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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. Optimization Probability Review pdf, cdf, E, Var

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Newsvendor Problem

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  1. 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

  2. Previously • Optimization • Probability Review • pdf, cdf, E, Var • Poisson, Geometric, Normal, Binomial, …

  3. Agenda • Final • Quiz • Inventory (Ch 12)

  4. 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

  5. Quiz • average 88% • “Write it in mathematical notation”

  6. Inventory Models • Capacity management: overbooking, admissions, … • Batching, order quantity, fixed costs • Probability + simple optimization

  7. 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

  8. 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

  9. Newsvendor Problem max E[Y(q,D)] s.t. q≥0 • 1 decision variable: • try all different q • analytical solution

  10. Analytical Solution • P(D ≤ q*) = b/(b+c) • round up if q* integer

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