I herein provide my computational and mathematical solutions to Clipboard Health’s Lyft Toledo case.
I found that the optimum driver cost for maximising the 12-month-total net revenue was essentially the one leading to the exact answering of all calls: $2.33 paid to a driver per provided ride (Fig. 1). Any further decrease would reduce costs from the fewer quitting and replenished drivers, but this would not compensate for the relatively higher decrease of income from the nevertheless all-answered calls (drivers offering more rides than requested).
Additionally, I’ve implemented a dynamic pricing scheme, which was not clearly asked by the problem’s already ill-defined prompt, under the scenario of fluctuating riders:drivers ratio. Under this fluctuating riders:drivers ratio, my simulations and mathematical derivations showed that a dynamic pricing is overall more profitable than the fixed pricing scheme’s optimum at $2.33. In specific, by regulating the driver cost linearly with the riders:drivers ratio, extra profit mainly arose when increasing the driver cost by $1 for every 18 fewer riders per driver.
My full report can be downloaded here [PDF 0.3 MB].
The code for reproducing my solutions is downloadable from here [ZIP 0.06 MB].
The prompt for Clipboard Health’s Lyft Toledo case by Bo Lu can be read here.
They haven’t communicated since I’ve sent my results, even for a mere confirmation of receiving my report, so take these results as something you might need to avoid. I nevertheless thought to share, in case it helps others anyhow. Good luck!