Im] k] dd]nYjY Yd \]k[m]flg ]f mfY ]fla\Y\ ^afYf[a]jY mf ]^][lg Y [gZjYj&
e) MfY YehdaY[af \] [YhalYd$ lglYde]fl] kmk[jalY q \]k]eZgdkY\Y ]f ]^][lang&
f) DY Y\imaka[af \] eYl]jaYk hjaeYk YZgfY\Yk Yd [gflY\g&
g) DY kgda[alm\ \] mf hj†klYeg hYjY ^afYf[aYj dY Y\imaka[af \] mf ]d]e]flg \] ljYfkhgjl]&
h) DY kgda[alm\ \] mf hj†klYeg hYjY dY Y\imaka[af \] eYl]jaYk hjaeYk&
i) =d YZgfg \] mfY \]m\Y hgj mf [da]fl]&
j) =d YZgfg \] mfY \]m\Y hgj mf hjgn]]\gj&

3. ¸;md k]jŠY ]d ]^][lg \] [Y\Y mfY \] dYk gh]jY[agf]k Yfl]jagj]k kgZj] ]d h]jag\g e]\ag \] eY\mjY[af7

4. ¸;md k]jŠY ]^][lg \] [Y\Y mfY \] dYk gh]jY[agf]k Yfl]jagj]k kgZj] ]d h]jag\g e]\ag \] eY\mjY[af ^afYf[a]jg7

84

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4Unidad

La gestión de las existencias

En esta unidad aprenderemos a:

 =dYZgjYj dYk hj]nakagf]k \] \]eYf\Y \]d
h]jag\g \] [Y\Y \]hYjlYe]flg aehda[Y\g&

 ;gfljYklYj dgk [gfkmegk `aklja[gk$ daklY
\] eYl]jaYd]k q h]\a\gk j]YdarY\gk$ ]f
^mf[af \]d [mehdaea]flg \] dgk gZb]langk
\]d hdYf \] n]flYk q hjg\m[[af&

 <]l]jeafYj dY [YhY[a\Y\ hlaeY
\] YdeY[]fYea]flg$ l]fa]f\g ]f [m]flY
dY hj]nakaf \] stocks.

 =dYZgjYj dYk j\]f]k \] kmeafakljg
\] eYl]jaYd]k [gf ^][`Y$ [Yfla\Y\ q dgl]k
af\a[Yf\g ]d ege]flg q \]klafg
\]d kmeafakljg Yd YdeY[†f&

Y estudiaremos:

 DY [dYka^a[Y[af \] dYk ]pakl]f[aYk&
 =d [gfljgd \] dgk eYl]jaYd]k&
 =d [d[mdg \] dgk [gkl]k \] _]klaf \]

[gehjYk q \] YdeY[]fYea]flg&
 =d ngdme]f hlaeg \] h]\a\g NGH!&
 =d hmflg \] h]\a\g&
 =d stock \] k]_mja\Y\ q kmk [gkl]k

Ykg[aY\gk&
 =d [d[mdg \]d hmflg \] h]\a\g

q \]d stock \] k]_mja\Y\ [mYf\g dY
\]eYf\Y ka_m] mfY \akljaZm[af fgjeYd&

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4 La gestión de las existencias

1. Las existencias: definición y clases

Hg\]egk \]^afaj dYk ]pakl]f[aYk [geg dgk Y[langk hgk]Š\gk hYjY k]j n]f\a\gk ]f ]d [mjkg fgj%
eYd \]d f]_g[ag \] dY ]ehj]kY ]ehj]kYk [ge]j[aYd]k!$ hYjY k]j [gfkmea\gk ]f ]d hjg[]kg \]
hjg\m[[af e]\aYfl] km ljYfk^gjeY[af g af[gjhgjY[af Yd hjg\m[lg ]ehj]kYk af\mkljaYd]k!$
g kaehd]e]fl] k]j [gfkmea\Yk \mjYfl] dY j]YdarY[af \] dY Y[lana\Y\ ]ehj]kYjaYd&

9kŠ hm]k$ dYk ]pakl]f[aYk kgf Za]f]k im] dY ]ehj]kY hgk]] hYjY2
 K]j n]f\a\gk ]f ]d [mjkg gj\afYjag \] dY ]phdglY[af& =b]ehdg2 mf l]d]nakgj ]f mfY ]ehj]kY

\] [gehjY%n]flY \] ]d][ljg\ge†kla[gk&!
 K]j [gfkmea\gk ] af[gjhgjY\gk ]f dY hjg\m[[af \] Za]f]k q k]jna[agk$ im] dm]_g k]jf n]f%

\a\gk Yd ]pl]jagj& =b]ehdg2 dY l]dY ]f mfY kYklj]jŠY&!
 K]j [gfkmea\gk ]f ]d hjg[]kg hjg\m[lang& =b]ehdg2 ]d [geZmklaZd] \] dY [Yd]^Y[[af&!

DYk ]pakl]f[aYk k] hm]\]f [dYka^a[Yj Yl]f\a]f\g Y \an]jkgk [jal]jagk& Dgk lj]k ek aehgjlYfl]k
kgf2
 =d lahg \] ]ehj]kY im] dYk [gfkme]&
 DY aehmlY[af \] ]k] [gfkmeg Y dY \]l]jeafY[af \]d [gkl] \]d hjg\m[lg l]jeafY\g&
 DY hgkaZada\Y\ \] YdeY[]fYj g fg dgk eYl]jaYd]k&

=f ^mf[af \]d tipo de empresa im] dYk [gfkme]$ dYk ]pakl]f[aYk hm]\]f k]j2

Claves y consejos Empresas comerciales

HYjY mfY \]^afa[af [gehd]lY \] Adquiridas +(! E]j[Y\]jŠYk :a]f]k Y\imaja\gk hYjY km n]flY kaf ljYfk^gjeY[af&
[Y\Y mfg \] dgk ]d]e]flgk im] j]% al exterior +*! Gljgk YhjgnakagfYea]flgk
hj]k]flYf dYk ]pakl]f[aYk hm]\]k Gljg lahg \] Y\imaka[agf]k Yd ]pl]jagj \] eYl]jaYd]k
j][mjjaj Y dY -&³ hYjl] \]d HdYf ?]% YmpadaYj]k j]hm]klgk$ [geZmklaZd]k$ eYl]jaYd
f]jYd \] ;gflYZada\Y\2 Definiciones \] g^a[afY$ ]l[&!&
y relaciones contables.

Empresas industriales

Adquiridas +)! EYl]jaYk hjaeYk :a]f]k Y\imaja\gk hYjY km ljYfk^gjeY[af ]f ]d hjg[]kg
al exterior +*! Gljgk YhjgnakagfYea]flgk hjg\m[lang&

Gljg lahg \] Y\imaka[agf]k Yd ]pl]jagj \] eYl]jaYd]k
YmpadaYj]k j]hm]klgk$ [geZmklaZd]k$ eYl]jaYd \] g^a[afY$
]eZYdYb]k$ ]fnYk]k$ ]l[&!

++! Hjg\m[lgk ]f [mjkg :a]f]k ]f hjg[]kg \] ljYfk^gjeY[af&

Producción +,! Hjg\m[lgk k]eal]jeafY\gk :a]f]k ^YZja[Y\gk hgj dY ]ehj]kY fg \]klafY\gk
propia +-! Hjg\m[lgk l]jeafY\gk fgjeYde]fl] Y dY n]flY q h]f\a]fl]k \] mfY
ljYfk^gjeY[af hgkl]jagj&

:a]f]k ^YZja[Y\gk hgj dY ]ehj]kY q daklgk hYjY dY n]flY&

+.! KmZhjg\m[lgk$ j]ka\mgk :a]f]k im] k] gZla]f]f \] ^gjeY Y[[]kgjaY ]f ]d hjg[]kg
q eYl]jaYd]k j][mh]jY\gk hjg\m[lang&

Tabla 4.1. Lahgk \] ]pakl]f[aYk k]_”f ]d lahg \] ]ehj]kY im] dYk [gfkme]& =d f”e]jg im] dd]nYf \]dYfl]
[Y\Y mfg \] dgk [gf[]hlgk ]k ]d Yka_fY\g hgj ]d HdYf ?]f]jYd \] ;gflYZada\Y\ Y dYk ]pakl]f[aYk&

Actividades  0(( b]jk†ak h]f\a]fl]k \] hYkYj Yd \]hYjlYe]flg \] Y[Y%
ZY\g nYdgjY\gk Y *+$(( € [Y\Y mfg&
1. DY[gklY$ K&D&$ ]k mfY ]ehj]kY \]\a[Y\Y Y dY ^YZja[Y[af \]
b]jk†ak \] dYfY \] Yf_gjY$ q hj]k]flY dgk ka_ma]fl]k ]d]e]f%  *&((( b]jk†ak l]jeafY\gk nYdgjY\gk Y *0$(( € [Y\Y mfg&
lgk ]f km YdeY[†f2
;Yd[mdY ]d [gkl] lglYd \] [Y\Y ]d]e]flg hYljaegfaYd q YkŠ_%
 )&*(( c_ \] dYfY hgj aehgjl] \] ,($(( €'c_& fYd] ]d [\a_g [gflYZd] im] d] [gjj]khgf\]&
 )&((( ZgZafYk \] `adg Y mf [gkl] mfalYjag \] +$(( €&
 1(( b]jk†ak ]f ^Yk] \] ]dYZgjY[af ]f ]d \]hYjlYe]flg

\] ^YZja[Y[af Y )0$(( € [Y\Y mfg&

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4La gestión de las existencias

K]_”f km imputación a la determinación del coste del producto, dYk ]pakl]f[aYk hm]\]f [dY%
ka^a[Yjk] ]f2

