Newsvendor Problem - Northwestern University

Newsvendor Problem - Northwestern University

Agenda Office Hours: Friday 2-3 Final: Friday 4pm - Sat. 4pm LP Shadow Prices (Lec 4) (Change in objective) / (Change in constraint right hand side) 0 for loose constraints Interpretation: Price for additional capacity Excel Solver -> options -> assume linear model

Solver -> Solve -> Sensitivity Report LP Piecewise linear (Lec 6) As a constraint: c(x) <= b Add decision variable z and replace constraint with z <= b x s1 + t 1 and x s1 + t1 <= z x s2 + t2 <= z x s2 + t 2

Diseconomy of Scale revenue or profit mathematically equivalent quantity cost quantity More Optimization Assignment Problem

Integer Programs / IF statements Lec 10 slides reviewed for the quiz Inventory Models Newsvendor Uncertain Demand (D) Single-period Specification q = # to have on hand b = contribution per sale c = cost per unsold item P(D q*) = b/(b+c)

round q* up to nearest integer Base Stock Uncertain Demand (D) Multi-period Inventory Lost-sales p= Service level Probability of running out P(D q*) = p

Safety Stock = q- E[D] = constant E[D] Order Quantity Model (EOQ) Deterministic Demand Continuous review Inventory No backlogging Solution Reorder when inventory at r = AL Order size q* =(2AK/H)1/2

(cycle stock, Economic Order Quantity) Specification Replenishment lead time L Order placement cost K (Independent of order size) Unit holding cost H Markov Decision Processes (MDP)

States i=1,,n Possible actions in each state Reward R(i,k) of doing action k in state i Law of motion: P(j | i,k) probability of moving ij after doing action k MDP as LP f(i) = largest expected current + future profit if currently in state i f(i) decision variables in LP

min j f(i) s.t. f(i) R(i,k) + j P(j|i,k) f(j) for all i,k current + future profit of doing action k in state i Tight if k is optimal action for state i

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