建模题求思路啊

ly01

All hail a cab!

(Disclaimer: for legal and moral reasons, all geographical locations and company names used in this problem statement are entirely fictional. Please make sure that your solution manuscript clearly states this. Any similarity to real companies and places  should be  deemed a coincidence;such similarities, however, may be useful in determining reasonable parameter values foryour model.)

Mythical is a vibrantcollege town in the middleof Dompkins County (upstateNY).

Local landmarks & destinations include parks, gorges and waterfalls, a lake, downtownwith shops, restaurants & theaters,a large university, a smallerliberal arts college,a shopping mall, and the Mythical-Dompkins RegionalAirport. The geographic layout is such that most locals own and use cars on a daily basis. Still, a significant portion of the population relies on public transportation and taxicabs.This is particularly true for those with lower incomesand temporary residents(e.g., the students). All othersuse taxis infrequently -- primarily when traveling to/from the airport or the bus station. Unfortunately, many customersare unhappy with both the quality and the price of servicesoffered by the local taxi companies. Numerous complaints can be found on Yelp and in other online forums. The well-established companies believethat several unlicensed upstarts (operating as “liveries”) are primarily responsible for this low customer satisfaction. The city and county officials are interested in improving the situation. But since the problem is complex,they would appreciate your help in assessing the currentneeds and the likelyconsequences of any reforms.

In your analysis, you should keep in mind the complicated structural division: the actual “City of Mythical” is a smaller geographic entity, surrounded by the larger “Town of Mythical”. The informally defined “Greater Mythical” includes both the city and the town + several adjacent areas (including the shopping mall and the airport) governed by the rules and regulations of adjacent towns/villages, Dompkins County& NY state.

Please address sub-problem 1 + any two of theremaining three sub-problems.

1.      What is the total number of cabs needed toserve the “GreaterMythical” area ?

The goal is to ensure that

a)      the average customerwaiting time is ≤ 15 minutes;

b)     less than 10% of customers end upwaiting more than25 minutes.

2.      As  of right now,  all  taxi ride prices originating  and  terminating within  “the  city” are determined  by  the  city government  (the  city map is divided  into zones,  with the  corresponding zone-to-zone prices listed in the eCode on the city website).Suppose the city decided to switch to meter-based prices:you pay $2.50 to board a cab, and then X centsper each mile. What is the value of X that would leave the revenuesof taxicab companiesroughly the same as they are right now? What are the advantages and disadvantages of switching to meters?

3.      The local taxi market is currently dominated by Mythical Dispatch, Inc – a conglomerate of three companies with a single dispatchcenter and 2/3 of all the cabs officially licensed in the city. Supposethese 3 companieshad to operateindependently from each other.Estimate the impact on the average wait times and on prices of the non-regulated rides (e.g.,between downtownandthe airport).

4.      What would bethelikely consequences of strengthening  the regulations against unlicensed/livery companies (currently controlling about 1/7 of allcabs in the city)?

百年孤独