 Materiales directos. Kgf Yim]ddgk im] k] Yka_fYf Yd gZb]lg \] [d[mdg \] mfY eYf]jY af]imŠ%
ng[Y g ]pY[lY& =d [gfkmeg \] l]dY hYjY [gf^][[agfYj mf ljYb] k]jŠY mf ]b]ehdg \] ]klY [Yl]%
_gjŠY& =d nYdgj \] ]klgk eYl]jaYd]k [gfkmea\gk ]f ]d hjg[]kg hjg\m[lang k] af[gjhgjY Yd
hjg\m[lg kaf mladarYj [jal]jagk \] j]hYjlg&

 Materiales indirectos. =pakl]f gljgk eYl]jaYd]k im] fg hm]\]f a\]fla^a[Yjk] \] mfY eYf]jY
]na\]fl] q k]f[addY [gf dgk hjg\m[lgk ^YZja[Y\gk& =f dY [gf^][[af \]d ljYb]$ k]jŠYf dgk hYljg%
f]k \] hYh]d mladarY\gk$ g dY [Yfla\Y\ \] ]f]j_ŠY ]d†[lja[Y mladarY\Y hYjY km ^YZja[Y[af& =d
nYdgj \] ]klgk eYl]jaYd]k [gfkmea\gk ]f ]d hjg[]kg hjg\m[lang k] af[gjhgjY Yd hjg\m[lg
mladarYf\g [jal]jagk \] j]hYjlg&

9l]f\a]f\g Y km capacidad de almacenamiento, dYk ]pakl]f[aYk hm]\]f k]j2

 Materiales almacenables. Kgf dgk im] km^j]f mf \]k^Yk] l]ehgjYd ]flj] ]d ege]flg \] km
j][]h[af q km mladarY[af ]f ]d hjg[]kg hjg\m[lang& <]fljg \] ]kl] _jmhg hg\]egk af[dmaj
lg\gk dgk ]d]e]flgk$ ]p[]hlg dgk \] kmeafakljgk [gflafmY\gk&

 Materiales no almacenables. Kgf dgk im] fg _grYf \] dY [YjY[l]jŠkla[Y \] hg\]j YdeY[]fYj%
k] ]f dm_Yj]k ^Ška[gk& <]fljg \] ]kl] _jmhg af[dmaegk lg\gk dgk eYl]jaYd]k ]f]j_†la[gk$ [geg
kgf dY dmr$ ]d _Yk fYlmjYd$ ]l[&$ im] k] j][g_]f ]f ]d HdYf ?]f]jYd \] ;gflYZada\Y\ ZYbg ]d
kmZ_jmhg \] ¿K]jna[agk ]pl]jagj]kÀ&

Productos
terminados

Materias primas Productos en Productos Subproductos Claves y consejos
Materiales curso semiterminados
auxiliares =f dY Mfa\Y\ / hjg^mf\arYj]egk
kgZj] dgk [gf[]hlgk \] eYl]jaYd]k
\aj][lgk ] af\aj][lgk$ Yd YfYdarYj ]d
[gkl] \] dgk hjg\m[lgk&

Residuos

Fig. 4.1. =d [a[dg \] ljYfk^gjeY[af \] dgk eYl]jaYd]k ]f mfY ]ehj]kY af\mkljaYd&

Actividades 87

2. =j]k ]d ”fa[g Y\eafakljYlang \] mfY [Yjhafl]jŠY q \]Z]k \Yj \] YdlY ]f ]d hjg_jYeY
af^gjela[g \] [gflYZada\Y\ dYk \aklaflYk ]pakl]f[aYk2

 LYZdYk \] eY\]jY
 K]jjŠf
 ;dYngk$ [gdY q ZYjfar
 =klYfl]jŠYk kaf Y[YZYj
 E]kYk q kaddYk l]jeafY\Yk

;dYka^Š[YdYk k]_”f ]d HdYf ?]f]jYd \] ;gflYZada\Y\&

3. Af\a[Y ]f im† [m]flY \]d H?; k] mZa[Yf dgk ka_ma]fl]k [gf[]hlgk2

 Dgk j]hm]klgk
 Dgk ]eZYdYb]k
 =d eYl]jaYd \] g^a[afY
 DYk eYl]jaYk hjaeYk
 Dgk hjg\m[lgk \] dYk ]ehj]kYk [ge]j[aYd]k
 Dgk eYl]jaYd]k \an]jkgk

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4 La gestión de las existencias

Importante 2. Funciones del departamento
de aprovisionamiento
=f ]klY mfa\Y\ fgk []fljYegk ]f dY
_]klaf \] dgk eYl]jaYd]k \]fljg \]d HYjY [gfk]_maj im] ]d ^dmbg dg_Škla[g \] hjg\m[lgk g k]jna[agk dd]_m] Y dgk [da]fl]k [mYf\g$ [mYf%
YdeY[†f& lg$ \gf\] q [geg \]k]Yf$ Yd e]fgj [gkl]$ \]Z]egk afa[aYj ]d hjg[]kg Y hYjlaj \] dYk j]dY[agf]k
[gf fm]kljgk hjgn]]\gj]k& Hgj dg lYflg$ ]d ^dmbg dg_Škla[g afl]_jYd hYjl] \]d hjg[]kg \] Yhjgnakag%
fYea]flg$ hYkY hgj ]d hjg[]kg \] hjg\m[[af q l]jeafY ]f ]d hjg[]kg \] \akljaZm[af ^Ška[Y&

=f dY mfa\Y\ Yfl]jagj fgk []fljYegk$ \]fljg \]d proceso de aprovisionamiento \] dgk eYl]jaY%
d]k$ ]f dY ^mf[af \] [gehjYk$ h]jg ]kl] hjg[]kg [gehj]f\] lYeZa†f dY ^mf[af \] YdeY[†f&

El proceso de aprovisionamiento ]k ]d [gfbmflg \] gh]jY[agf]k im] hgf] Y \akhgka[af
\] dY ]ehj]kY$ ]f dYk e]bgj]k [gf\a[agf]k hgkaZd]k \] [Yfla\Y\$ [Yda\Y\$ hj][ag q la]ehg$
lg\gk dgk eYl]jaYd]k q hjg\m[lgk \]d ]pl]jagj f][]kYjagk hYjY ]d ^mf[agfYea]flg \] dY
eakeY q \] km YdeY[]fYea]flg$ \] Y[m]j\g [gf dgk gZb]langk im] dY \aj][[af \] dY ]e%
hj]kY `Y \]^afa\g&

A. Fase de la gestión de compras

=d departamento de compras la]f] [geg gZb]lang hjaf[ahYd hjghgj[agfYj dgk ]d]e]flgk f][]%
kYjagk im] k] \]ZYf Y\imajaj ]f ]d ]pl]jagj hYjY j]YdarYj ]d hjg[]kg \] hjg\m[[af$ ]f dY canti-
dad necesaria q [gf ]d mínimo coste. =k ]d \]hYjlYe]flg j]khgfkYZd] \] f]_g[aYj ]d hj][ag
\] dgk eYl]jaYd]k [gf dgk hjgn]]\gj]k&

<]fljg \] dYk funciones propias de compra hg\]egk ]fme]jYj dYk ka_ma]fl]k2

 Dg[YdarYj$ k]d][[agfYj q ]klYZd][]j dYk ^m]fl]k \] YZYkl][aea]flg \] dgk eYl]jaYd]k q \]ek
kmeafakljgk \] dY ]ehj]kY&

 K]d][[agfYj Y dgk hjgn]]\gj]k ]f ^mf[af \] [jal]jagk hj]naYe]fl] ]klYZd][a\gk&
 ;gl]bYj dgk hj][agk$ [Yda\Y\ q ljYfkhgjl] \] dgk eYl]jaYd]k&
 F]_g[aYj [gf\a[agf]k \] ]flj]_Y q \] hY_g$ YkŠ [geg dYk \] \]ngdm[af$ ]f km [Ykg$ \] dgk

eYl]jaYd]k&
 =ealaj dYk j\]f]k \] [gehjY$ k]_”f dYk [gf\a[agf]k Y[gj\Y\Yk [gf dgk hjgn]]\gj]k&
 J][]h[af q YdeY[]fYb] \] dgk eYl]jaYd]k& =klY ^mf[af \]h]f\] \]d \]hYjlYe]flg \] YdeY%

[†f$ q dY ]klm\aYj]egk ]f dY Mfa\Y\ -&
 =^][lmYj dY [dYka^a[Y[af \] dgk eYl]jaYd]k&
 Dd]nYj ]d [gfljgd \] ]pakl]f[aYk&

HYjY j]YdarYj lg\Yk ]klYk ^mf[agf]k \]Z] \akhgf]j \] dgk [gfljgd]k \] af^gjeY[af f][]kYjagk
hYjY [gfg[]j$ ]f lg\g ege]flg$ [YfYd]k Ydl]jfYlangk \] hjgn]]\gj]k$ hj][agk \] e]j[Y\g \]
dgk ]d]e]flgk$ ]l[&$ hYjY im] lg\Yk dYk Y\imaka[agf]k k] j]Yda[]f Yd eŠfaeg [gkl] [gf ]d fan]d
hlaeg \] [Yda\Y\&

Actividades De qué se Qué ofrece Con qué eslogan se
aprovisiona daría a conocer
4. ;gehd]lY dY lYZdY&  
     
Organización  
     
Mf ^YZja[Yfl] \] l]d]nakgj]k
Mf g\gfldg_g    
MfY j]ka\]f[aY \] Yf[aYfgk
MfY daZj]jŠY    

88

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4La gestión de las existencias

