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 acceptablepreferred in class10 Fri noon-Sat94 Fri 4pm - Sat114 Sat noon-Sun71 Sat 4pm-Sun51 Sun noon-Mon41 Sun 4pm-Mon41 Mon 11am-Tue22

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

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