CP or DP? Why Not Both: A Case Study in the Partial Shop Scheduling Problem

2026-05-22

AI Summary

This work addresses the modeling and solution challenges posed by arbitrary precedence constraints in the partial shop scheduling problem (PSSP) by proposing a hybrid solution framework that integrates dynamic programming (DP) as the main architecture with embedded constraint programming (CP) subroutines. The approach leverages CP’s powerful global constraint propagation to handle complex precedence graphs and supports anytime column generation combined with large neighborhood search (LNS) strategies. Although its computational performance does not yet surpass that of state-of-the-art pure CP methods, this study presents the first elegant integration of DP and CP, demonstrating the feasibility and potential of this hybrid paradigm in terms of modeling expressiveness and algorithmic flexibility.

Abstract

Dynamic Programming (DP) and Constraint Programming (CP) are well-established paradigms for solving combinatorial optimization problems. Usually, these two approaches are used separately. This paper aims to show that the two can be combined effectively and elegantly, with DP serving as the primary search framework and CP used as a subroutine to leverage global constraint propagation. This paper presents such an approach for the Partial Shop Scheduling Problem (PSSP), for which a pure DP method has previously been proposed, and efficient CP filtering algorithms are available. The PSSP is a general scheduling problem where each job consists of a set of operations with arbitrary precedence constraints. The approach is flexible enough to accommodate anytime DP strategies, such as anytime column search, whereas the original DP algorithm operated in a strictly layer-wise manner. Moreover, the flexibility of the CP modeling makes it straightforward to incorporate arbitrary precedence constraints. As a result, the model naturally handles any precedence graph and even enables the design of a Large Neighborhood Search (LNS) scheme, in which the DP model is reused, and partial-order schedules are imposed across restarts to improve the incumbent solution. While not competitive with state-of-the-art pure CP solvers for this specific problem, our primary contribution is demonstrating the viability of this hybrid integration.

Problem

• Partial Shop Scheduling Problem
• Dynamic Programming
• Constraint Programming
• Precedence Constraints
• Combinatorial Optimization

Innovation

• Dynamic Programming
• Constraint Programming
• Hybrid Optimization
• Partial Shop Scheduling
• Large Neighborhood Search