Production planning 2

Optim

Introd

In the fowarehouterms wi

The calcuvariationproducti

In the ex(month,

Purpo1. T2. T3. T4. T5. T

Invent1. H2. C3. S4. C5. O6. C7. S8. C

Invent1. S

2. M

3. F

The “to1. O2. O

mal Servic

duction

llowing we wusing. Since till be used in

ulation will bn. In additionion, logistic a

xample givenquarter, etc

ses of InvTo maintain To meet variTo allow flexTo provide a To take adva

tory CostsHolding (or cCosts for capSetup (or proCosts for arraOrdering cosCosts of somShortage cosCosts of canc

tory SysteSingle‐Period

a. One b. Seek

Multi‐Perioda. Fixedb. Even

Fixed‐Time Pa. Time

oo much/Order too mOrder too litt

ce Level i

will show howthe problem terchangeab

be based on kn will sales usand warehou

n below the s.). The prod

ventory independencation in prodxibility in prodsafeguard fo

antage of eco

s carrying) costpital, storageoduction chaanging specifsts meone placingsts celing an ord

ems d Inventory Mtime purchaks to balance Inventory Md‐Order Quant triggered (Period Modee triggered (E

/too little uch and invetle and sales

n Produc

w sales forecdiscussed is bly.

knowledge osually have a using costs.

sales forecastduction lead t

ce of operatiduct demandduction scheor variation ionomic purch

ts , handling, “sange) costs fic equipmen

g an order, e

der, etc.

Model sing decision the costs of

Models ntity ModelsExample: runls Example: Mo

problem”entory is left are lost.

of 1

ction and

casts can be uthe same for

of the sales dseasonal var

ts will thereftime will the

ions d eduling n raw materhase‐order si

shrinkage,” i

nt setups, etc

tc.

n (Example: vf inventory ov

s nning out of

onthly sales c

” over at the e

1

d Wareho

used to set ler both produ

istribution, briance creati

fore have to bn determine

ial delivery tize

nsurance, et

c.

vendor sellinverstock and

stock)

call by sales r

end of the se

ousing

evels in production and wa

both expecteng a balance

be viewed ase the product

ime

tc.

g t‐shirts at ad under stock

representativ

eason

uction or in arehousing, t

ed sales and ie act between

s a periodic ftion planning

a football gak

ve)

multi‐level the two

its n

forecast g (timing).

me)

To maximgain on t

I.

Where Cknown –

Cu = The known –

)Q(F = P

Rearrang

II.

The ratio

The usua

III. Q

Demthe enum

The op

The wareimplies tproducti

If we formarkup

ExpectThe figurheavily s

mize expectethe Qth unit:

)Q(FCo =×

Co = The cost – or the incre

cost of orde– or the incre

Probability D

ge terms in t

Prob{Dema

o Cu / (Co + Cu

al way of solv

Q = m + z * s

mand howeveexact distribu

merically find

ptimal ser

ehouse (or pthat the probion costs.

r the momen(%) determin

ted sales re below indskewed to th

ed profit orde

( F1Cu −×=

of ordering oease in profit

ering one fewease in profit

Demand for q

he above eq

Q}dan =<=

u) is called th

ving this is to

, where: z= (

er has seldomution at all. Wthe Q satisfy

rvice level

production) lebability for st

t assume thane the optim

icates the sae right so the

er Q units so

( ))QF ,

one more unenjoyed by h

wer unit thant enjoyed by

q<= Q

uation

oCCF(Q) ==

he critical rat

o assume tha

Q‐m)/s is no

m a normal diWe can only ying equation

l

evel should btock out (lost

at all these comal warehous

ales distributiere is a possi

of 1

that the exp

nit than whathaving order

what wouldhaving orde

u

u

CC+

io (CR).

at the deman

ormal distrib

istribution an‘find’ it by Mn I.

be set to maxt sales) shoul

osts can be rse level.

ion. Expectedibility of sale

1

pected loss o

t would havered one fewe

have been ored one mor

nd is normal d

uted N(0,1)

nd to make tMonte Carlo si

ximize profit ld be weighe

regarded as a

d sales are 18s exceeding

on the Qth un

e been ordereer unit,

ordered if dere unit, and

distributed N

hings worse imulation an

given the saed against wa

a variable cos

819 units, buexpected sal

it equals the

ed if demand

emand had b

N(m,s) giving

we usually dnd thus have

les distributiarehousing, l

st, will the pr

ut the distribles:

expected

d had been

een

Q as:

don’t know to

ion. This ogistic and

roduct

ution is

By settinon the sa

Profit The loss more tha

The prof

The figurstock‐outhat exp

ng the producales forecast

and Loss is calculatedan can be ex

fit is calculate

re below indut. We can seected profit

ct markup – t.

