Reference no: EM133298818

Protection Levels: Assume we only have 175 seats on our plane, all the same classification (i.e., this is a Southwest flight with no business class etc designations which would complicate the problem)

We know that typical last minute demand in the final week for a specific flight has an average demand of 29 but a standard deviation of 8. These customers are willing to pay $570 per ticket. Since that clearly won't fill the plane, the rest of the tickets are offered through advance sales at $354 each.

We can calculate the protection level which is the ideal number of seats to reserve for last minute. Or we can then use that vs the number of total seats on that flight to calculate the booking limit which is the number of seats we allow at the advanced sales price. For this problem: Calculate the protection level. The Booking Limit would then be (175 minus these seats) . Enter to the nearest seat. It's set to take +/- 2 so round to the nearest seat.

REMINDER: when the probability of demand is given by a normal distribution with mean μ and standard deviation σ, we need to start at the average and add some number of standard deviations to achieve our target Service Level. You should recall the formula

μ + zSL σ

where zSL is taken from the standard normal distribution based on the target SL = cs/(cs+ce). If SL = 0.50 we do exactly the average demand. If SL = 84.1% we need +1 standard devation (μ + σ); SL = 97.7% gives us z=2 (μ + 2σ). A SL< 50% would have a negative z value, adjusting us down from the average demand to avoid over-supplying the demand and ensuring we are more likely to use all available units. You can find this in a z-table but the easiest option is to open Excel and type =normsinv(SL) where SL is the probability you need. E.g. =normsinv(0.841) will yield a result near 1.0 and =normsinv(0.159) would give a result of -1.