Recommendation Systems (RS) are gaining popularity and they are widely used for dealing with information on education, e-commerce, travel planning, entertainment etc. Recommender Systems are used to recommend items to user(s) based on the ratings provided by the other users as well as the past preferences of the user(s) under consideration. Given a set of items from a group of users, Group Recommender Systems generate a subset of those items within a given group budget (i.e. the number of items to have in the final recommendation). Recommending to a group of users based on the ordered preferences provided by each user is an open problem. By order, we mean that the user provides a set of items that he would like to see in the generated recommendation along with the order in which he would like those items to appear. We design and implement algorithms for computing such group recommendations efficiently. Our system will recommend items based on modified versions of two popular Recommendation strategies– Aggregated Voting and Least Misery. Although the existing versions of Aggregated Voting (i.e. Greedy Aggregated Method) and Least Misery perform fairly well in satisfying individuals in a group, they fail to gain significant group satisfaction. Our proposed Hungarian Aggregated Method and Least Misery with Priority improves the overall group satisfaction at the cost of a marginal increase in time complexity. We evaluated the scalability of our algorithms using a real-world dataset. Our experimental results evaluated using a self-established metric substantiates that our approach is significantly efficient.