This study deals with a variant of the orienteering problem faced by managers of some department stores during peak-sale periods. We want to find a set of paths to be traveled by each vehicle that leaves a department store and arrives at a specified destination after visiting customers. The problem is formulated into the mathematical model with the objective of maximizing the sum of the rewards collected by the vehicles within a given time limit and a given capacity constraint. Since the problem is known to be NP-hard, a heuristic algorithm and a priority-based Genetic Algorithm (pGA) are developed to find the solution. For small sized problems, the performances of the algorithms are compared with the optimum solutions obtained from CPLEX.