## 2 Literature Review
The two-step procedure is getting more attention in solving IRP, researchers in [19] performed a comparative analysis of a series of heuristics for manufacturing supply chain with a MIP formulation and two-step procedure development. The first step is to estimate the daily delivery quantities and followed by solving a VRP in the second step. A previously developed branch-and-price algorithm is used and the production decision and inventory flow balance were taken into account in the model. Besides IRP, the integrated LIP is also gaining popularity. An optimization model for perishable products with fuzzy capacity and carbon emission constraints for integrated LIP is proposed by [20]. They formulated a Mixed-Integer Nonlinear Programming (MINP) and is solved by using two methods which are Hybrid Genetic Algorithm (HGA) and Hybrid HS (HHS). They found that HHS gave a better solution but needed higher computing time when compared to the HGA. The LIP under vendor-managed inventory was considered by [21]. They solved the multi-objective LIP model based on the Non-dominated Sorting Genetic Algorithm (NSGA-II). This method gave promising solutions when compared with the well-known multi-objective evolutionary algorithm. By using the same approach as in [21] but hybridized with the Multi-objective Particle Swarm Optimization (MOPSO), a bi-dynamic closed-loop LIP under facility disruption risk is proposed in [22]. They considered the effectiveness of returned products in a period and retailer demand in the next period. The bi-level programming problem where the upper level is for determining the appropriate location of 3 rd checking sites and the lower level is to present the coordinated inventory replenishment is studied by [23]. They considered the location and inventory policies in the supply chain when product returns are allowed. Other related study of LIP can be found in [24]. The authors focused on three decisions which are the determination of depot locations, the allocation of flows, and the shipment sizes. Nonlinear continuous programming is formulated and an iterative heuristic is developed to estimate the depot flows, to solve the linear program, and to improve the flow depot. Meanwhile, researchers in [25] explored the continuous non-linear formulation for LIP with uncertain demand that integrates location, allocation, and inventory decisions. They solved the linear program using a heuristic algorithm and used the solution to improve the variable estimators for the next iteration. A closed-loop LIP is considered by [26] that determines which depot and remanufacturing centre need to be opened. An exact two-phase Lagrangian relaxation algorithm is developed and a mixed-integer nonlinear location-allocation model is formulated. Extension to the study in [26], an equivalent formulation with fewer nonlinear terms in the objective function is proposed in [27]. They used piecewise linearization to transform and solve it using CPLEX. Then the solution in CPLEX is compared with two previously published Lagrangian relaxation-based heuristic. With respect to the LIRP, some of the researchers focus only on the non-defect items in reverse logistics such as in [28]. They solved the LIRP of the e-supply chain environment by using a Hybrid Genetic Simulated Annealing Algorithm (HGSAA) and compared it to a standard GA. Reference [29] used a Pseudo-Parallel Genetic Algorithm Integrating Simulated Annealing (PPGSA) to solve stochastic LIRP with continuous review inventory policy. Reverse logistics considering both defect and non-defect items of returned products has also been studied by [30]. They considered both quality of returned products in the e-commerce supply chain system. They found that the Hybrid Ant Colony Optimization algorithm (HACO) was considerably efficient and effective compared to a standard ACO. New TS (NTS) has been proposed by [31] to simultaneously integrate the LIRP and considered the minimization of manufacturing goods for new products and remanufacturing goods for damaged products in the objective function.