$1.$ In the multiple$-$fare class capacity allocation problem, companies use heuristics to estimate the booking limits for the different classes.$$ A well$-$known heuristic named Expected Marginal Seat Revenue$-$b $($EMSR$-$b$)$ works as follows:

a$.$ Finds the protection levels for a class relative to each of the higher classes using Littlewood's rule.

b$.$ Finds the protection levels for a class relative to each of the higher classes using Littlewood's rule and sums them up to create the protection level for the class.

c$.$ It creates an $$artificial class$$ with demand equal to the sum of the demands for all the future periods and a fare equal to the expected fare from future bookings. It then uses Littlewood$$s rule to calculate the protection level of the current class j with respect to the artificial class.

Finds the booking limits for a class relative to each of the higher classes using Littlewood's rule and sums them up to create the protection level for the class