On solving the progressive party problem as a MIP

Abstract The ‘Progressive Party Problem’ (Smith et al. [9]) has long been considered a problem intractable for branch-and-bound mixed integer solvers. Quite impressive results have been reported with constraint programming systems for this problem. As a result the problem has become a standard example in texts on constraint programming. Fortunately, there has been progress in the mixed integer programming arena: we can solve now larger and more difficult problems than ever before. Improvements in algorithmic theory, solvers, modeling environments and computer hardware created a new situation, where reported cases of unsolvable instances of mixed integer programming models need to be re-examined, possibly with another outcome. In this paper we will show that we can solve the ‘Progressive Party Problem’ formulated as a large MIP problem, using standard, off-the-shelf hardware and software. A simple myopic heuristic is also implemented and can solve the problem in a fraction of the time. Scope and purpose The problem of creating a schedule for a progressive party event for a yacht club can be formulated as a very large and difficult mixed integer programming (MIP) problem. Several papers report that researchers were unable to solve this problem using MIP software: the problem was too difficult. In this paper we show in detail how by careful modeling we arrive at a formulation that can be solved efficiently. Building integer models has been called both a science and an art. This lesson in practical modeling is an illustration of this. The text is intended for an audience of both novice and expert modelers.