Robotics Matrix-Structure Assembly System Scheduling Problem

The increasing demand for customized products with short life cycles and rapid delivery requirements has driven industries to adopt Robotics Assembly Systems (RAS) as a solution to these challenges. An RAS is an integrated manufacturing environment composed of one or multiple workstations capable of assembling diverse product types, interconnected through a material handling system, and coordinated by a centralized control unit. An RAS can be designed in various configurations: Robotic Assembly Lines (RAL), Robotic Assembly Cell (RAC) with one or multiple robots, and, more recently, a configuration known as the Robotic Matrix-Structure Assembly System (RMSAS) has emerged.

P=[1, 2,…,|P|] be the set of product types. J_p=[J_1p, J_2p,…,J_np] the ordered set of assembly tasks required to produce product p ∈ P, where n denotes the total number of tasks for product p. M=[1, 2,…,|M|] the set of available assembly workstations. Each assembly task J_jpcorresponds to a set of operations required for product p. A workstation m ∈ M can execute only a subset of tasks, depending on its technological capabilities. This relationship is defined by the feasibility set:

Φ(J_jp) ⊆ M, ∀J_jp ∈ J_p, p ∈ P

Where Φ (J_jp) denotes the set of workstations capable of processing task J_jp. Since the RMSAS is designed to handle multiple product types, every product must have at least one feasible workstation for each of its tasks:

Φ(J_jp) ≠ ∅, ∀J_jp ∈ J_p, p ∈ P

Conversely, a workstation mmm can process tasks from different products, represented as:

Ψ(m) = {J_jp ∈ J_p ∣ m ∈ Φ(J_jp), p ∈ P}

Where Ψ(m) is the set of tasks executable at workstation m. Thus, the assignment of tasks to workstations is determined by the intersection between product requirements and workstation capabilities, with each Ψ(m) representing only a fraction of the global task set across all products.

Instances:

Group I

The execution of assembly operations by industrial robots tends to exhibit consistent and low variability across multiple runs. In contrast, stochastic processing times are typically associated with scenarios involving human–robot interaction within the same assembly system. Some studies suggest that processing times can be modeled using a uniform probability distribution; however, the range of this distribution may vary depending on the type of assembly task being analyzed. For example, processing times in the electronics industry are usually short—often measured in seconds—while in the automotive industry, assembly tasks tend to be longer, typically measured in minutes. Based on this distinction, the present study evaluates each instance under two different processing time scenarios. For Group_I of products, task durations are modeled using a uniform distribution in the range [2-10] time units, representing short-cycle tasks.

Matrix-Structure 2 x 2

Int_1