of opportd as the valuepected to be

ed as value o

icates what wee as we succwill increase

in the examp

tunity e of lost salese sold.

of sales less p

will happen acessively move to a point o

of 1

ple below it i

s (stock‐out)

production co

as we producve to higher f maximum,

1

is 300% ‐ we

and the cost

osts of both

ce and stock production (the same po

can calculat

t of having p

sold and uns

at different (from left to oint where lo

e profit and

roduced and

sold items.

levels of proright on the oss is minimiz

loss based

d stocked

obability of x‐axis) zed:

At that pit is at th

ProductThe optiroom for

the acce

If we putdistributproducti

The OpThe opticurve (refrom thecumulati

point we can his point that

t markup mal stock or r a higher lev

ptance of sto

t it all togethtion giving thion level give

ptimal stomal stock leved) for optime markup axisive probabili

expect to hat profit is max

production vel of unsold

ock‐ out:

her we get the probabilityen the marku

ock and prvel is then fomal stock leves to the probty) and the p

ave some excximized, so t

level will be items while

he chart belowy of the levelup.

roductionound by drawel, and down bability axis (probability fo

of 1

cess stock anthis is the opt

a function ofa low level w

w. In this the of sales and

n level wing a line froto the x‐axisleft y‐axis) wor having a st

1

nd in some catimal stock (

f the productwill necessita

e green curved the red curv

om the right s giving the swe find the prtock level in e

ases also lostproduction)

t markup. A hate a focus on

e is the cumuve give the o

markup axis tock level. Byrobability levexcess of dem

t sales. But relevel.

high markupn cost reduct

ulated sales ptimal stock

(right y‐axis)y continuing vel for stock‐mand:

egardless,

p will give tion and

k or

) to the the line out (1‐the

By using would noanywher

Even if ahave givedistribut

In this camarkup, The leve

In the caas a simu

the sales disot have beenre on the cur

single pointen wrong antion would ha

ase with the to high. Witl would have

ase of multi‐lultaneous sy

stribution wen possible wirve for foreca

forecast maswers aboutave been unk

sales distribuh a left skewe been too hi

evel warehostem.

e can find theth single poiasted sales.

anaged to fint the optimalknown.

ution having wed sales distigh and with

using, the ab

W

of 1

e optimal stont sales fore

d expected s stock/produ

a right tail thtribution thelow markup

bove analyse

We can do t

1

ock/productiocasts – that c

sales – as meuction level, s

he level wou result would probably to

s have to be

this!

on level givecould have e

ean, mode orsince the sha

ld have beend have been o low.

performed o

n the markuended up alm

r median – it ape of the sa

n to low – or the other wa

on all levels a

p and this most

would les

with low ay around:

and solved

Risk anIncreaseshows hoband whlevel. Th

On the ocourse lithat mar

nd Reward profit comow profit inchere the actuere is no suc

other hand wes in the factrkup is positi

rd mes at a pricecreases with ual profit will ch thing as a

will the uncertt that losses ve (300%) an

: increased rservice levelfall, and thisfree lunch.

tainty band adue to lost snd will easily

of 1

isk. The grap. The spreads shows how

around loss asales diminishcover the co

1

ph below des between ththe uncerta

as the servicehes as the seost of over‐p

scribes the site green and inty in profit

e level increaervice level inroduction.

tuation; the red curves in increases w

ases decreasncreases and

blue curve ndicates a ith service

e. This of the fact

Coeffi

Actual

cient of v

l sales

variation

of 11

Profit

t

of 11

Loss

Under

r producction

of 11

Overpproduction

of 111

Data a

Data The data

1. P2. D3. L4. W5. L6. P7. M8. S

S

Result1. O2. O3. P4. O

FurtheThis studBalance

and analy

a needed to p

Production cData on distrLogistic costsWarehousingLogistic costsProduct grouMarkup on pSales forecasS@R in corpo

ts Optimal wareOptimal prodProbability dOptimal ware

er analysidy and prograsimulation a

ysis

perform the

costs ribution strucs from produg costs s from warehup prices product grousts for produoration with

ehousing levduction leveldistribution foehousing str

s am can be a nd further d

analysis sket

cture (existinuction plants

houses to sho

ps ct groups anRappala)

vels in a multl per productor profit/lossucture (given

basis for an ecision maki

of 1

tched above

ng and propoto warehous

ops

d regions (co

ti‐level structt group s n proposed a

EBITDA/Budng and valua

11

will be found

osed) ses

ountries or c

ture per prod

alternatives)

geting modeation.

d in the inter

ities etc.) (w

duct group

el , that again

rnal accounts

ill have to be

n can be use

s:

e done by

d for

Production planning 2

Business

Transcript of Production planning 2