## 1 Introduction
In any case, these interruptions lead to a delay in the estimated arrival of the AGV to its destination, which disrupts and affects the optimal operation of the production plant [9]. The idea of this research is inspired by a real case. With the goal of minimizing total time required in completing a series of tasks, production managers need to determine the order of tasks assigned to an AGV under dynamic conditions. Hence, the associated travel and processing times are dynamic in the sense that they vary with time. This is due to potential disruptions in some tasks that might occur at different times during the working hours. The problem under consideration can be viewed as a generalized (dynamic) version of the single-machine scheduling problem, with the AGV serving as a single machine. Because most single-machine scheduling problems are NP-hard [10], the dynamic version considered here might require a fast and reactive heuristic approach if real-time decisions are to be made using dynamic inputs. Hence, this paper proposes an \"agile\" optimization algorithm [11] for the mobile robotics AGV problem. The proposed algorithm is an extremely fast reactive heuristic procedure that aims at minimizing the total time required by an AGV to complete all the assigned tasks under a dynamic scenario with potential disruptions. Thus, our reactive approach makes use of a dynamic matrix which accounts for such delays. In order to build the aforementioned matrix, we employ historical data to estimate the delay associated with a given circuit at any point in time. Therefore, our reactive approach uses estimated delays and dynamically adjusts the initial agenda as new information on potential delays is obtained by the system. We study the creation of the permutation of tasks for the proposed reactive heuristic and compare it to other approaches. In a nutshell, our proposed reactive algorithm does the following: (i) it makes use of a delay matrix to estimate circuit delays for different daily times; (ii) it employs these estimates to define an initial itinerary of tasks for an AGV; and (iii) it dynamically adjusts the initial agenda as new information on actual delays is obtained by the system. The optimization problem is depicted in Figure 1. Let us consider a warehouse layout where each product has to be processed in different workstations. Each product can visit these stations in any order. Initially, all products are located at a depot station. An AGV has to move each product (one at a time) from the depot station to each workstation and then, once it has been processed, bring the product back to the depot station. The expected time required to complete a circuit (i.e., the sequence depot station-specific working station-depot station) is given by the sum of the travel times in ideal conditions plus the sum of the expected delays throughout the circuit. Unfortunately, delay times are dynamic, i.e., they are a function of the system conditions at each moment in time. The objective is to assign and re-assign the itineraries of the tasks to be completed by the AGV in order to minimize the total time required for the AGV to complete all the assigned tasks. To the best of our knowledge, the scientific literature has not previously investigated minimizing the total time employed by an AGV in completing a series of tasks under a dynamic scenario in which disruptions in the form of unexpected or random delay times might occur while the AGV is moving along defined pathways. We propose a method for determining the order of tasks assigned to an AGV using estimated circuit delays and dynamically adjusting the initial agenda as new information on actual delays becomes available.