B. Fase de la gestión de almacén Vocabulario

=d YdeY[†f ]k ]d dm_Yj ^Ška[g \gf\] k] j][aZ] dY e]j[Yf[ŠY \]d ]pl]jagj hjgn]]\gj]k! g \] gljYk Estacionalidad: `Y[] j]^]j]f[aY Yd
k][[agf]k \] dY ]ehj]kY ^Zja[Y!$ [gf dY ^afYda\Y\ \] j]k]jnYjdYk q [mklg\aYjdYk hYjY im] k]Yf [gehgjlYea]flg [Š[da[g \] mfY nY%
mladarY\Yk ]f ]d hjg[]kg hjg\m[lang eYl]jaYk hjaeYk$ hjg\m[lgk k]eal]jeafY\gk$ ]l[&! g hm]k% jaYZd]& Hgj ]b]ehdg$ ]d [gfkmeg \]
lYk Y \akhgka[af \] dgk [da]fl]k hjg\m[lgk l]jeafY\gk!& `]dY\gk ]k emq ]d]nY\g ]f n]jYfg$
q ek ZYbg ]f afna]jfg&
DY ^afYda\Y\ \] dY hgk]kaf \] afn]flYjagk g stocks ]f ]d YdeY[†f ]k :

 =nalYj im] dY ]ehj]kY k] \]egj] ]f dYk ]flj]_Yk Y kmk [da]fl]k&

 ?YjYflarYj dY [gflafma\Y\ \]d hjg[]kg hjg\m[lang&

=d ngdme]f \] ]pakl]f[aYk ]f dgk YdeY[]f]k ]kl [gf\a[agfY\g hgj \gk nYjaYZd]k:

 DY demanda.

 =d plazo de entrega \] dgk hjgn]]\gj]k&

=klgk hYje]ljgk fg k] [gfg[]f [gf []jl]rY$ hgj dg im] gZda_Yf Y l]f]j ]f YdeY[†f mfY [Yfla%
\Y\ \] stocks im] ]nal]f dY jmhlmjY \]d hjg[]kg hjg\m[lang&

Hgj gljg dY\g$ dY ]klY[agfYda\Y\ \] dgk hjg\m[lgk gZda_Y Y dY ]ehj]kY Y eYfl]f]j mf stock eŠ%
faeg hYjY Yl]f\]j Y dY \]eYf\Y& =f †hg[Yk \] ^m]jl] \]eYf\Y k]j f][]kYjag [gfl]ehdYj mf
eYqgj af[j]e]flg \] stocks ]f dgk YdeY[]f]k \] dY ]ehj]kY&

Actividades 89

5. Af\a[Y Y im† Y[lana\Y\ \] YhjgnakagfYea]flg [gehjY g YdeY[†f! h]jl]f][] [Y\Y mfY
\] dYk ka_ma]fl]k ^mf[agf]k2
a) EafaearYj dY afn]jkaf ]f ]d afn]flYjag&
b) ;gfk]_maj im] ]d hdYrg \] j][]h[af k]Y ]d ghgjlmfg&
c) :mk[Yj dY e]bgj j]dY[af [Yda\Y\%hj][ag&
d) <akeafmaj Yd epaeg dgk [gkl]k \] YdeY[]fYea]flg&
e) :mk[Yj dgk hjgn]]\gj]k Y\][mY\gk&
f) EafaearYj dYk h†j\a\Yk hgj \YŽgk$ gZkgd]k[]f[aY q YjlŠ[mdgk h]j][]\]jgk&
g) ;gfk]_maj mf fan]d \] ]pakl]f[aYk km^a[a]fl] hYjY im] fmf[Y d] ^Ydl]f eYl]jaYk hja%
eYk Yd \]hYjlYe]flg \] hjg\m[[af&
h) ;gfljgdYj dY [Yda\Y\ \] dgk eYl]jaYd]k hYjY dgk ^af]k im] k] \]\a[Yf&
i) EYfl]f]j mf ljYfkhgjl] ]^a[a]fl] \] dgk afn]flYjagk&
j) L]f]j mf kakl]eY ]^a[a]fl] \] af^gjeY[af \]d afn]flYjag&
k) J]YdarYj af^gje]k kgZj] ]d nYdgj \]d afn]flYjag hYjY [gflYZada\Y\&
l) ;ggh]jYj [gf ]d \]hYjlYe]flg \] [gehjYk hYjY dg_jYj Y\imaka[agf]k ][gfea[Yk
]^a[a]fl]k&
m) @Y[]j hj]\a[[agf]k kgZj] f][]ka\Y\]k \]d afn]flYjag&
n) J][aZaj dYk kgda[alm\]k \] dgk eYl]jaYd]k f][]kYjagk&
ñ) J]YdarYj dYk _]klagf]k ghgjlmfYk hYjY im] dgk eYl]jaYd]k dd]_m]f Y dgk afn]flYjagk
\] dY ]ehj]kY&
o) =dYZgjYj mf kakl]eY \] [gfljgd \] dgk afn]flYjagk&
p) <ak]ŽYj dgk ]khY[agk \]d YdeY[†f&
q) K]d][[agfYj Y dgk hjgn]]\gj]k&
r) ;gf^][[agfYj dY ]kljYl]_aY \] f]_g[aY[af [gf dgk hjgn]]\gj]k&
s) J]YdarYj dY j][]h[af \] dgk h]\a\gk&

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4 La gestión de las existencias

Vocabulario 3. El control de los materiales
Índice de rotación: f”e]jg \] n]%
[]k im] dgk hjg\m[lgk k] j]fm]nYf =d ngdme]f \] eYl]jaYd]k im] [aj[mdYf hgj dgk YdeY[]f]k \] dY ]ehj]kY k] ljY\m[] ]f mf [gkl]$
]f ]d YdeY[†f ]f mf h]jag\g \]l]j% im] Y n][]k hm]\] k]j ]p[]kang& Hgj ]ddg ]k f][]kYjag l]f]j ]klgk eYl]jaYd]k [gfljgdY\gk ]f
eafY\g& lg\g ege]flg hYjY [gfg[]j km ]klY\g& Dgk \Ylgk hjaf[ahYd]k \] dgk im] k] \]Z] hgk]]j af^gj%
Importancia técnica: \a^a[mdlY\ \] eY[af kgf2 dY [dYk] \] YjlŠ[mdgk$ ]d [gkl] \] [Y\Y mfg \] ]ddgk$ dYk ]fljY\Yk$ dYk kYda\Yk q km
[gflafmYj [gf ]d hjg[]kg ]f [Ykg \] mZa[Y[af&
[Yj]f[aY&
Importancia económica: ngdme]f A. Aplicación del método ABC para el control de inventarios
\] j][mjkgk ^afYf[a]jgk afn]jla\g ]f
[Y\Y lahg \] eYl]jaYd]k& =pakl]f \an]jkgk e†lg\gk hYjY ]d [gfljgd \] dgk eYl]jaYd]k& <] lg\gk ]ddgk$ ]d]_aegk ]d e†lg\g
Picking: ]k ]d hjg[]kg \] hj]hYjY% ABC, [gfg[a\g lYeZa†f [geg método de Pareto, hgj km k]f[add]r$ qY im] ]klYZd][] mfY [dYka%
[af \] dgk h]\a\gk$ ]f ]d [mYd k] ^a[Y[af hgj ]p[]h[af$ ]k \][aj$ Zmk[Y [gfljgdYj [gf eYqgj \]\a[Y[af Yim]ddgk eYl]jaYd]k im]
]pljY]f mfa\Y\]k g [gfbmflgk ]e% la]f]f mf hgj[]flYb] \] nYdgj ek ka_fa^a[Ylang3 hYjY ]ddg$ k] j]YdarY mfY [dYka^a[Y[af \ana\a]f\g
hYim]lY\gk hYjY hj]hYjYj gljgk hY% dgk hjg\m[lgk \] dY ]ehj]kY ]f lj]k [Yl]_gjŠYk 9$ : q ;! ]f ^mf[af \] km aehgjlYf[aY l†[fa[g%
im]l]k dgk im] kgda[alY ]d [da]fl]!& ][gfea[Y&

Importante Dgk YjlŠ[mdgk h]jl]f][a]fl]k Y dY [Yl]_gjŠY 9 kgf dgk ek nYdagkgk$ ea]fljYk im] dgk im] h]jl]%
=d nYdgj \] [gfkmeg YfmYd k] [Yd[m% f][]f Y dY [Yl]_gjŠY ; kgf dgk e]fgk nYdagkgk& =kl] e†lg\g la]f] [geg gZb]lang ddYeYj dY
dY emdlahda[Yf\g dY \]eYf\Y YfmYd Yl]f[af `Y[aY ]d [gfljgd \] dgk hg[gk YjlŠ[mdgk \] aehgjlYf[aY [jm[aYd YjlŠ[mdgk 9! ]f dm_Yj \]
hgj ]d [gkl] mfalYjag& `Y[aY dgk em[`gk YjlŠ[mdgk ljanaYd]k YjlŠ[mdgk ;!&

90 Dgk artículos A kgf Za]f]k [mqg nYdgj \] [gfkmeg YfmYd ]k ]d ek ]d]nY\g$ kmhgfa]f\g hgj
lYflg mfY afn]jkaf ^afYf[a]jY [gfka\]jYZd]$ q fgjeYde]fl] j]hj]k]flYf mf hgj[]flYb] ZYbg \]
dYk [Yl]_gjŠYk \] YjlŠ[mdgk ]f ]d YdeY[†f&

Dgk artículos C kgf$ Yd [gfljYjag$ YjlŠ[mdgk [gf ]d e]fgj nYdgj \] [gfkmeg$ h]jg g[mhYf mf
hgj[]flYb] emq ]d]nY\g \]fljg \]d YdeY[†f&

