Resource constraint scheduling on two dedicated machines: Application to avionics

In civil aircraft, two partially redundant hydraulic circuits typically power various systems. During assembly, a critical phase involves simultaneously rinsing and purging these hydraulic circuits using loops. Precedence constraints are necessary to prevent the recontamination of already rinsed loops, leading to increased rinsing time. This paper presents this problem as a unique instance of the Resource Constrained Parallel Machine Scheduling Problem, where each circuit represents a machine, pipe loops to be rinsed represent jobs, and machines share a hydraulic power source. For two dedicated processors and a single resource, an optimal schedule minimizing the makespan can be generated in polynomial time. However, due to the requirement of rinsing certain pipe loops on a circuit before others, there are precedence constraints between some jobs within the same circuit. By employing a reduction of the 3-partition problem, we demonstrate that this situation results in a problem that is NP-hard in the strong sense. We evaluate several Mixed-Integer Linear Programming and Constraint Programming formulations of the problem, using Cplex, CPO, Gurobi, and Z3, against several proposed heuristics. Given that the size of the instances we need to solve exceeds what can be solved in acceptable time by solvers, we propose a heuristic and compare its performance with the optimum. •Makespan minimization for flushing two independent hydraulic circuits during civil aircrafts assembly, using a shared input pressure device.•Representation of the problem as a scheduling problem PD2|res1.., localprec|Cmax, consisting in minimizing the makespan of a schedule of jobs executed on two dedicated processors, sharing one resource (the common pressure), where jobs co-located on a processor may be subject to precedence constraints.•Proof of the NP-hardness of the problem PD2|res111, localprec|Cmax using a reduction of the 3-partition problem, showing that even in the simplest case where a shared resource has only a single instance, as soon as some local precedence constraints exist, the problem is NP-hard in the strong sense.•Evaluation of two formulations of the problem as mixed-integer linear programs: one using discrete-time variables (DT-formulation), the other using the fact that two processors only are shared, called the disjunctive formulation.•Four solvers, CPLEX, CPO, Z3 and Gurobi are compared for both formulations: for instances larger than 5 jobs per processor, the discret