Leisure enables one to break from the norm of everyday life and do something for self satisfaction. The leisure industry is wide and ranges over several different sectors one can choose from to indulge themselves into. In this study we looked at the computational methods used in solving problems in the restaurants, cafés, tourist arrivals and room booking. In recent years, many new cafés have emerged onto the market. Other than view cafés, beautiful cafés that seem as if they came from Paris or New York have gradually appeared in leisure. This study uses the analytical hierarchy process (AHP) to explore the selection of café styles, in order to provide references for café operators to achieve successful and sustainable operations. In the highly competitive coffee shop business a more accurate menu-pricing method is needed to maximize profit. The managers can be informed about the contribution of each method by using the activity-based costing method. This study illustrates the viability of a modified menu-engineering method using ABC theory applied to the operation of a coffee shop. The results show that ABC can be an efficient method for maximizing overall profit of a coffee shop business. Tourism has become a popular global leisure activity. It can be domestic or international; international tourism has both incoming and outgoing implications on a country’s balance of payments. Today it is a major source of income for many countries and affects their economy both the source and host countries.ths is because it has a direct effect on the social, cultural ,educational and economic sectors of national societies and on their international relations. There is an increased growth in the use of internet in businesses worldwide. One business that uses such is in the hotel booking. Before the introduction of the online booking system, the process of finding an appropriate hotel in a required place was a time consuming and a tedious job and was done mostly through human agents who may not be trust-worthy. Hence people find it convenient and easy to book hotels over the Internet via the e-hotel booking services. The discovery of high speed communication media brings the hotel reservation closer to the client. Also by developing a connection with world-wide-web and also e-commerce have essential part with term connected with commercial activities. Most of the online hotel booking systems does not provide the required level of security service because of which many problems arise in the systems such as denying, losing, misusing, stealing, double-spending etc hence development of an agent based secured online booking system. We consider problems involving groups of data, where each observation within a group is a draw from a mixture model, and where it is desirable to share mixture components between groups. We assume that the number of mixture components is unknown a priori and is to be inferred from the data. In this setting it is natural to consider sets of Dirichlet processes, one for each group, where the well-known clustering property of the Dirichlet process provides a nonparametric prior for the number of mixture components within each group. We discuss representations of hierarchical Dirichlet processes in terms of a stick-breaking process, and a generalization of the Chinese restaurant process that we refer to as the “Chinese restaurant franchise.