Transportation industry activities have a significant negative impact on the environment, economy and human health. To reduce the environmental impact strategies, such as using electric vehicles, is taken into account. This paper presents a new mathematical model related to the electric vehicle INVENTORY-ROUTING PROBLEM. The objective function of the proposed model is to minimize the total cost of this system. Vehicles are considered as electrical device and due to the limited capacity of the batteries, the driving range is limited. Hence, if the battery is over, there is a possibility of swapping the battery at the battery swapping stations. In the proposed model, the shortage is not allowed and the customer demand is certain and determined. Because the proposed PROBLEM is categorized as NP-hard one, a meta-heuristic algorithm, namely variable neighborhood search (VNS), is proposed to solve large-scale PROBLEMs. To evaluate the performance of the proposed VNS, numerical results are compared with the exact method and the simulated annealing (SA) method. The computational results show the proper performance of the proposed VNS.

Manufacturers, who re-supply a large number of customers, continually struggle with the question of how to formulate a replenishment strategy. The purpose of this paper is to determine the optimal set of routes for a group of vehicles in the transportation network under defined constraints–which is known as the Vehicle ROUTING PROBLEM (VRP)–delivering new items, and resolving the INVENTORY control decision PROBLEM simultaneously since the regular VRP does not. Both the vehicle ROUTING decision for delivery and the INVENTORY control decision affect each other and must be considered together. Hence, a mathematical model of vehicle ROUTING PROBLEM with INVENTORY is proposed whose demands are assumed to be hybrid variables (HVRPI) in which fuzziness and randomness are considered together. Then, the PROBLEM is transformed into its equivalent deterministic form and presented as a multi-objective mixed integer nonlinear programming. Since finding the optimal solution (s) for HVRPI is aNP -hard, a solution algorithm is presented composed of the constrained Nelder–Mead method and a Tabu search algorithm for the vehicle ROUTING to solve the complex PROBLEM. The usefulness of the model is validated by experimental results. The findings indicate that the proposed model can provide a practical tool to significantly reduce the logistic cost.

In recent decades, there are intensive researches on deteriorating INVENTORY. However, only a few researchers focus on the INVENTORY ROUTING PROBLEM for deteriorating item. There are many items such as foods, electronic products that deteriorate with time, and many other products in the market also have perishable characteristic. The items not only decay during the stockpiling period but they also deteriorate throughout transportation time. Since deteriorated rate and time is necessary, in this paper, an INVENTORY ROUTING PROBLEM with time windows for deteriorating items is developed. Particle Swarm Optimization (PSO) is used to solve the PROBLEM since PSO can solve PROBLEMs in a reasonable period with near optimal solutions. We use two examples to illustrate the model. In a sensitivity analysis, way parameters that impact costs are demonstrated. Our results show that the deteriorating rate in INVENTORY has bigger effects than deteriorating rate in the vehicle, so this research has a significant contribution and managers can give more effort to reduce deteriorating in INVENTORY than the deteriorating rate in vehicles.

In this paper we developed an uncertain LNG marine INVENTORY-ROUTING PROBLEM. For this purpose, we set a scenario for a hypothetical LNG manufacturer in Iran selling products in long-term and spot contracts. The purpose of the study was to compare shipping expenses of split and non-split delivery strategies in deterministic and uncertain situations. The objective function was to minimize total costs consisting operational costs, contract penalties, and spot fees regarding liquefaction port operational constraints, ship flows, customer and contractual constraints. Considering uncertainty in the PROBLEM is one of this paper's contributions which is modeled by assuming vessels speed a fuzzy parameter. As a solution method, we propose a metaheuristic that combines a heuristic with GA. According to the computational results, split delivery policy is only cost effective in the deterministic PROBLEM, hence split delivery is not recommended in maritime transportation with uncertain nature.

