On-demand platforms face the fundamental challenge of fulfilling time-sensitive jobs with independent workers who may decline offers. To minimize delays and unfulfilled jobs, platforms frequently raise the offered wage sequentially following each rejection. However, the interaction between these dynamic price adjustments and the specific sequence in which workers are approached has been overlooked. In particular, if the best-suited workers (e.g., closest to the job) are also ranked earliest in the sequence, then those workers would see the lowest offered wages and may decline, leading to poor system outcomes where less-suited workers end up seeing the raised wages and accepting the job. We study the sequential offering problem to maximize expected welfare or platform profit by jointly optimizing the ranking of workers and the pricing trajectory. Surprisingly, our main result establishes that if the reservation wage distribution exhibits a non-increasing and convex density function (e.g., Uniform, Exponential), welfare is maximized by greedy ranking and wages optimized via backward induction. For arbitrary distributions, we prove that greedy ranking achieves a tight $n/(2n - 1)$ fraction of the prophet benchmark. Numerical results for settings beyond the distributional assumptions find welfare losses well below those allowed by the universal guarantee, even in families where greedy is provably suboptimal. This suggests that rather than sending initial "low ball'' offers to worse matches, platforms should stick with greedy ranking and optimize the wage offerings by appropriately taking the continuation value of the downstream offers into consideration.

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