Conveyor Optimizer

In an industrial plant, blocks of variable dimensions must be transported through a conveyor belt network to laser-guided loading robots (LGV) located at the network's endpoints. Each robot has a maximum capacity and strict dimensional limits. The network forms a complex directed graph and the problem splits into two critical sub-problems: deciding which blocks to load onto which robots to maximise total loaded area whilst minimising robots used and distance travelled, and finding the optimal sequence of physical movements to transport blocks to the target configuration.

The solution is structured in three phases: first, plant modelling as a directed graph (NetworkX) with pre-computed constraint matrices (Floyd-Warshall distances, dimensional constraints, capacities and compaction lines). Second, optimal assignment formulated as Integer Linear Programming (ILP) solved with PuLP/CBC, with a multi-criteria objective function that maximises loaded area and penalises robots used and distance travelled, subject to capacity, dimension, unique assignment, fixed block, loading direction and full loading mode constraints. Third, route planning via A* search over the state space (binary block×node matrices), with an admissible heuristic based on average distance to target and reachable state generation through matrix multiplication with sequential movement, one-time load and full loading mode filters.