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 in class Fri noon-Sat Fri 4 pm - Sat noon-Sun Sat 4 pm-Sun noon-Mon Sun 4 pm-Mon 11 am-Tue acceptable 1 9 11 7 5 4 4 2 preferred 0 4 4 1 1 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 • 1 decision variable: – try all different q • analytical solution max E[Y(q, D)] s. t. q≥ 0
Analytical Solution • P(D ≤ q*) = b/(b+c) • round up if q* integer
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