Consider a residential area and two shopping centers that are possible destinati
ID: 3170554 • Letter: C
Question
Consider a residential area and two shopping centers that are possible destinations. From 7:00 to 8:00 m. on Friday night, 1000 vehicle-based shopping trips leave the residential area for the two shopping centers. A int shopping-trip mode-destination choice logit model (choice of either auto or bus) is estimated, giving the coefficients: Initial travel times to shopping centres 1 and 2 are as follows: If shopping center 2 has 300,000 ft^2 of commercial floor space and shopping center 1 has 250,000 ft^2, determine the distribution of Friday night shopping trips by destination and mode.Explanation / Answer
The utility function coefficients indicates that as model travel time increases, the liklihood of selecting the mode-destination combination declines. Also, as the destination's floor space increases, the probability of selecting that destination increases, as suggested by the positive coefficient(+0.01).
This reflects the fact that bigger shopping center tend to have a great variety of products so gets more attraction. Note that as this is joint mode destination choice model, there are 4 mode destination combination and 4 corresponding utility function.
Let UA1 be the auto mode of shopping center 1, UA2 be the auto mode of shopping center 2, and UB1 and UB2 be the bus mode of shopping center 1 and 2 respectively.
So the utilities are,
UA1 =0.5 - 0.3*10 + 0.01*250
=0
UB1=0-0.3*20+0.01*250
=-3.5
UA2 =0.5 - 0.3*15 + 0.01*400
=0
UB2=0-0.3*30+0.01*400
=-5
PA1=e0/(e0+e-3.5+e0+e-5)
=1/(1+0.0301+1+0.00673)
=0.491
PB1=e-3.5/(e0+e-3.5+e0+e-5)
=0.0301/(1+0.0301+1+0.00673)
=0.0148
PA2=e0/(e0+e-3.5+e0+e-5)
=1/(1+0.0301+1+0.00673)
=0.491
PB2=e-5/(e0+e-3.5+e0+e-5)
=0.00673/(1+0.0301+1+0.00673)
=0.00330
Now we will multiply this probability with total vehical i.e 1000
Auto to shopping centre 1 =0.491*1000=491 trips
Bus to shopping centre 1=0.0148*1000=14.8=15 trips
Auto to shopping centre 2 =0.491*1000=491 trips
Bus to shopping centre 2=0.00330*1000=3.3=3 trips
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