This thesis focuses on the interface of operation research and accounting. Owing to the transparency and the uniqueness of the audit market, this thesis discusses the demand-side and supply-side problem of the audit market, where the audit market has not been discussed extensively in the operation research. In addition, this thesis further incorporates both sides to examine the simultaneous effect of the auditor choice and pricing strategy of the auditor firm. The result of the first research in this thesis indicates the client would incur a significant switching cost when switching audit firms but the client would have different reactions (e.g. willing to negotiate or being loyal) when facing a fee discount, suggesting that the audit client would switch the audit firm for better audit quality rather than due to the lowballing effect. On the supply side, the second research approached in this thesis shows that audit firms have varied strategies for assessing their client portfolio, even among the Big Four. The specialist auditor is more likely to maintain their client-auditor relationship with the large companies when the cost increases based on the economies of scale while the auditor who owns most of the clients in the market is inclined to provide services to all sizes of the client based on economies of scope. The third research matches the demand with the supply in the audit market. The findings indicate that the client would consider differently and so the model of Bertrand competition could interpret the audit market the sample better but the predictive analysis shows the audit firms may still engage in tacit collusion with respect to a specific client, which should raise attention from the regulatory perspective. By allowing heterogeneity among the audit clients and audit firms, this thesis can engage with the random coefficients and discuss the individual effect rather than the fixed effect, which has not yet been considered in prior accounting literature and is expected to shed light on the objectives of future accounting research.