A variation of the partitioning problem is solved using linear programming techniques. In this class of problems, the optimal partition of objects must follow an apriori sequential ordering of objects. We examine a program segmentation application of this problem and formulate this sequential partitioning problem as an integer programming problem. The integer programming model of the problem possesses special structure such that the extreme points of its LP relaxation are integer and can be solved using LP techniques. We present computational results for randomly generated problems. We show how the LP approach can handle various side conditions and clustering criteria that arise across different problem types.Scope and Purpose--Partitioning a set of objects into mutually exclusive groups is a research problem which finds real-world applications in many disciplines. The general case of the partitioning problem belongs to a class of hard problems for which there are presently no efficient solution procedures for finding an optimal solution. The research effort has concentrated on developing heuristic solution approaches and identifying special cases for which optimal solutions can be determined efficiently. This article examines a special class of partitioning problems and demonstrates that linear programming (LP) can be used to find optimal solutions for this class of problems. Unlike other optimal approaches where specific models and software code must be developed for each situation, the LP model can readily accomodate many of the side conditions and clustering criteria that occur across various disciplines, and standard LP software can be used for solution.