Researchers and urban administrators have often considered the ROUTING PROBLEM as one of the fundamental phases in developing hazard management systems. In this research, a ROUTING PROBLEM is investigated and analyzed by proposing an enhanced metaheuristic algorithm based on biogeography. In this PROBLEM, the production planning, INVENTORY management, and distribution planning have been considered, and the purpose is to minimize the total costs of production setup, INVENTORY holding, and distribution of relief products. Then, to avoid the PROBLEM of premature convergence to local optima and to improve the efficiency and convergence rate of the algorithm on large-scale and constrained PROBLEMs, a new optimization algorithm based on biogeography with a new migration operator is proposed. With regard to the instances of ROUTING PROBLEMs, the performance of the proposed algorithm is compared to other methods based on the running time, convergence speed, robustness, best and average of the results and statistical superiority. The statistical assessment verifies the efficiency improvements and obtaining better results by the proposed strategy in tackling the temporal relief ROUTING task.

In this paper a multi-commodity multi-period INVENTORY ROUTING PROBLEM in a two-echelon supply chain consisting of a manufacturer and a set of retailers has been studied. In addition to INVENTORY management and distribution planning, production planning has also been considered in the above PROBLEM. The objective is to minimize total system cost that consists of production setup, INVENTORY holding and distribution costs. The commodities are delivered to the retailers by an identical fleet of limited capacity vehicles through direct shipment strategy. Also it is assumed that production and storage capacity is limited and stockout is not allowed. Since similar PROBLEMs without distribution planning are known as NP-hard, this is also an NP-hard PROBLEM. Therefore, in this paper, a new improved particle swarm optimization algorithm has been developed consisting of two distinguished phases for PROBLEM solving. First, the values of binary variables are determined using the proposed algorithm and then, the continuous variables are calculated by solving a linear programming model. Performance of the proposed algorithm has been compared with genetic and original particle swarm optimization algorithms using various samples of random PROBLEMs. The findings imply significant performance of the proposed algorithm.

Background and Purpose: Organizations are working to reduce warehousing and transportation costs, expanding supply chain management. Transportation and INVENTORY are the two main elements in the supply chain. The issue of ROUTING-INVENTORY is the consistent distribution of the product from one or more distribution points among the consumer group, which minimizes the average cost of distribution along the planning horizon without creating a shortage for the organization is the primary goal of this study. This study addresses this issue in perishable products with a fixed lifespan. A very critical area of vehicle ROUTING is the INVENTORY ROUTING issue. The most important objectives of this research were to review the studies conducted in the field of ROUTING-INVENTORY, INVENTORY management, ROUTING of perishable goods, implementing the cost minimization goal in the proposed mathematical model, and developing appropriate approaches to solve the proposed model under the assumptions of this research. Method: Given the nature of the PROBLEM that comes from NP-hard types, It is impossible to arrive at a definitive answer for its large dimensions, so this study proposes a method based on the ant colony algorithm algorithm, which solves the INVENTORY ROUTING PROBLEM under new assumptions. In this study, this issue was addressed in perishable products with a fixed lifespan. Findings: Conclusion: It was shown that the proposed algorithm is capable of solving PROBLEMs in different dimensions, especially where it seems impossible to achieve global optimality. Experiments on different benchmarks all confirmed the optimality of the results over competing algorithms and guided us to achieve the research objective of minimizing costs.

INVENTORY ROUTING PROBLEMs arise as simultaneous decisions in INVENTORY and ROUTING optimization. In the present study, vendor managed INVENTORY is proposed as a collaborative model for reverse supply chains and the optimization PROBLEM is modeled in terms of an INVENTORY ROUTING PROBLEM. The studied reverse supply chains include several return generators and recovery centers and one collection center. Since the mathematical model is an NP-hard one, finding the exact solution is time consuming and complex. A hybrid heuristic model combining dynamic programming, ant colony optimization and tabu search has been proposed to solve the PROBLEM. To confirm the performance of proposed model, solutions are compared with three previous researches. The comparison reveals that the method can significantly decrease costs and solution times. To determine the ant colony parameters, four factors and three levels are selected and the optimized values of parameters are defined by design of experiments.