Dgk artículos B kgf YjlŠ[mdgk \] mfY [dYk] afl]je]\aY$ [gf mf nYdgj \] [gfkmeg e]\ag q mf
nYdgj lYeZa†f e]\ag ]f ]d YdeY[†f \] dY ]ehj]kY&

9 ljYn†k \] ]klY [Yl]_gjarY[af$ k] hm]\]f a\]fla^a[Yj hmflgk [dYn] ]f dY _]klaf \] dgk afn]f%
lYjagk$ k]hYjYf\g dgk YjlŠ[mdgk aehgjlYfl]k \] dgk im] fg dg kgf ]kh][aYde]fl] \] Yim]ddgk
im] kgf fme]jgkgk h]jg [gf emq ZYbY j]flYZada\Y\!$ \]\a[Yf\g dgk ]k^m]jrgk eYqgj]k Yd [gf%
ljgd \] dgk hjg\m[lgk 9&

DY \anakaf \] dgk hjg\m[lgk fg la]f] hgj im† k]j ]klja[lYe]fl] 9$ : q ;$ kafg im] dY ]ehj]kY
mladarYj mfY \anakaf \] ek g e]fgk [gehgf]fl]k ]f ^mf[af \] km aehgjlYf[aY&

B. La generalización del método ABC para el control
de otras variables

Dgk YjlŠ[mdgk$ dgk hjgn]]\gj]k q dgk [da]fl]k hm]\]f ljYlYjk] e]\aYfl] mfY _]klaf mfalYjaY im]
h]jealY dY Yhda[Y[af \]d e†lg\g 9:;& Hgj ]b]ehdg$ k] hm]\] j]YdarYj mf ]klm\ag \] [gfljgd \]
dgk hjgn]]\gj]k ]f ^mf[af \] dY [Yfla\Y\ \] [gehjYk im] k] j]YdarY Y [Y\Y mfg$ ]k \][aj$ emd%
lahda[Yf\g km \]eYf\Y YfmYd ]f mfa\Y\]k hgj dY ^j][m]f[aY \] picking h]\a\gk!& HYjY ]ddg k]
gZl]f\jf \Ylgk \] dY af^gjeY[af ]klY\Škla[Y \] im] \akhgf] dY ]ehj]kY&

;gfna]f] \]klY[Yj im] em[`gk YdeY[]f]k mladarYf hYjY ]kl] Yfdakak ]d Šf\a[] \] jglY[af \]
dgk hjg\m[lgk$ dg [mYd hm]\] k]j mf ]jjgj$ qY im] mf hjg\m[lg [gf em[`g egnaea]flg hm]\]
l]f]j mf ZYbg Šf\a[] \] jglY[af g na[]n]jkY& @Yq im] l]f]j ]f [m]flY im] dY jglY[af ]k mf
af\a[Y\gj \]d hjge]\ag \] n][]k im] mf hjg\m[lg k] j]fm]nY ]f ]d YdeY[†f$ \] lYd eYf]jY im]
mf YjlŠ[mdg hm]\] l]f]j em[`g egnaea]flg [gf mf Šf\a[] \] jglY[af ZYbg \]Za\g Y mf ]p[]kg
\] stocks.

Af[dmkg \]fljg \] mfY [Yl]_gjŠY$ k] hm]\]f j]YdarYj \aklaflgk [gfljgd]k 9:;& 9kŠ$ dgk [da]fl]k [gf
dgk im] k] la]f] dY eYqgj [a^jY \] n]flYk fg kgf ^gjrgkYe]fl] dgk eakegk im] hgk]]f ]d \]k%
[mZa]jlg ek ]d]nY\g& Dgk hmflgk \] naklY q dgk [jal]jagk \] [dYka^a[Y[af! kgf \a^]j]fl]k hYjY
]d b]^] \] n]flYk q hYjY ]d j]khgfkYZd] \] dY [m]flY \] aehY_Y\gk&

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4La gestión de las existencias

100 % C Vocabulario
90 %
% de valor en el almacén 80 % B Descubierto: [Yfla\Y\ im] mf \]%
70 % l]jeafY\g [da]fl] Y”f fg `Y YZg%
60 % fY\g ]f dY ^][`Y \] km n]f[aea]flg&
50 % =d l†jeafg k] mkY$ kgZj] lg\g$ ]f dY
40 % ZYf[Y$ Yd j]^]jajk] Y dgk [da]fl]k [m%
30 % qYk [m]flYk k] ]f[m]fljY ]f f”e]%
20 % jgk jgbgk$ ]k \][aj$ ]f f]_Ylang&
10 %
0% A

1111111167502134376821495.................0000000000000000000000000000000000000000000000000000
Cantidad de artículos

Fig. 4.2. =f ]d e†lg\g 9:; k] hgf]f ]f j]dY[af dgk nYdgj]k Y[memdY\gk
\] afn]jkaf q \] mfa\Y\]k YdeY[]fY\Yk&

 Dgk hjae]jgk *&-(( hjg\m[lgk )- ! j]hj]k]flYf ]d /( \] dYk n]flYk&
 Dgk ka_ma]fl]k ,&((( hjg\m[lgk *- ! j]hj]k]flYf ]d *( \] dYk n]flYk&
 Dgk ”dlaegk )(&-(( hjg\m[lgk .( ! j]hj]k]flYf ]d )( \] dYk n]flYk&

=d e†lg\g 9:; fgk af\a[Y af\aj][lYe]fl] [md \]Z] k]j dY mZa[Y[af \] dgk eYl]jaYd]k g hjg%
\m[lgk ]f ]d YdeY[†f2 dgk \] eYqgj Y[lana\Y\ \]Z]f ]klYj kalmY\gk dg ek []j[Y hgkaZd] \] dYk
rgfYk \] ]ph]\a[af$ hYjY [gfk]_maj mfY ][gfgeŠY q jYha\]r ]f ]d ljYfkhgjl] afl]jfg& Ka]ehj]
im] k]Y hgkaZd]$ lYeZa†f dgk [gdg[Yj]egk ]f dY ^gjeY ek Yk]imaZd] hYjY km dg[YdarY[af fan]d
ZYbg \] mZa[Y[af!$ qY im] \] ]klY eYf]jY ]d picking k] hg\j j]YdarYj \] ^gjeY ek ]^a[a]fl]&

Caso práctico 1 Importante
HYjY dY kgdm[af \] ]kl] lahg \]
DY ]ehj]kY >jmlYk D]nYfl]$ K&9&$ \]\a[Y\Y Y dY [gehjY%n]flY \] ^jmlY$ \]k]Y e]bgjYj ]d hjgZd]eYk ]k [gfn]fa]fl] mlada%
[gfljgd \] km YdeY[†f mladarYf\g ]d kakl]eY 9:; & Dgk \Ylgk \] dgk Yj lŠ[mdgk kgf dgk rYj dY `gbY \] [d[mdg&
ka_ma]fl]k2
Web
Artículo Porcentaje sobre el total Valor anual =f dY h_afY \] dY Mfan]jka\Y\
en el inventario de las compras (€) FY[agfYd \] Dmbf 9j_]flafY!
FYjYfbYk hm]\]k ]f[gfljYj mf \g[me]flg
HdlYfgk )( +((&((($(( ddYeY\g ¿=d _j^a[g 9:; [geg
HaŽYk )( )*&((($(( l†[fa[Y \] _]klaf \] afn]flY%
?jYfY\Yk )( ).&((($(( jagkÀ$ ]k[jalg hgj Lgek 9& J&
EYf_g )( ,-&((($(( >m[[a& K] ljYlY \] mf ]b]j[a[ag
E]dgf]k )( j]km]dlg kgZj] ]d e†lg\g \] [dY%
MnYk )( .+(&((($(( ka^a[Y[af 9:; \] afn]flYjagk$ q
;ajm]dYk )( +&((($(( ]d ]fdY[] \aj][lg Yd \g[me]flg
E]dg[glgf]k )( ]k2 http://www.unlu.edu.
KYf\ŠYk )( /1&((($(( ar/~ope 20156/pdf/abc.pdf
)( )-&((($((
+(&((($(( (Continúa)
,(&((($((
91
<]l]jeafY dY aehgjlYf[aY j]dYlanY \] [Y\Y mfg \] dgk hjg\m[lgk$ [Yd[mdYf\g lYeZa†f dgk
hgj[]flYb]k Y[memdY\gk&

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4 La gestión de las existencias

Caso práctico 1 (continuación)

Solución

NYegk Y gZl]f]j dY aehgjlYf[aY j]dYlanY \]d nYdgj \] [Y\Y mfg \] dgk YjlŠ[mdgk$ lYflg ]f
mfa\Y\]k [geg ]f ]mjgk2

Producto Valor en € % acumulado sobre el Acumulación de Acumulado en €
número de artículos porcentajes
EYf_gk .+(&((($(( .+(&((($((
FYjYfbYk +((&((($(( -+$0- -+$0- 1+(&((($((
MnYk /1&((($(( *-$., /1$,1 )&((1&((($((
?jYfY\Yk ,-&((($(( .$/- 0.$*, )&(-,&((($((
KYf\ŠYk ,(&((($(( +$0- 1($(1 )&(1,&((($((
E]dg[glgf]k +(&((($(( +$,* 1+$-( )&)*,&((($((
HaŽYk ).&((($(( *$-. 1.$(/ )&),(&((($((
;ajm]dYk )-&((($(( )$+/ 1/$,, )&)--&((($((
HdlYfgk )*&((($(( )$*0 10$/* )&)./&((($((
E]dgf]k +&((($(( )$(+ 11$/, )&)/(&((($((
10 artículos 1.170.000,00 ($*. )(($((
100,00
 

<] dY lYZdY Yfl]jagj hg\]egk dd]_Yj Y dYk ka_ma]fl]k [gf[dmkagf]k2

Acumulado en % sobre el valor total del almacén a) =d *( \] dgk YjlŠ[mdgk eYf_g q fYjYfbYk! j]hj]k]flY ]d
100 % /1$,1 \]d nYdgj \] dYk ]pakl]f[aYk&

80 % b) =d +( ka_ma]fl] \] dgk YjlŠ[mdgk mnYk$ _jYfY\Yk q kYf\ŠYk!
kgdg j]hj]k]flY ]d ), \]d nYdgj \] dYk ]pakl]f[aYk&
60 %
c) HYjY dgk YjlŠ[mdgk A eYf_gk q fYjYfbYk! k] \]Z] mkYj mf ]k%
40 % lja[lg kakl]eY \] [gfljgd$ [gf j]nakagf]k [gflafmYk \] dgk fa%
n]d]k \] ]pakl]f[aYk q mfY eYj[Y\Y Yl]f[af hYjY dY ]pY[lalm\
20 % \] dgk j]_akljgk& 9\]ek$ \]Z]f ]nalYjk] dgk ]p[]kgk \] stocks.

