Inventory Routing Problem Model Research Articles

Robust inventory routing problem under uncertain demand and risk-averse criterion

Inventory routing problem (IRP), which plays an important role in implementing vendor-managed-inventory strategy, is to determine the optimal timing and quantity of products to be delivered as well as the optimal vehicle delivery routes from the vendor to retailers. Retailers’ demand is usually uncertain and their distributions are ambiguous. We utilize limited historical demand data of retailers to construct a series of scenarios to characterize demand uncertainties. Moreover, we develop a framework to construct ambiguity sets and describe the ambiguities in demand distributions. To cater to the new feature of IRP as being exposed to downside risk and balance the mean and risk level of cost, we incorporate the worst-case mean-conditional value-at-risk (M-CVaR) criterion into the objective function and present a new distributionally robust IRP model. We transform the proposed model into a tractable formulation based on duality theory. A case study demonstrates the feasibility of the proposed method. The results indicate that our model can provide a robust delivery solution for immunizing against the influence of ambiguous demand distributions. In addition, an out-of-sample performance analysis shows that the delivery solution provided by our model can effectively reduce the product shortage rate.

Metaheuristic Algorithms for the Many-to-one IRP with Dynamic Velocity

Inventory Routing Problem (IRP) is a combination of inventory management and transportation optimization problems that involve route selection, number of product pickups, and customer demands. In the many-to-one IRP model, the vehicle is sent from the depot and goes to pick up products from several suppliers to the assembly plant. Vehicle loads on this model will increase every time a product is taken from the supplier. It can decrease vehicle speed in the next travel process (dynamic velocity). There are still a few papers that discuss many-toone IRP models with dynamic velocity. Therefore, this study aims to develop a new model called the many-to-one IRP model with dynamic velocity. A modified threshold accepting, variable neighborhood search, and record-to-record travel algorithm with the first improvement local search strategy is used to solve the IRP model. Small datasets many-to-one IRP from previous researches and experimental tests are used to test the algorithms. The results showed that the best-proposed algorithm is competitive when compared to the best-known solution in the previous studies (the average deviation is only 1.86%).

A hybrid heuristic algorithm for cyclic inventory-routing problem with perishable products in VMI supply chain

The VMI supply chain can bring benefit to concerned parties. The paper studies cyclic inventory-routing problem (IRP) under VMI policy. Cyclic IRP as a variant of the IRP belong to long-term decision. It means once the replenishment policy and vehicle routing are determined, they will stay the same in the following periods. This paper considers the loss cost caused by perishability of perishable products and assumes the demand is dependent on price and stock. Based on the above consideration, three different cyclic IRP models for perishable products with stock and price dependent demand in VMI supply chain are put forward. They are IRP model ending with shortage, IRP model starting with shortage, and IRP model with no shortage. These models are composed of a single manufacturer and multiple retailers. The objective is to minimize the average total cost. The total cost includes not only fixed and transportation cost of vehicles, inventory (order and holding) and shortage cost of retailers, but also startup and holding cost of manufacturer. The proposed models are nonlinear mixed integer programming models and NP-hard problem. In order to solve these models, a hybrid heuristic algorithm that is developed by combining cuckoo algorithm with improved Clarke-Wright savings algorithm is developed. In computational experiments, the proposed algorithm is compared with the optimization solver. The results demonstrate the proposed algorithm outperforms the optimization solver. In addition, the results show the average total cost may be reduced by using the strategy of stockout in some cases. Sensitivity analysis is also implemented to study the influence of parameters on optimal solution. The results of computational experiments validate the applicability of the proposed models and the effectiveness of hybrid heuristic algorithm. The study also provides policymakers with management implications. Finally, the conclusions and future research directions are given.

