## 2 Literature Review  
The warehouse LRP (WLRP) is first proposed by [8]. The problem is decomposed into three sub-problems: Multi-Depot Vehicle Routing Problem (MDVRP), Warehouse Location-Allocation Problem (WLAP), and Multi-Depot Routing Allocation Problem (MDRAP) and is solved using the heuristic approach. Some other studies divided the problem into two phases [9]. The first phase is a LAP and the VRP follows in the second phase. The problem is solved sequentially and iteratively by SA. Reference [10] discussed the capacitated LRP under disruption and implemented several approaches in problem-solving such as metaheuristic based on maximum-likelihood sampling method, route-allocation improvement, two-stage neighborhood search and SA. A two-phase hybrid heuristic search approach for LRP is introduced in [11]. The problem is decomposed into LAP and VRP. For the construction of the location distribution, they proposed a Tabu Search (TS) to determine a good configuration of the facilities to be used. Meanwhile, an Ant Colony Algorithm (ACO) was used at the routing phase to obtain good routes for the given configuration. The combination of Particle Swarm Optimization (PSO) with several heuristic algorithms is called Hybrid PSO (HybPSO-LRP) and is introduced in [12]. They combined the Multiple Phase Neighborhood Search-Greedy Randomized Adaptive Search Procedure (MPNS-GRASP) algorithm, the Expending Neighborhood Search (ENS) strategy, and a Path Relinking (PR) strategy into the PSO. With the same approach used in [12], reference [13] combined the same techniques with the Honey Bee Mating Optimization (HBMO). They solved the problem using a hybrid HBMO for LRP (HBMO-LRP). We found several studies on the integrated IRP from literature. For example, reference [14] solved a multi-objective coordination in a supply chain with three objective functions: maximizing the firm's profit, minimizing vendor's routing, and maximizing the average service level of buyers. They determined the vehicle routing, the router assigned and the amount delivered for each buyer. A HS algorithm is proposed due to the complexity of the problem. Considering the environmental impact, authors in [15] proposed a green IRP to minimize the total cost of inventory and routing, vehicle fixed cost, and emissions that are determined by load, distance, speed, and vehicle characteristics. They employed an exact method which is a Branch-and-Cut Algorithm (BCA) to add user cuts to the model and used a commercial solver to solve the linear programming relaxation problem. Similar to [16], they analyzed the benefits of collaborative energy use (CO\({}_{2}\) emission) and perishability in IRP with uncertain demand. The authors minimized the cost of routing, based on fuel and wage cost, waste, driving time and inventory. The problem is solved by the ILOG-OPL development studio and CPLEX 12.6 optimization. A new bi-objective mathematical model which takes into account the economic, social, and environmental issues in the distribution of perishable products with a specified expiration date in IRPs is considered in [17]. They focused on inventory and distribution costs for the first objective and then looked at social issues to shape the second objective by considering the rate of accidents for the vehicle and the number of expired products. The Torabi-Hassani method was used and included vehicle noise emission as a constraint. The integrated Production, Inventory, and Distribution Routing Problem (PIDRP) was developed and solved heuristically with two solutions approach [18]. In the first phase, they solved the Mixed-Integer Program (MIP) with CPLEX MIP solver and in the second phase, they solved an associated consolidation problem to handle the potential inefficiency of direct shipments involving routing and inventories by Extended Optimal Partitioning (EOP) procedure. This approach can simultaneously coordinate the production, inventory, and transportation operation in PIDRP.