Final answer:
To determine the number of Flex routes that cannot dispatch, consider the last delivery time, block times, and Flex acceptance rate. Calculating the total potential dispatched routes (112) against the routes required (116) for the packages reveals that 4 routes will not be dispatched by the cutoff time.
Step-by-step explanation:
To calculate the number of routes that will not be able to dispatch, we need to consider the start time, the route length, and the delivery cutoff time. Since each Flex route is 4 hours and the last delivery can happen at 21:00, the latest block that can be dispatched to complete delivery is at 17:00. Starting the first block at 14:00 and scheduling blocks every 30 minutes provides opportunities for six blocks (14:00, 14:30, 15:00, 15:30, 16:00, 16:30, and 17:00).
Given an 80% Flex acceptance rate per block time and a maximum capacity of 20 routes, we get the expected number of active routes by multiplying the acceptance rate by the maximum wave capacity of each block. It is: 0.80 × 20 = 16 routes per block. Thus, over the seven blocks, the total number of potential dispatched routes is 16 × 7 = 112 routes.
To determine the total number of routes needed for all packages, we divide the total packages (4640) by the average SPR of 40. This results in 4640 / 40 = 116 routes. Comparing this to the potential dispatched routes (112), we find that 116 - 112 = 4 routes cannot be dispatched due to block length and time of day restrictions. Therefore, 4 routes will not be able to dispatch.