0% 100 d) HYjY dgk YjlŠ[mdgk B mnYk$ _jYfY\Yk q kYf\ŠYk!$ ZYklYj [gf
10 20 30 40 50 60 70 80 90 dd]nYj Y [YZg mf [gfljgd Y\eafakljYlang afl]je]\ag&

Fig. 4.3. J]dY[af ]flj] ]d nYdgj \] dY afn]jkaf q dYk ]pakl]f[aYk e) HYjY dgk YjlŠ[mdgk C e]dg[glgf]k$ [ajm]dYk$ hdlYfgk$ haŽYk q
YdeY[]fY\Yk& e]dgf]k! k] j][gea]f\Y mladarYj mf [gfljgd e]fgk jŠ_a\g2 hg%
\jŠY k]j km^a[a]fl] mfY e]fgj ]pY[lalm\ ]f dgk j]_akljgk& K] hg%
\jŠY mladarYj mf kakl]eY \] j]nakaf h]ja\a[Y hYjY ljYlYj ]f [gf%
bmflg dYk j\]f]k \] [gehjY Yl]f\a\Yk hgj mf eakeg hjgn]]\gj&

Actividades

6. MfY ]ehj]kY \] af^gjela[Y \akhgf] ]f kmk afn]flYjagk \a]r YjlŠ[mdgk nYdgjY\gk \] dY ka_ma]fl] ^gjeY2

Ordenadores Placas Ordenadores Memorias Memorias Memorias Memorias Memorias Memorias Cajas
portátiles base sobremesa 90 MB 120 MB 210 MB 220 MB 250 MB 300 MB disquetes

Precio .(( )(( -(( )* *( *- +- ,( /( )(
unitario

Cantidad )( ,( *- )*( *(( )+( 0( .( +( -(

J]YdarY ]d Yfdakak 9:; \] ]klgk hjg\m[lgk j][m]j\Y Yqm\Yjl] \] dY `gbY \] [d[mdg!&

92

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4La gestión de las existencias

Caso práctico 2

DY ]ehj]kY N]dYj\] q H]dY\addY$ K&9&$ k] \]\a[Y Y dY hjg\m[[af \] lmjjf& =f km YdeY[†f
la]f] \a]r lahgk \aklaflgk$ nYdgjY\gk \] dY ka_ma]fl] eYf]jY2

Artículo Guirlache Turrón Chocolate Almendra Pistacho Café Tutti-fruti Naranja Praliné Moka
/ ,
Valor ), - * )(( ). *+ ) 0

HYjY ]klYZd][]j ]d [jal]jag \] \akljaZm[af ]khY[aYd g rgfa^a[Y[af$ f][]kalYj]egk$ ]f hja%
e]j dm_Yj$ gj\]fYj ]klgk hjg\m[lgk ]f ^mf[af \] km nYdgj& Gj_YfarYj]egk dgk \Ylgk ]f
mfY lYZdY$ [geg dY im] hm]\] n]jk] Y [gflafmY[af2

Artículo Unidades Valor % valor % % acumulado Importante
unidades valor
9de]f\jY )( )(( --$-. MladarY dY `gbY \] [d[mdg hYjY [ge%
;Y^† )( *+ )*$/0 )( --$-. hjgZYj dgk [d[mdgk \] dYk lj]k ”dla%
HaklY[`g )( ). 0$01 *( .0$++ eYk [gdmefYk$ YkŠ [geg hYjY j]Yda%
?majdY[`] )( ), /$/0 +( //$** rYj ]d _j^a[g \]d Y [memdY\g \]
FYjYfbY )( 0 ,$,, ,( 0-$(( nYdgj&
HjYdaf† )( / +$01 -( 01$,,
Lmjjf )( - *$/0 .( 1+$++
EgcY )( , *$** /( 1.$))
;`g[gdYl] )( * )$)) 0( 10$++
Tutti-fruti )( ) ($-. 1( 11$,,
)(( )0( )(( )(( )(($((

<] dY lYZdY Yfl]jagj hm]\]f gZl]f]jk] ]klYk [gf[dmkagf]k2 100 A B C
80
 <gk hjg\m[lgk \] [dYk] 9 Yde]f\jY q [Y^†! kmhgf]f 60
.0$++ \]d nYdgj \] dgk hjg\m[lgk YdeY[]fY\gk& 40
20
 <gk hjg\m[lgk \] [dYk] : haklY[`g q _majdY[`]! kmhg% 0
f]f ]d ).$./ \]d nYdgj \] dgk hjg\m[lgk YdeY[]fY\gk&

 . hjg\m[lgk \] [dYk] ; dgk j]klYfl]k! kmhgf]f )- \]d
nYdgj \] dgk hjg\m[lgk YdeY[]fY\gk&

Fig. 4.4. NYdgj]k Y[memdY\gk$ Almendra
]f hgj[]flYb]k \]d nYdgj lglYd& GPiuisrtlaaCccahhfeéo

Naranja
Praliné
Turrón
ChocMoloaktae
Tutti-fruti

Actividades

7. DY ]ehj]kY EYjak[g J][ag$ K&D&$ \]k]Y j]YdarYj mf [gfljgd ]p`Ymklang \] km YdeY[†f [gf
dY ^afYda\Y\ \] j]ZYbYj [gkl]k& =f kmk [eYjYk ^ja_gjŠ^a[Yk eYfla]f] dY j]dY[af \] hjg%
\m[lgk im] k] em]kljY ]f dY lYZdY ka_ma]fl]&

Artículo ImakimaddY DmZafY ;a_YdY E]jdmrY DYf_gklafg H]j[]Z] Jg\YZYddg ;Yf_j]bg KYdef :g_YnYfl]
Valor +(( -(( *&-(( *(( ,(( +&((( *(( 1( *+( +&(((

J]YdarY mf [gfljgd \] dYk ]pakl]f[aYk hgj ]d e†lg\g 9:;$ q em]kljY dgk j]kmdlY\gk Y
ljYn†k \] mfY lYZdY q mf _j^a[g&

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4 La gestión de las existencias

4. Los costes de la gestión

Vocabulario de las compras

Stockout: [gkl] im] \]Z] kghgjlYj =d ngdme]f \] stock ]k mfg \] dgk hjgZd]eYk ^mf\Ye]flYd]k im] k] hdYfl]Y ]f ]d [gfljgd \] dgk
dY ]ehj]kY hgj dY h†j\a\Y \] [da]f% afn]flYjagk ]f dY ]ehj]kY& DY kgdm[af [gfkakl] ]f ]f[gfljYj mf equilibrio ]flj] \gk ^m]jrYk \]
l]k Yd fg l]f]j \akhgfaZd]k dgk hjg% k]fla\g ghm]klg2
\m[lgk im] kgda[alYf&
 DY f][]ka\Y\ \] eYfl]f]j dY [Yfla\Y\ km^a[a]fl] \] eYl]jaYd]k hYjY YZYkl][]j Yd hjg[]kg
hjg\m[lang q Y dgk [da]fl]k&

 DY afn]jkaf im] kmhgf] dY Y\imaka[af \] dgk eYl]jaYd]k q dgk _Yklgk \] [gfk]jnY[af \] dgk
eakegk&

9mfim] ]d \]hYjlYe]flg \] [gehjYk fg k]Y mfY mfa\Y\ \] hjg\m[[af$ k] hm]\] \][aj im] km
_]klaf la]f] mfY ¿producciónÀ [dYjYe]fl] \]^afa\Y2 dgk h]\a\gk& Lg\Y dY Y[lana\Y\ \] [gehjYk
_ajY Ydj]\]\gj \] dY [gfk][m[af \] ]kl] ¿productoÀ&

HYjY kYZ]j ka ]d \]hYjlYe]flg \] [gehjYk YŽY\] nYdgj Y dY ]ehj]kY$ k]j f][]kYjag j]YdarYj mf
[gfljgd kgZj] ]d eakeg& HYjY ]ddg$ km]d] ]klYZd][]jk] ]d h]\a\g [geg ]d j]^]j]fl] Y [gfljgdYj2
la]f] im] Zmk[Yjk] mfY rentabilidad ]f dY [gf^][[af \]d h]\a\g$ ]k \][aj$ hjg[mjYj optimizar
la relación entre el importe del pedido y el coste total de realizar y gestionar dicho pedido.

