Newsboy Problem

7/26/2019 Newsboy Problem

1/5

Newsboy Problem

1

Consider the problem faced by a Newsboy who has todecide everyday on the number of papers to stock inthe face of uncertainty in daily demand.

Daily demand is uncertain and given by the discreteprobability distribution

Price of newspaper = 6 cost = ! salvage value = 1

Demand Probability

"# #."

"1 #.$

"" #.!

Indian Institute of Management Calcutta, India


2/5

Problem %ormulation and &olution

Production = K

0.2

0.5

0.3

Demand = 20

Sales = Min (20, K)

Demand = 21

Sales = Min (21, K)

Demand = 22

Sales = Min (22, K)

In each case, Profit = (Price)X(Sales) + (Salvage value)X(Unsold

quantity) (Cost)X(Production)

"



3/5

Problem %ormulation and &olution 'Contd.(

K = 20

0.2

0.5

0.3

Demand = 20; Sales = 20

Profit = !20 " 3!20 = 0


Profit = !20 " 3#20 = 0


Profit = !20 " 3#20 = 0

!"ected Profit = #$%X + #$'X + #$X =

K = 22

0.2

0.5

0.3


Profit = !20 $1!(22"20) " 3!22 = 5


Profit = !21 $ 1!(22%21) " 3!22 = 1


Profit = !22 " 3!22 =

!"ected Profit = #$%X'& + #$'X& + #$X&& = &$'

K = 21

0.2

0.5

0.3


Profit = !20 $ 1!(21%20) "3!21 = 5&


Profit = !21 " 3!21 = 3


Profit = !21 " 3!21 = 3

!"ected Profit = #$%X'* + #$'X& + #$X& = &%

ence "ti-al Ca"acity = %. Corres"onding Profit = /

!



4/5

)*pected Profit +able

Demand

,ction

"# '."( "1 '.$( "" '.!( )*pected

Profit

&tock "# 6# 6# 6# 6#

&tock "1 $- 6! 6! 6"

&tock "" $6 61 66 61.$

Ma#imum '#ected Profit under uncertaint = 2. *ence decision + Stoc 21

-ote+ '#ected Profit under certaint = 0 # .2 $ 3 # .5 $ # .3 = 3.3

'#ected alue of erfect information ('/P) = 3.3 " 2 = 1.3


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)*pected pportunity /oss ')/( +able

Demand

,ction

"# '."( "1 '.$( "" '.!( )/

&tock "# # ! 6 !.!

&tock "1 " # ! 1.!

&tock "" 0 " # 1.-

est decision imlies minimum ', i.e. Stoc 21

-ote+ ' of t4e est decision is same as '/P = 1.3

Newsboy Problem

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