A global constraint for the capacitated single-item lot-sizing problem
This addresses optimization challenges in production planning for industries like manufacturing, though it is incremental as it builds on existing dynamic programming algorithms.
The paper tackles the NP-hard capacitated single-item lot-sizing problem with time-varying bounds and costs by formulating it as a global constraint, achieving bound consistency in pseudo-polynomial time and polynomial time without costs. It shows this approach finds solutions where decomposed models fail and can be competitive with mixed integer linear programming and dynamic programming, especially with side constraints.
The goal of this paper is to set a constraint programming framework to solve lot-sizing problems. More specifically, we consider a single-item lot-sizing problem with time-varying lower and upper bounds for production and inventory. The cost structure includes time-varying holding costs, unitary production costs and setup costs. We establish a new lower bound for this problem by using a subtle time decomposition. We formulate this NP-hard problem as a global constraint and show that bound consistency can be achieved in pseudo-polynomial time and when not including the costs, in polynomial time. We develop filtering rules based on existing dynamic programming algorithms, exploiting the above mentioned time decomposition for difficult instances. In a numerical study, we compare several formulations of the problem: mixed integer linear programming, constraint programming and dynamic programming. We show that our global constraint is able to find solutions, unlike the decomposed constraint programming model and that constraint programming can be competitive, in particular when adding combinatorial side constraints.