=flj] dgk [gkl]k Y [gfljgdYj ]f dY _]klaf \]d h]\a\g hg\]egk ]fme]jYj2

Importante  Km]d\gk q kYdYjagk \] dYk h]jkgfYk im] j]YdarYf ]d h]\a\g&

 ?Yklgk \] [Yj[l]j Y\eafakljYlang f][]kYjagk hYjY j]YdarYj ]d h]\a\g$ [geg l]d†^gfg$ ^Yp q
eYl]jaYd Y\eafakljYlang f][]kYjag&

 LjYfkhgjl]k$ ]eZYdYb] q k]_mjg `YklY dY j][]h[af \] dYk e]j[Yf[ŠYk ]f ]d YdeY[†f&

Costes fijos: k] kghgjlYf af\]h]f% 9mfim] Yd_mfgk \] ]klgk [gkl]k kgf ^abgk [geg km]d\gk g Ydimad]j]k!$ dY eYqgjŠY kgf nYjaYZd]k$
\a]fl]e]fl] \]d ngdme]f \] hjg% ]k \][aj$ ]klf j]dY[agfY\gk [gf ]d f”e]jg \] h]\a\gk im] k] j]YdarYf$ q `YZj im] afl]flYj
\m[[af& eafaearYjdgk j]\m[a]f\g ]d f”e]jg \] h]\a\gk \] ]k[Ykg aehgjl]& HYjY dg_jYj ]kl] gZb]lang
hm]\]f k]_majk] nYjagk hjg[]\aea]flgk2
Costes variables: ]klf Ykg[aY\gk
Yd ngdme]f \] hjg\m[[af&  9_jmhYj dgk h]\a\gk \] eYl]jaYd]k hgj ^YeadaYk g _jmhgk `geg_†f]gk \] eYl]jaYd]k g hjg%
n]]\gj]k&

 =klYZd][]j mf eŠfaeg \] eYl]jaYd]k Y kgda[alYj$ eYfl]fa]f\g mf eŠfaeg \] hjg\m[lgk ]f dgk
YdeY[]f]k \] dY ]ehj]kY&

HYjY gZl]f]j ]d [gkl] mfalYjag \]d h]\a\g k] kmeYf lg\gk dgk [gkl]k YfmYd]k \]d \]hYjlYe]flg
q k] \ana\] ]flj] ]d f”e]jg \] h]\a\gk j]YdarY\gk ]f ]d h]jag\g&

Actividades

8. Af\a[Y$ \] dY ka_ma]fl] j]dY[af \] [gf[]hlgk$ ka kgf [gkl]k hYh]d& <]d \]hYjlYe]flg \] [gehjYk k] ]f[Yj_Yf \gk h]j%
\aj][lY g afn]jkYe]fl] hjghgj[agfYd]k Y dY j]YdarY[af \] kgfYk [gf km]d\gk YfmYd]k \] *0&((( € q +(&((( € j]kh][%
mf \]l]jeafY\g f”e]jg \] h]\a\gk2 lanYe]fl]& =d [gkl] YfmYd \] dY [m]flY \] Comunicaciones
]k \] *&+(( €& DY [m]flY \] Primas de seguros [gjj]khgf%
a) F”e]jg \] h]jkgfYk im] afl]jna]f]f ]f km j]YdarY[af& \a]fl] Y dg YZgfY\g hgj ]d k]_mjg \] dY e]j[Yf[ŠY `Y Yk[]f%
b) F”e]jg \] mfa\Y\]k h]\a\Yk& \a\g Y +&((( €& Hgj ]d ljYfkhgjl] \] dY e]j[Yf[ŠY kgda[a%
c) LjYfkhgjl] \] dgk eYl]jaYd]k& lY\Y k] YZgfYjgf *&*** €& DY ]f]j_ŠY ]d†[lja[Y [gfkmea\Y
d) K]_mjg \] dgk eYl]jaYd]k& ]f dY ]ehj]kY ]f ]d ”dlaeg YŽg `Y Yk[]f\a\g Y *&((( €& DY
]ehj]kY hjgjjYl]Y ]d [gfkmeg \] dmr ]flj] dgk \]hYjlY%
9. DY ]ehj]kY =d ?dgZg$ K&9&$ hmZda[Y mfY j]naklY k]eYfYd [gf e]flgk ]f ^mf[af \]d f”e]jg \] lmZgk ^dmgj]k[]fl]k im]
dgk YjlŠ[mdgk ek hgd†ea[gk im] k] `Yf hmZda[Y\g Y dg dYj_g la]f] [Y\Y \]hYjlYe]flg2
\] dgk ”dlaegk ka]l] \ŠYk& Km hjaf[ahYd eYl]jaY hjaeY ]k ]d

Aprovisionamiento Prensa Troquelado Comercialización Ventas

)*( lmZgk *(( lmZgk -( lmZgk ,( lmZgk .( lmZgk

=d f”e]jg \] h]\a\gk j]YdarY\g Y dg dYj_g \]d YŽg `Y ka\g \] ,-(&
9 hYjlaj \] ]klY af^gjeY[af$ [Yd[mdY ]d [gkl] mfalYjag \] [Y\Y h]\a\g&

94

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4La gestión de las existencias

5. Los costes de almacenamiento Importante

Dgk [gkl]k \] YdeY[]fYea]flg g hgk]kaf kgf dgk \]janY\gk \] YdeY[]fYj YjlŠ[mdgk q eYfl]% EYfl]f]j ]pakl]f[aYk ]f dgk YdeY%
f]jdgk \mjYfl] ]d la]ehg im] h]jeYf][]f ]f ]d YdeY[†f& =klgk kgf Yd_mfgk ]b]ehdgk \] ]kl] []f]k la]f] mf [gkl]& Hgj ]klg$ [mYf%
lahg \] [gkl]k2 lg eYqgj k]Y dY [Yfla\Y\ YdeY[]fY%
\Y \] [mYdima]j lahg \] eYl]jaYd g
 9dimad]j \]d YdeY[†f& hjg\m[lg$ eYqgj k]j ]d [gkl] \]
 9egjlarY[af \] dY [gfkljm[[af$ ]f ]d [Ykg \] im] k]Y hjgha]\Y\ \] dY ]ehj]kY& YdeY[]fYb] hYjY dY ]ehj]kY&
 ?Yklgk \] j]hYjY[af q [gfk]jnY[af&
 ?Yklgk \] [Yd]^Y[[af g j]^ja_]jY[af&
 K]_mjgk \] dYk e]j[Yf[ŠYk q \] dgk ]\a^a[agk&
 9dmeZjY\g&
 EYfahmdY[af ^Ška[Y \] dgk ]d]e]flgk&
 H†j\a\Yk hgj \]l]jagjg \] nYdgj Yfl] dY YhYja[af \] ]d]e]flgk ek ]^a[a]fl]k ]f ]d e]j[Y\g&

GZk]jnYegk [eg ]pakl]f [gkl]k \] \an]jkY fYlmjYd]rY& 9d_mfgk k]jf ^[ad]k \] [Yd[mdYj$ [geg
]d [gkl] \]d Ydimad]j \]d YdeY[†f$ im] fgk n]f\j ]f dY [gjj]khgf\a]fl] ^Y[lmjY& Gljgk$ kaf ]e%
ZYj_g$ fg k]jf ^[ad]k \] Yka_fYj \] ^gjeY mfalYjaY$ hm]k ]klYjf \akljaZma\gk ]flj] lg\gk dgk
\]hYjlYe]flgk \] dY ]ehj]kY hgj ]b]ehdg$ ]d [gkl] \] dY ^Y[lmjY \]d [gfkmeg \] ]d][lja[a\Y\!&
=klg fgk gZda_Yj Y Y\ghlYj Yd_mf [jal]jag g hYje]ljg \] aehmlY[af hYjY j]hYjlaj km aehgjl]
]flj] [Y\Y mfg \] ]ddgk&

9kŠ hm]k$ dgk stocks, [mYdima]jY im] k]Y dY fYlmjYd]rY \] dgk hjg\m[lgk g eYl]jaYk hjaeYk im]
dgk [gehgf]f$ j]hj]k]flYf mf [YhalYd im] im]\Y afegnadarY\g ]f dY ]ehj]kY \mjYfl] ]d la]ehg
im] h]jeYf][] ]f ]d YdeY[†f&

<]k\] gljg hmflg \] naklY$ dgk [gkl]k \] YdeY[]fYea]flg k] kmZ\ana\]f ]f \gk [Yl]_gjŠYk2

 ;gkl]k ^afYf[a]jgk afl]j]k]k q [gkl]k \] ghgjlmfa\Y\!&

 ;gkl]k hjghagk \] eYfl]faea]flg dgk ljYlY\gk Yfl]jagje]fl]!&

DY kmeY \] dgk [gkl]k ^afYf[a]jgk ek dgk \] eYfl]faea]flg k]j ]d [gkl] \] YdeY[]fYea]flg&
=kl] ”dlaeg k]j \]l]jeafYfl] hYjY [gfkljmaj af\a[Y\gj]k \] [gfljgd [geg dY tasa de posesión
del stock.

