## 1 Introduction  
The increasing utilization of robots in various settings such as Industry 4.0 [1]--namely, smart factories, and intelligent warehouses [2]--and healthcare in tackling COVID-19 [3] have underscored the importance of coordinating production and transportation processes in reducing waste. In contrast to earlier manufacturing environments where items are either transported manually by human labor or human driven vehicles, automation requirements of Industry 4.0 mandate the use of fully automated transporters such as automated guided vehicles (AGVs) for transporting items between various job shops for processing. To satisfy operational demands and to also bridge the gap between practice and theory in smart manufacturing scheduling, algorithms are needed to address both scheduling and routing needs concurrently to meet the aforementioned automation requirements. A flexible job shop problem with transportation (FJSPT) was first proposed by [PERSON] and [PERSON] [4]. It integrates two NP-hard problems: the flexible job shop problem (FJSP) [5; 6; 7; 8] and the vehicle routing problem (VRP) [9]. By synchronizing machine operations and transportation tasks, it addresses the issue of inflexible and underestimated schedules arising from the lack of process flexibility in JSPT [10] and transportation in FJSP. Due to the NP-hard nature of the problem, heuristics and metaheuristics have dominated FJSPT solution methodologies thus far, under different solution representations. [PERSON], [PERSON] and [PERSON] [11] extended [PERSON], et al. [12] by incorporating flexibility of machine assignment through invoking greedy heuristics for machine and transporter assignment within Differential Evolution (DE). [PERSON], [PERSON] and [PERSON] [13] hybridizedGenetic Algorithms (GA) and Tabu Search (TS), where GA is used for machine and transporter assignment, and TS is used for scheduling improvements. [PERSON], [PERSON] and [PERSON] [14] further employed a disjunctive graph representation and applied the Modified Shifting Bottleneck (MSB) heuristic. [PERSON] [15] hybridized Particle Swarm Optimization (PSO) with Stochastic Local Search (SLS) to combine the diversification strength of the former with the intensification strength of the latter. [PERSON] et al. [16] also used a disjunctive graph and solved it using hybridized Neighborhood-based Genetic Algorithms (NGA) and Tabu Search (TS). While heuristics and metaheuristics are inherently fast, they are prone to local optimality. To resolve this, Constraint Programming (CP) [17] and Mixed Integer Linear Programming (MILP) approaches [18] were proposed recently. The proposed MILP model was only used for small-sized instances, while the Late Acceptance Hill Climbing (LAHC) heuristic was used for larger instances. Recent works have also incorporated new considerations to the FJSPT problem. [PERSON] et al. [19] considered additional constraints such as setup time and energy consumption and solved their MILP model using an improved Jaya (IJaya) algorithm. [PERSON] et al. [20] proposed a novel proactive-reactive methodology to jointly dynamically optimize an FMS modeled using MILP, which is solved using a novel PSO algorithm integrated with genetic operators developed to respond to dynamic events for rescheduling. In this work, an iterative, two-phase MILP-based heuristic is proposed. It comprises MILP models: a FJSP augmented with only intermachine transportation times alongside unlimited transportation resources (FJSP + T) and its derivative job shop scheduling problem with transportation (JSPT). Both are solved for a fixed number of iterations before returning the best solution. This approach differs from conventional decomposition approaches in two ways:  
1. While certain problems of other domains apply feedback to guide the solution search, the FJSP + T model serves as a heuristic to mitigate the lack of it by providing good machine-operation assignments. 2. In conventional approaches, first-phase solutions might sometimes be infeasible for the second phase.