Newsvendor Problem

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# Newsvendor Problem - PowerPoint PPT Presentation

Newsvendor Problem. must decide how many newspapers to buy before you know the day’s demand q = #of newspapers to buy b = contribution per newspaper sold c = loss per unsold newspaper random variable D demand. Previously. Optimization Probability Review pdf, cdf, E, Var

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## PowerPoint Slideshow about 'Newsvendor Problem' - benjamin

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Presentation Transcript
Newsvendor Problem
• must decide how many newspapers to buy before you know the day’s demand
• q = #of newspapers to buy
• b = contribution per newspaper sold
• c = loss per unsold newspaper
• random variable D demand
Previously
• Optimization
• Probability Review
• pdf, cdf, E, Var
• Poisson, Geometric, Normal, Binomial, …
Agenda
• Final
• Quiz
• Inventory (Ch 12)
Final Survey

acceptable preferred

in class 1 0

Fri noon-Sat 9 4

Fri 4pm - Sat 11 4

Sat noon-Sun 7 1

Sat 4pm-Sun 5 1

Sun noon-Mon 4 1

Sun 4pm-Mon 4 1

Mon 11am-Tue 2 2

Quiz
• average 88%
• “Write it in mathematical notation”
Inventory Models
• Capacity management: overbooking, admissions, …
• Batching, order quantity, fixed costs
• Probability + simple optimization
Newsvendor Problem
• must decide how many newspapers to buy before you know the day’s demand
• q = #of newspapers to buy
• b = contribution per newspaper sold
• c = loss per unsold newspaper
• random variable D demand
Newsvendor Problem

revenue = b · #sold - c · #unsold

#sold = min(D,q), #unsold = max(q-D,0)

revenue Y(q,D) = b·min(D,q) - c·max(q-D,0)

max E[Y(q,D)]

s.t. q≥0

data we need:

b, c, distribution of D

Newsvendor Problem

max E[Y(q,D)]

s.t. q≥0

• 1 decision variable:
• try all different q
• analytical solution
Analytical Solution
• P(D ≤ q*) = b/(b+c)
• round up if q* integer