In this paper, we study an on-demand housekeeping platform in which suppliers have heterogeneous opportunity costs, and customers are sensitive to service quality, price, and waiting time. The platform charges fees from customers and divides revenue with service suppliers in a certain proportion. We analyze two types of market coverage, namely full market coverage and partial market coverage. We find that as the potential demand market capacity expands, the platform will choose to lower prices to attract more customers and service suppliers until it reaches the partial market, thereby obtaining higher revenue, and suppliers will provide lower quality services to serve more customers and thus obtain more wages. Moreover, we show that the partial market is more favorable to the platform than the full market. However, for service suppliers, the partial market is not always more favorable. Meanwhile, as customers are more sensitive to the service value, suppliers will tend to lower their service rates to improve service quality, and the platform will tend to set higher service prices. Interestingly, we observe that when the sensitivity of service value is relatively small, the sensitivity of service value has even the opposite effect on the platform’s revenue and service suppliers’ payoffs, as well as the equilibrium number of service suppliers in different market scenarios. In addition, different market scenarios also will lead to the opposite effect of the service cost on the optimal equilibrium price, arrival rate, and service rate. However, the increase in the service cost will lead to a decrease in platform revenue and service supplier payoffs and the number of service suppliers in both market scenarios.