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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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newsvendor problem
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
Previously
  • Optimization
  • Probability Review
    • pdf, cdf, E, Var
    • Poisson, Geometric, Normal, Binomial, …
agenda
Agenda
  • Final
  • Quiz
  • Inventory (Ch 12)
final survey
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

slide5
Quiz
  • average 88%
  • “Write it in mathematical notation”
inventory models
Inventory Models
  • Capacity management: overbooking, admissions, …
  • Batching, order quantity, fixed costs
  • Probability + simple optimization
newsvendor problem7
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 problem8
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 problem9
Newsvendor Problem

max E[Y(q,D)]

s.t. q≥0

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