## 5 Experimental Setup  
Numerical experiments are carried out in two different layouts. The first one is the benchmark layout from [5], also used in [16] (see Figure 7). It features a square topology measuring 50 m \(\times\) 40 m, and comprising the following: (i) three origins for work pieces, I1-I3; (ii) three destinations for work pieces, O1-O3; (iii) six machines, M1-M6; (iv) eighteen working (W) stations, S1-S18, with half designated as pick-up stations and the remainder as drop-off stations; and (v) ten parking (P) stations, C1-C10. At the beginning of the simulation, every source point, Ii, is equipped with twenty work pieces, labeled as Part-i type. These pieces are to be individually retrieved from the adjacent W station next to Ii, transported consecutively to two machines, where each piece is deposited, undergoes 20 s processing, is then retrieved, and is ultimately delivered to the W station corresponding to the designated sink point, Oj.  
The route to be followed by each type of piece is:  
* Part 1: (I1)-S7-S14-(M4)-S13-S5-(M3)-S6-S12-(O3);
* Part 2: (I2)-S10-S3-(M2)-S4-S16-(M5)-S15-S9-(O2);
* Part 3: (I3)-S11-S1-(M1)-S2-S18-(M6)-S17-S8-(O1),  
where parentheses indicate sources, sinks, and machines. Therefore, three distinct transportation assignments are linked to each route: from the source W station to the W drop-off station of the first machine, from the W pick-up station of the first machine to the W drop-off station of the second machine, and from the W pick-up station of the second machine to the W drop-off station of the sink. This entails a total of 180 tasks to be allocated to the available AGVs within the layout (comprising 3 types of pieces, 20 pieces of each type, and 3 movements per piece). The AGVs commence from the P stations C1-C10, move at a speed of 1 m/s, and the simulation concludes when the last piece is deposited, and the transporting AGV returns to its designated parking position.  
The second layout corresponds to an industrial workspace of 25 m \(\times\) 30 m with seven pick-up stations, W1 to W7, two drop-off stations, W8 and W9, and ten parking stations, P1 to P10, see Figure 8. Transportation assignments are generated at random and in real time at pick-up stations with time intervals following a uniform distribution. The assignments are subsequently allocated to idle AGVs by searching for the first idle one within the list of AGVs, which is ordered according to the AGV labels, \(R_{i}\). The total simulation time is set to five hours.  
For IDRR and IDRRP, both layouts are modeled as in Section 4.2, namely, with WP stations and TX crossings as nodes. Instead, three types of discretization are studied for DRR according to Section 3.2: the same as IDRR and IDRRP, labeled as DRR, and two additional ones with nodes placed at 2 m and 1 m intervals, labeled as DRR-2m and DRR-1m, respectively. In turn, the selected control periods of the allocation procedure are 1 s, 0.5 s, 0.2 s, 0.1 s, 0.05 s, and 0.02 s. In all the cases, the AGVs run at a constant speed of 1 m/s and show equal acceleration and deceleration values. Finally, numerical simulations were carried out using the commercial software Flexsim (version 23.1.4).  
Figure 7: The benchmark layout. II–I3: sources of work pieces; O1–O3: sinks to work pieces; M1–M6: machines; S1, S3, S5, S8, S9, S12, S14, S16, S18: drop-off stations; S2, S4, S6, S7, S10, S11, S13, S15, S17: pick-up points; C1–C10: parking stations.