Solving the Group Cumulative Scheduling Problem with CPO and ACO

Abstract

The Group Cumulative Scheduling Problem (GCSP) comes from a real application, i.e., order preparation in food industry. Each order is composed of jobs which must be scheduled on machines, and the goal is to minimize the sum of job tardiness. There is an additional constraint, called Group Cumulative (GC), which ensures that the number of active orders never exceeds a given limit, where an order is active if at least one of its jobs is started and at least one of its jobs is not finished. In this paper, we first describe a Constraint Programming (CP) model for the GCSP, where the GC constraint is decomposed using classical cumulative constraints. We experimentally evaluate IBM CP Optimizer (CPO) on a benchmark of real industrial instances, and we show that it is not able to solve efficiently many instances, especially when the GC constraint is tight. To explain why CPO struggles to solve the GCSP, we show that it is NP-Complete to decide whether there exist start times which satisfy the GC constraint given the sequence of jobs on each machine, even when there is no additional constraint. Finally, we introduce an hybrid framework where CPO cooperates with an Ant Colony Optimization (ACO) algorithm: ACO is used to learn good solutions which are given as starting points to CPO, and the solutions improved by CPO are given back to ACO. We experimentally evaluate this hybrid CPO-ACO framework and show that it strongly improves CPO performance.