Agenda Office Hours: –M 4-5, W 5-6, F 2-3 Wednesday: case discussion –1 page memo per group Friday: another case? Today: –Final review –Will post another sample final

Optimization LP –Shadow prices –Piece-wise linear Integer programs –Using binary variables instead of if statements Assignment problems

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* = (2AKH) 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 i  j after doing action k

current + future profit of doing action k in state i 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 Tight if k is optimal action for state i