DY tasa de posesión del stock ]k ]d [g[a]fl] ]flj] dgk [gkl]k \] YdeY[]fYea]flg q ]d
nYdgj \]d stock g afn]flYjag e]\ag&

Hgj ]b]ehdg$ mfY ]ehj]kY [gf mfgk [gkl]k \] YdeY[†f \] *((&((( € q mf nYdgj e]\ag \] af%
n]flYjag \] )&(((&((( €$ l]f\j mf lYkY \] hgk]kaf \]d *( & =k aehgjlYfl] [gfg[]j dY lYkY
\] hgk]kaf hYjY afl]flYj j]\m[ajdY Y ljYn†k \] dgk [gehgf]fl]k \] dY eakeY&

Actividades 95

10. <] dY j]dY[af \] _Yklgk \] hgk]kaf im] k] `Yf [alY\g ]f ]d YhYjlY\g$ af\a[Y [md]k
kgf nYjaYZd]k q [md]k kgf ^abgk&

11. ;Yd[mdY ]d [gkl] \] hgk]kaf \]d hYh]d YdeY[]fY\g hgj mfY ]ehj]kY \] hYh]d]jŠY im]
`Y gZl]fa\g dgk ka_ma]fl]k \Ylgk2
 Afl]j]k]k YfmYd]k \] hj†klYegk kgda[alY\gk2 *&-(( €
 9dimad]j \] dgk dg[Yd]k g[mhY\gk g YegjlarY[af ka kgf hjghagk2 )&-(( €
 ;gfk]jnY[af \]d eYl]jaYd2 )-( €
 H†j\a\Yk hgj \]l]jagjg$ e]jeYk g ]pljYnŠgk2 +(( €
 ?Yklgk _]f]jYd]k q \] Y\eafakljY[af \] YdeY[†f2 )&*(( €

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4 La gestión de las existencias

Importante 6. El volumen óptimo de pedido (VOP)
DY jglmjY \] stocks k] hjg\m[] [mYf%
\g ]d \]hYjlYe]flg \] YdeY[†f fg =d hjgZd]eY ^mf\Ye]flYd \] dY _]klaf \] stocks k] []fljY ]f \]l]jeafYj [md la]f] im] k]j dY
\akhgf] \] eYl]jaYd]k km^a[a]fl]k [Yfla\Y\ im] k] \]Z] eYfl]f]j ]f ]d YdeY[†f hYjY ]nalYj dY jmhlmjY \]d hjg[]kg hjg\m[lang&
hYjY Yl]f\]j dYk \]eYf\Yk \]d \]%
hYjlYe]flg \] hjg\m[[af& =klY [Yfla\Y\ ]klYj ZYkY\Y ]f ^Y[lgj]k [geg ]d ngdme]f \] h]\a\g q ]d la]ehg \] Yhjgnakag%
fYea]flg& =f \]^afalanY$ ]f [Yd[mdYj ]d fan]d af\akh]fkYZd] \] afn]jkaf ]f ]pakl]f[aYk&
Recuerda
El volumen óptimo de pedido k] J][m]j\Y im] dgk h]\a\gk [gfdd]nYf \gk lahgk \] [gkl]k2 ^abgk q nYjaYZd]k& ;mYflg eYqgj k]Y ]d
gZl]f\j ]f ]d hmflg ]f im] k] a_mY% h]\a\g e]fgj k]j dY hYjl] hjghgj[agfYd \] [gkl]k ^abgk im] d] [gjj]khgf\] Y [Y\Y h]\a\g$ Y dY
d]f dgk [gkl]k \] hgk]kaf q dgk \] hYj im] k] hm]\]f gZl]f]j n]flYbYk [ge]j[aYd]k [geg \]k[m]flgk hgj ngdme]f& H]jg Y eYqgj
_]klaf \] h]\a\gk& ngdme]f \] h]\a\g lYeZa†f k]jf eYqgj]k dgk [gkl]k \] YdeY[]fYea]flg g hgk]kaf Y\]ek
\] dgk afl]j]k]k q ]d [gkl] \] ghgjlmfa\Y\!&

DY ]ehj]kY \]Z]j YjegfarYj$ hgj lYflg$ dgk [gkl]k \] hgk]kaf q dgk \] _]klaf \] h]\a\gk
hYjY im] k]Yf eŠfaegk&

=flj] dgk eg\]dgk \] YdeY[†f im] ljYlYf \] \]l]jeafYj ]d stock hlaeg$ k] hm]\]f \]klY[Yj
dgk ka_ma]fl]k2

 Dgk modelos de previsión perfecta, im] k] [YjY[l]jarYf hgjim] ]d jaleg \] kYda\Y \] dgk
YjlŠ[mdgk YdeY[]fY\gk ]k [gfg[a\g&

 Dgk modelos estocásticos. =f ]ddgk fg k] [gfg[] ]d jaleg \] kYda\Y$ dg im] gZda_Y Y afljg\m%
[aj dY hjgZYZada\Y\ hYjY dY j]kgdm[af \] dgk \aklaflgk hjgZd]eYk \] YdeY[†f&

9 [gflafmY[af fgk nYegk Y []fljYj ]f mf eg\]dg \] hj]nakaf h]j^][lY&

A. El volumen óptimo de pedido

=flj] dgk eg\]dgk \]l]jeafaklYk g \] hj]nakaf h]j^][lY ]d ek \]klY[Y\g ]k ]d eg\]dg de
Wilson$ ^gjemdY\g ]f )1).& =kl] eg\]dg ]klm\aY ]d [Ykg \] mf ]klYZd][aea]flg [ge]j[aYd$
hYjla]f\g \] dgk ka_ma]fl]k kmhm]klgk2

 DYk n]flYk k] kmhgf]f h]j^][lYe]fl] [gfg[a\Yk q$ Y\]ek$ k] \akljaZmq]f mfa^gje]e]fl] Y
dg dYj_g \]d YŽg&

 =pakl]f mfgk [gkl]k ^abgk \] h]\a\g q mfgk [gkl]k nYjaYZd]k \] YdeY[†f&

=f ]klYk [aj[mfklYf[aYk k] \]Z] [Yd[mdYj ]d ngdme]f hlaeg \] h]\a\g$ im] h]jealY eafaearYj
dgk [gkl]k lglYd]k& =^][lmYj h]\a\gk _jYf\]k \akeafmq] ]d [gkl] YfmYd \] h]\a\g$ h]jg aehda[Y
im] dgk YjlŠ[mdgk lYj\Yjf ek ]f n]f\]jk]$ dg im] Yme]flY ]d [gkl] YfmYd \] hgk]kaf g \]
YdeY[†f& Dg [gfljYjag km[]\]j [gf dgk h]\a\gk h]im]Žgk&

=d volumen óptimo de pedido k]j ]d im] a_mYd] dgk [gkl]k \] hgk]kaf q dgk \] _]klaf \]
h]\a\gk&

=d coste total \] h]\a\g k] [Yd[mdY [geg mfY kmeY \] nYjagk [gf[]hlgk2

 Coste de adquisición Hj][ag \] [gehjY P! Ù ;Yfla\Y\ \]eYf\Y YfmYde]fl] D!

 Coste de gestión del pedido = ;gkl] \]d h]\a\g Cpe! ⋅ ;Yfla\Y\ \]eYf\Y D!
Ngdme]f \] h]\a\g Q!

 Coste de posesión g YdeY[]fYea]flg2
Cp! ;gkl] \] eYfl]faea]flg hgj mfa\Y\ \] hjg\m[lg Ù Stock e]\ag Q
*

=d coste total k] `YddY Yhda[Yf\g dY ka_ma]fl] ][mY[af2

CT = P ⋅ D + Cpe Q + Cg D
*Q

96

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4La gestión de las existencias

Dgk [gkl]k hjghagk \] Y\imaka[af \]d hjg\m[lg (P ˜ D) fg kgf j]d]nYfl]k hYjY \][a\aj ]d ngdm%
e]f hlaeg \] h]\a\g$ hm]k ]kl] kgdg \]h]f\] \] dgk \] _]klaf \]d h]\a\g q \] dgk \] hgk]%
kaf g YdeY[]fYea]flg&

9kŠ$ ]d ngdme]f hlaeg \] h]\a\g k]j Yim]d im] a_mYd] dgk costes de posesión q dgk \] ges-
tión de pedido&

=d [gkl] \] _]klaf \] dgk h]\a\gk ]k a_mYd Y2 D Recuerda
Cg Q  Dgk [gkl]k \] hgk]kaf kgf eY%

Hgj gljg dY\g$ dgk [gkl]k \] hgk]kaf kgf a_mYd]k Y2 qgj]k [mYflg eYqgj ]k dY [Yfla%
\Y\ h]\a\Y&
Cp Q  Dgk [gkl]k \] _]klaf \]d h]\a\g
* \akeafmq]f [mYflg eYqgj ]k dY
[Yfla\Y\ h]\a\Y&
Cg = D = Cp ⋅ Q
Q* Importante
=^][lmYj h]\a\gk _jYf\]k \akeafmq]
=^][lmYf\g gh]jY[agf]k2 ]d [gkl] YfmYd \] h]\a\g$ h]jg ae%
hda[Y im] dgk YjlŠ[mdgk lYj\Yjf ek
Cg ˜ D ˜ * = Q* ˜ Cp → Q* = Cg ⋅ D ⋅ * ]f n]f\]jk]$ dg im] Yme]flY ]d [gk%
Cp l] \] hgk]kaf& ;gf h]\a\gk h]im]%
Žgk km[]\]j dg [gfljYjag&
Q = Cg ⋅ D ⋅ *
Cp 97

Caso práctico 3

Kmhgf_Yegk im] dY ]ehj]kY HYhYddYeY$ K&D&$ im] k] \]\a[Y Y dY n]flY \] l]d†^gfgk ena%
d]k$ la]f] mfY \]eYf\Y YfmYd (D) \] +(&((( mfa\Y\]k3 [Y\Y n]r im] j]YdarY mf h]\a\g
(Cpe) km _]klaf d] [m]klY ** €$ q ]d [gkl] \] YdeY[]fYea]flg (Cp) \] [Y\Y mfa\Y\ ]k \]
)$-( €& Ka hj]l]f\] l]f]j hg[Yk mfa\Y\]k YdeY[]fY\Yk hYjY \akeafmaj dgk [gkl]k \] YdeY%
[]fYea]flg$ Yme]flYjf dgk [gkl]k \] ]eakaf \] h]\a\gk$ qY im] dgk ^gjemdYj [gf ek
^j][m]f[aY3 hgj ]d [gfljYjag$ ka ima]j] j]YdarYj hg[gk h]\a\gk [Y\Y mfg d] [m]klY ** €!$
\]Z]j l]f]j em[`Yk mfa\Y\]k YdeY[]fY\Yk q [Y\Y mfY d] [m]klY )$-( €&

