Generally, the Inventory Routing Problem occurs in a supply chain where customers consider the supplier responsible for Inventory replenishment. In this situation, the supplier finds the answer to questions regarding the time and quantity of delivery to the customer as well as the sequence of customers in the routes. Considering the effect of Production decisions on answering these questions, the present paper examines the integrated decision making on Production, Routing and Inventory in a two-echelon supply chain composed of a manufacturer and multiple retailers. Transshipment, as a policy in supply chain logistic which increase integration and decrease Inventory cost, is also allowed between retailers. The mathematical formulation for the Problem is developed and an adaptive large neighborhood search heuristic is proposed to solve this complicated Problem. The results of numerical experiments showed that the solutions yielded by the heuristic method have high efficiency.

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 this study, a two echelons supply chain system in which a supplier is producing perishable product and distribute it to multiple customers is considered. By allowing lateral transshipment mechanism, it is also possible to deliver products to some customers in some periods in bulk, then customers using their own vehicle to transship goods between each other seeking further reduction in the overall cost. The aim here is minimizing the Production, Inventory carrying cost, and distribution as the first objective, and transshipment cost as the second objective, which is contrary objectives, without facing any shortage anywhere in the chain during the planning horizon. This Problem is formulated as a bi-objectives mixed integer programming (BOMIP), and then a proper Pareto front as a set of multiple decision alternatives is provided using NSGAII and NRGA approach. Novelty of this research is providing a bi-objectives mathematical modeling of perishable product Inventory Routing with Production and transshipment (BO-P-PIRPT) that help the decision maker to choose the best mixture of Routing and transshipment.

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.