A Multi-Scenario Bi-objective Optimization Model for Robotic Parcel Sorting System

This study contributes to the robotic-based sorting system, specifically in the parcel industry, due to the lack of multi-objective consideration that prior studies neglected. This study examines a robotic parcel-sorting system with two loading stations and a fleet of robots that sorts parcels to their respective collection points. The parcel-to-station, robot-to-station, and parcel-to-robot assignment decisions are considered. A mixed-integer programming model with two important yet conflicting objective functions, namely the makespan and fleet size of robots, is proposed. To regulate workload balance of parcel assignments between stations and robots, we evaluate two scenarios regarding to the number of parcels to be processed: Scenario 1 with lower limit only and Scenario 2 with both lower and upper limit. The ε-constraint method with a branch-and-cut algorithm and lazy constraint procedure is used to generate solutions using the Gurobi solver. The results show that the model can produce optimum non-dominated solutions that govern the Pareto front for all scenarios. Furthermore, in most cases, Scenario 2 outperformed Scenario 1 in terms of hypervolume values.