# 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

## Recently Viewed Presentations

• Difference between allegory and symbolism. Although an allegory uses symbols, it is different from symbolism.An allegory is a complete narrative (story) which involves characters, and events that stand for an abstract idea or an event. A symbol, on the other...
• Draw these forces as arrows with tails at the dot (object). ... Hence Fx = 12 N and Fy = 0 N The net force F : the y component is zero because the normal Force and the weight cancel....
• Dispelling the Fog About Cloud Computing November 2, 2012 Dan Kusnetzky Founder Required Cloud Picture Every presentation on cloud computing simply must include a lovely photo of a cloud. Here's my photo of Siesta Key Beach in Sarasota, Fla. Now...
• This presentation uses a free template provided by FPPT.com. www.free-power-point-templates.com. Media Training:How Not to Become Famous. About Me. Degree in broadcast journalism from Penn State. 2 years in TV News, 9 in newspapers, 4 in radio.
• Promoting effective learning of mathematics: a national perspective Celia Hoyles, April 2008 Director
• Sirenews : Newsletter of the IUCN/SSC Sirenia Specialist Group. Courrier de l´Armée d´Italie; Le. Environmental Defense Newsletter. Cognitive Philology (formerly: Rivista di Filologia Cognitiva) Relatório de Atividades / Instituto Nacional da Propriedade Industrial. Exchange Online Journal. Bulletin de la Société...
• WoT Thing Description (TD) With context extensionsfor semantic annotations(e.g., SAREF, [email protected]) WoT Thing Description. Information model and representation formatfor rich semantic metadata
• All children over 12 taken to Carlisle Indian school in Pennsylvania. Tom Torlino - Navajo. Next stop of imprisonment. Mobile Alabama. Then moved to Fort Sill Oklahoma 1896. From several thousand at contact. 388 in1896 . In 1913 Chiricachua released.