Throughput optimization for the Robotic Cell Problem with Controllable Processing Times

Abstract

In this paper, we present a MIP-based heuristic and an effective genetic algorithm for the Robotic Cell Problem with Controllable Processing Times (RCPCPT). This problem arises in modern automated manufacturing systems and requires simultaneously scheduling jobs, machines, and transportation devices in order to maximize the throughput or minimize the makespan. The RCPCPT is modeled as a flow shop problem with blocking constraints, a single transport robot, and controllable processing times. This latter feature of the model refers to the fact that the processing times are not fixed but vary linearly with the acceleration cost and therefore should be determined as part of the problem output. We formulate the problem as a nonlinear mixed-integer programming formulation and we use its linearized form to derive LP- and MIP-based heuristics. In addition, we proposed a genetic algorithm consistently yields near-optimal solution and it encompasses several novel features including, an original solution encoding as well as a mutation operator that requires iteratively solving MIPs in order to generate feasible processing times. Finally, we present a computational study for the proposed formulation, heuristics and genetic algorithm and we provide an empirical evidence of the effectiveness of the MIP-based heuristic for small instances and the genetic algorithm for large instances.