Decision tree: square: decision and circle is an event + first branch(different decision) and second branch(what happens in each case)
In decision trees: cost willing to pay= difference between different decisions starting with the optimal one
Capacity control: leisure travelers(price sensitive, book early and schedule insensitive) busn travelers(price insensitive, book later, schedule sensitive)
Either marginal analysis calculating the cost and the revenue of selling one more discount ticket or if Fd> Ff* P(D>s)
P(Dfull fare> or equal X) = Max X + 1 /Max – min + 1 =k% then E(revenue)=price * k% if E(revenue)<discount price ticket then sell discount ticket
How many seats to reserve: set discount price< P(Dfull>X)*(price full fare) then P(Dfull>X)=MaxX+1/MaxMin+1 then solve for X which is # of seats
If both discount and full prices increase by same % then answer the same but if change by different % it will change
Maximum value of gift = expected profit of custumers for the # of years they want to recover their cost= proba*(profit) + proba*(Profit)=max value of gift
Booking limit: too low( spoilage left over seats) or too high ( cannabilization sell discount when you can sell at full price) Denied boarding risk=overbooked
Random variable with normal distribution: z=meanx/SD then P(z<x)= z score or if P(z>x)=1zscore
Uniformly distributed: Q/maxmin = service level
If both X and Y normally distributed then mean of X+Y= mean x + mean y and SD of X+Y=sqrt((SDx)^2+(SDy)^2)
Why hold Inventory: smooth production, scale economies, setup time and cost, uncertainty of supply/demand/cost and transportation time
Inventory classified by location= WIP
If order Q units every tiem then average I= Q/2
If order more every time then annual holding cost larger
/ If EOQ increase then annual setup cost Increase // if EOQ increase then annual holding cost
increase // if setup cost increase then EOQ increase // holding cost increase if you order more frequently
Number of order/year = D/EOQ
Annual holding cost= (EOQ/2)*H
Total annual cost= annual purchase cost + annual ordering cost + annual holding cost= TC= DC + (D/Q)S +(Q/2)H where D=demand C=cost Q=quantity
ordered and H= holding cost 
EOQ=optimal order quantity= sqrt(2DS/H)= sqrt(2*annual demand* setup cost/ annual holding cost/unit)
Inventory related cost= (D/Q)*S + (Q/2)*H
Newsvendor assumptions: Assumptions –Demand is random –Distribution of demand is known –No initial inventory –Setup cost is equal to zero –Single
period –Zero lead time –Linear costs: •Purchasing (production) •Salvage value •Revenue •Goodwill
S=setup cost/order … H=holding cost/unit/order…C=purchasing cost/unit… v=salvage value… p=revenue/unit… g=goodwill cost
Profit= sales revenue + salvage revenue purchase cost
D< purchases
overage cost= cv
D> purchases
underage cost= pc
Use marginal analysis if
marginal value>0 then purchase additional unit or
Optimal order quantitiy: P(D<k) = j < pc/pv then yes do that until it says no so the optimal order Q is the last yes
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 Spring '07
 Vaitsos
 Management, average service time, target inventory level, setup cost increase

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