@]egk \] [gfka\]jYj im]$ ka dY \]eYf\Y ]k [gfklYfl]$ ]d fan]d e]\ag \] ]pakl]f[aYk ]f
YdeY[†f k]j dY ealY\ Q'*!&

N]Yegk mf ]b]ehdg ]f dY lYZdY ka_ma]fl]$ l]fa]f\g ]f [m]flY im]2

F&´ h]\a\gk Ù Q [Yfla\Y\ kgda[alY\Y ]f [Y\Y h]\a\g! <]eYf\Y YfmYd

Número Q Q Coste de Coste de Coste total
de pedidos 2 gestión de almacenamiento (€)
pedidos (Cpe)
*-( (€)
+(( (€) (N.º
-(( pedidos · 22) 1,5 ˜ Q
/-( 2
)&(((
.( -(( )&+*($(( +/- )&.1-$((
-( .((
+( )&((( )&)(($(( ,-( )&--($((
*( )&-((
)- *&((( ..($(( /-( )&,)($((

,,($(( )&)*- )&-.-$((

++($(( )&-(( )&0+($((

(Continúa)

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4 La gestión de las existencias

Caso práctico 3 (continuación)

Solución

<]k[gfg[a]f\g dY [Yfla\Y\ kgda[alY\Y ]f [Y\Y h]\a\g$ a_mYdYegk dgk [gkl]k lglYd]k \]
]eakaf \] h]\a\gk Y dgk [gkl]k \] YdeY[]fYea]flg [gf gZb]lg \] `Y[]jdgk eŠfaegk2

Recuerda +(&((( F&´ h]\a\gk ⇒ +(&((( ˜ ** € [gkl] \] _]klaf g ]eakaf \] h]\a\gk&
=d eg\]dg \] Oadkgf k] [YjY[l]jarY Q Q
hgjim] ]d jaleg \] kYda\Y \] dgk Yj%
lŠ[mdgk YdeY[]fY\gk ]k [gfg[a\g$ )$-( ⋅ Q = ;gkl] YfmYd \] YdeY[]fYea]flg&
h]jg ]klg fg ka]ehj] km[]\] YkŠ& *

98 A_mYdYegk dgk [gkl]k lglYd]k \] ]eakaf \] h]\a\gk [gf dgk \] YdeY[]fYea]flg2

+(&((( = )$-( ⋅ Q
Q*

<]kh]bYegk Q:

Q = Cg ⋅ D ⋅ * = +(&((( ⋅ ** ⋅ * = 1+0$(0 ≈ 1+0 mfa\Y\]k
Cp )$-(

F&´ h]\a\gk YfmYd]k +(&((( = +)$10 ≈ +* h]\a\gk
1+0

DY j]hj]k]flY[af _j^a[Y \]d [gkl] \] dgk h]\a\gk k] j][g_] ]f dY >a_mjY ,&-$ \gf\]2

 Cg ;gkl] \] _]klaf \] h]\a\gk
 Cp ;gkl] \] YdeY[]fYea]flg
 CT Cg Cp

2.000,00 500 600 1.000 1.500 2.000
1.800,00
1.600,00
1.400,00
1.200,00
1.000,00

800,00
600,00
400,00
200,00

0,00

Coste de gestión de pedidos

(Cpe) (€) (N.º pedidos ˜ 22)

( )Coste de almacenamiento (€) 2 ˜ Q
2

Coste total (€)

Fig. 4.5. J]hj]k]flY[af \]d ngdme]f hlaeg \] h]\a\g& (Continúa)

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4La gestión de las existencias

Caso práctico 3 (continuación) Recuerda

9 dgk [gkl]k Yfl]jagje]fl] ]phm]klgk `YZj im] kmeYj dgk \] Y\imaka[af \]d hjg\m[lg HYjY [Yd[mdYj ]d ngdme]f hlaeg \]
Q ˜ hj][ag \] Y\imaka[af!& h]\a\g `Yq im] l]f]j ]f [m]flY ]d
[gkl] \] ]eakaf$ ]d [gkl] mfalYjag
9d k]j dY \]eYf\Y [gfklYfl] q ^mf[agfYj afafl]jjmeha\Ye]fl] fm]kljg hjg[]kg hjg\m[% \] YdeY[]fYea]flg q ]d ngdme]f
lang \mjYfl] dgk +.- \ŠYk \]d YŽg$ ]^][lmYj]egk mf h]\a\g [Y\Y2 \] mfa\Y\]k hj]naklYk YfmYde]fl]&

+.- ))$,( \ŠYk
+*

Ka ]d hdYrg \] YhjgnakagfYea]flg (Pe) ]k \] [af[g \ŠYk$ ]^][lmYj]egk ]d h]\a\g (Pp) \]
1+0Âmfa\Y\]k [mYf\g ]d fan]d \] stock k]Y \] ,)( mfa\Y\]k&

Cpe ;gfkmeg \mjYfl] ]d hdYrg \] ]flj]_Y D ˜ Pe
+.-
D <]eYf\Y YfmYd

pe HdYrg \] ]flj]_Y

Pp Hmflg \] h]\a\g

Pp Cpe

Ka dY ]ehj]kY `mZa]jY ]klYZd][a\g stock \] k]_mja\Y\ hYjY `Y[]j ^j]fl] Y dYk hgkaZd]k
\]egjYk ]f dgk kmeafakljgk$ ]d hmflg \] h]\a\g k] ]^][lmYjŠY [mYf\g ]d stock Yd[YfrYjY ]d
fan]d \] [gfkmeg f][]kYjag \mjYfl] ]d hdYrg \] ]flj]_Y YŽY\a\g Y \a[`g stock \] k]_mja%
\Y\ (Ss).

Pp Cpe Ss

Caso práctico 4 Importante
HYjY j]YdarYj dgk [d[mdgk \] ]kl]
J]hm]klgk >]jff\]r q @]jff\]r$ K&9&$ [gehjY Y <akljaZm[agf]k H]jak$ K&9&$ mf \]l]jea% [Ykg hj[la[g ]k j][ge]f\YZd]
fY\g YjlŠ[mdg Y ($+- €'m\& DY \]eYf\Y \] \a[`g YjlŠ[mdg ]k hj[la[Ye]fl] [gfklYfl] ] mladarYj dY `gbY \] [d[mdg&
a_mYd Y )&((( mfa\Y\]k Yd \ŠY$ \mjYfl] dgk *00 \ŠYk \]d YŽg ]f im] h]jeYf][] YZa]jlY dY
]ehj]kY& DY ]ehj]kY \akljaZma\gjY k] ]f[Yj_Y \]d ljYfkhgjl] \]d YjlŠ[mdg ]f [Yeagf]k \] (Continúa)
km hjgha]\Y\$ q k] `Y [Yd[mdY\g im] dgk _Yklgk \] ljYfkhgjl] ek dgk \] dY ]eakaf \]d 99
h]\a\g Yk[a]f\]f Y *(($(( € hgj naYb] ]^][lmY\g& J]hm]klgk >]jff\]r q @]jff\]r$ K&9&$
fg ]kl \akhm]klY Y km^jaj mfY jglmjY ]f kmk stocks im] kmhgf_Y dY hYjYdarY[af \]d hjg[]kg
hjg\m[lang&
=d [gkl] \] YdeY[]fYea]flg \]d YjlŠ[mdg ]k \] )-$(( € Yd YŽg hYjY [Y\Y )&((( ha]rYk$
k]_”f dgk [d[mdgk ]^][lmY\gk hgj dY ]ehj]kY&

9d eakeg la]ehg$ ]klY ]ehj]kY \akljaZma\gjY la]f] mf [gkl] \] [YhalYd \]d )( kgZj] ]d
[YhalYd afn]jla\g& ;geg ]d hj][ag \] Y\imaka[af \]d YjlŠ[mdg ]k \] ($+- €'m\$ ]d afl]j†k
im] [gjj]khgf\] Yd nYdgj \] mfY mfa\Y\ YdeY[]fY\Y k]j a_mYd Y ($(+- afl]j†k YfmYd!&
=d [gkl] YfmYd hgj eYfl]faea]flg \] dYk ]pakl]f[aYk k]j2 ($()- ($(+- ($(- €'m\&

DY ]ehj]kY ima]j] kYZ]j [md ]k dY [Yfla\Y\ \] YjlŠ[mdgk im] \]Z] ljY]j ]f [Y\Y naYb]$ \]
^gjeY im] k]Y eŠfaeY dY kmeY \] dgk [gkl]k \] ljYfkhgjl] q \] eYfl]faea]flg \]d stock
f][]kYjag hYjY fg km^jaj mfY jglmjY ]f kmk stocks.

Solución

=f ]kl] [Ykg$ hg\]egk [Yd[mdYj ]d h]\a\g hlaeg ka_ma]f\g \gk e†lg\gk2 hgj j]al]jY[af
q hgj dY ^jemdY \]d ngdme]f hlaeg \] h]\a\g& Dgk n]egk Y [gflafmY[af&

a) Por reiteración

9fl]k \] hjg[]\]j Y j]kgdn]j ]d ]b]j[a[ag e]\aYfl] dY ^jemdY Yfl]jagje]fl] ]phm]klY$
nYegk Y hj]k]flYj dY kgdm[af \] mfY eYf]jY ek aflmalanY e]\aYfl] dgk [gkl]k g[Ykag%
fY\gk k]_”f dYk \aklaflYk [mYflŠYk \] dgk dgl]k2

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