Nested Monte-Carlo Search for Scheduling an Automated Guided Vehicle in a Blocking Job-Shop

We consider a job-shop scheduling problem where a single automated guided vehicle (AGV) transports jobs between workstations. There are multiple but few job types, each with a specific path through the workstations and a specific processing time per workstation. The AGV can transport one job at a time, and there are no buffers, meaning each workstation must be empty before the AGV can deliver a new job. The goal is to schedule the AGV to minimize the makespan, which is the time when the last job is processed. We provide an Integer Linear Programming (ILP) formulation to find an optimal solution, and observe that within few minutes it can only solve small instances. As a remedy, we design a heuristic algorithm using the Nested Monte-Carlo Search (NMCS) paradigm. We compare its performance with two greedy algorithms and a local search approach. In the experiments, the NMCS-heuristic significantly outperforms traditional ILP methods and greedy algorithms under limited time resources.