NewsvendorProblem.pptVIP

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 Newsvendor Problem 1 decision variable: try all different q analytical solution Analytical Solution P(D ≤ q*) = b/(b+c) round up if q* integer * data we need: b, c, distribution of D max E[Y(q,D)] s.t. q≥0 *