## 1 Introduction  
Automated guided vehicles (AGVs) are capable of automatic material transportation without the need for a driver. AGVs are employed in manufacturing and service industries, including automobile production plants, semiconductor manufacturing workshops, flexible manufacturing systems (FMSs), seaport container terminals, and the health sector [1; 2; 3]. Material handling has a significant impact on production costs in every production activity [4]. In Industry 4.0, AGVs are an indispensable solution and AGV developers must find solutions to customer-specific and personalized demands, but solutions must fulfil economic expectations [5; 6; 7]. Employment of AGVs is a capital investment that requires analysis of station locations, optimal route design, determination of the optimal number of AGVs and types, AGV positioning, assignment of the AGVs to collection requests, AGV routing and dispatch, resolving deadlocks and conflicts, scheduling and determination of the capacity, and other factors. The AGV fleet size has a significant impact on the work conditions of AGVs and the economy of AGV installation and implementation [8; 9; 10]. High investment costs force companies to adopt low-cost AGV solutions. Utilization of low-cost AGVs in industry is increasing every day, but the efficiency of these systems is low due to the lack of a central management system [11; 12]. Although various numerical and experimental studies have previously been conducted, the problem of grouping AGV circuits and AGV assignments to parking stations to minimize the number of AGVs while meeting demand is still being researched in the field of manufacturing. Low-cost AGVs' main characteristic is navigation via magnetic sensors, which they follow by magnetic tape on the ground, and they require a low level of automation, so they include a PLC or an embedded system [13]. These systems lack central control systems. A centralized control system manages all AGVs, but it has some drawbacks mainly due to the expensive cost, lack of flexibility, robustness, and scalability [11]. Therefore, decentralized solutions are attracting attention in industry. On the other hand, low-cost AGVs are assigned to a single AGV path, resulting in a low AGV efficiency. They reduce the AGV cost, but growing the AGV fleet does not create an optimum investment cost. All AGV circuits contain a waiting time, and if this time cannot be used for another part transfer, the AGV will remain in a waiting state, which will cause the efficiency of the AGV to decrease. Creating an AGV pool also makes use of these waiting times. The aim of this research is to determine the optimum number of AGVs for decentralized low-cost AGV systems and also to examine the effect of the change in system parameters on the required number of AGVs when a change in production requirements is necessary. This study begins by calculating the required AGV number for each AGV circuit combination assigned to every parking station by the time window approach with a developed algorithm. To determine the best solution, a mathematical model is presented to determine the minimum number of AGVs for one or multiple automated guided vehicle pools. The analytical mixed integer linear programming (MILP) method was introduced to achieve an optimal solution. Mathematical-solution-based mixed integer programming provides the optimum solution [14]. It was observed that the variables increased exponentially with the number of AGV circuits, reducing the utility of the model in complex applications. It becomes more complex with the increase in the number of stations. It is very difficult to implement the MILP approach in complex problems since it takes time to determine the equations and build the model for a particular problem. The problem turned in to an NP hard problem. Thus, a heuristic genetic algorithm was proposed to determine the number of AGVs with time windows for further complex situations.