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.

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Presentation transcript:

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, …

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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

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