This paper introduces the Twin Robot Palletising Problem (TRPP) in which two robots must be scheduled and routed to pick up and deliver products at specified locations along a rail. The robots are initially located at the opposite ends of the rail and must preserve a minimum safe distance from one another. The objective is to minimise the makespan, defined as the time required to complete all operations and for both robots to return to their starting positions. The paper presents a proof of NP-Hardness of the TRPP, as well as two mixed integer linear programming models. Local search operators are introduced, before an iterated local search and a genetic algorithm are developed, in which a linear-time scheduling algorithm and dynamic programming are utilised to evaluate the quality of solutions. Extensive computational results demonstrate the limits of the mathematical models, the effectiveness of the metaheuristics, and the savings obtained by using twin robots instead of a single one.

The Workload Assignment Problem consists of assigning a sequence of |S| operations to workers. The order of these operations is fixed. Each operation consists of a batch of B units, hence a total of |J| jobs have to be performed. Each worker is assigned to an ordered subset of consecutive jobs. Workers have different skills, and therefore jobs take a variable time to process, depending on the assigned worker. The study of this problem is rooted in the operations of Calzedonia. In this paper, we briefly introduce the application before presenting algorithms for solving the problem exactly and heuristically. Our computational results compare the performance of a stand-alone mathematical formulation solved by CPLEX, a sequential exact algorithm, and a metaheuristic, with a simple heuristic implemented in the company.

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