A new model for multi-period bi-objective inventory routing problem with stochastic demand, inventory holding, shortage and customer satisfaction

This paper presents a new multi-period, bi-objective inventory routing problem model with stochastic demand in two echelon network supply chain including some suppliers with several vehicles to satisfy customers' demands. Reducing the number of vehicles is also considered when each vehicle belongs to one route. The difference between this paper and the others is that the shortages and inventory holdings are kept at the customers' parts not in distribution centres. Customers' review of records costs and customer satisfaction and its relationship with shortage and inventory holding are the objective functions. The customer satisfaction increased by decreasing inventory holdings and shortage amount. The goal is to determine the delivery quantities to customers taking account of shortage and inventory holding amount per period. The objective of this paper is to minimise transportation routing costs, customers' review of records costs, inventory holding costs and shortage costs, and maximise customer satisfaction. The presented model is analysed by e-constraint method and run in GAMS software.

A credibilistic goal programming model for inventory routing problem with hazardous materials

Hazardous materials are harmful to both the environment and human health due to their toxic ingredients. However, they are essential to sustain the industrial lifestyle, and frequently appear in the cargo transport. Since the damage is generally huge once an accident occurs, it is very important to evaluate the transportation risk of hazardous materials, and then make the best inventory routing decisions. In this paper, we study a three-level supply chain problem with hazardous materials inventory and transportation among suppliers, manufacturers and retailers. The goal is to obtain the best balance between risk and cost under the assumption that the demands of retailers are fuzzy variables. Considering that the variation of vehicle loading has a significant influence on the transportation risk, we formulate a loading-dependent transportation risk model and propose a credibilistic goal programming model to minimize the positive deviations of expected risk and expected cost from the given risk level and cost level. An improved genetic algorithm whose chromosomes contain two types of genes is designed to handle the goal programming model. Numerical experiments are given to illustrate the efficiency of the proposed model and algorithm.

Multi-period inventory routing problem under carbon emission regulations

This paper analyzes the impacts of carbon emission regulations on the traditional inventory routing problem (IRP). We first present the traditional IRP model, which is an inbound commodity collection system consisting of one assembly plant and a set of geographically dispersed suppliers. At the beginning of each period, a fleet of capacitated identical vehicles depart the depot to pick up products from suppliers to meet the assembly plant’s demand, which is deterministic and time-varying. We use fixed transportation cost, fuel consumption cost and inventory holding cost to evaluate the system’s total cost, in which fuel consumption cost is determined by fuel consumption rate, distance and fuel price. Then we investigate the impacts of carbon emission regulations on the traditional IRP problem, wherein carbon emissions are generated by fuel consumption. A series of mixed integer nonlinear programming models are constructed and linearization methods are used. A hybrid genetic algorithm based on allocation first and routing second is proposed to find near-optimal solutions for these problems. Numerical tests are performed to show the effectiveness of the proposed algorithm, and several managerial insights are observed from parameter sensitive analyses which may help both the government and the industry to adopt appropriate carbon reduction regulations.

Modeling The Inventory Routing Problem (IRP) With Multiple Depots With Genetic Algorithms

This paper presents the application of Inventory Routing Problem (IRP) for the distribution of goods between multiple clients (n) and multiple suppliers (m), which is based on the concept of collaboration between companies through vendor managed inventory (VMI). A review of the processes of distribution and routing of goods including the variable inventory and the IRP model with multiple warehouses are presented and it is proposed a genetic algorithm for its solution. The distribution of goods is a key process in the supply chain, since it plays a decisive role in the business logistics costs and in service level provided to customers. The current competitive environment has led companies to work together through partnerships of cooperation and collaboration processes, leading to find new forms of distribution involving multiple suppliers and multiple customers. The main results of the model and the proposed genetic algorithm, reductions in inventory costs and transportation to the problem studied are obtained.

Modeling an Inventory Routing Problem for perishable products with environmental considerations and demand uncertainty

The transition to sustainable food supply chain management has brought new key logistical aims such as reducing food waste and environmental impacts of operations in the supply chain besides the traditional cost minimization objective. Traditional assumptions of constant distribution costs between nodes, unlimited product shelf life and deterministic demand used in the Inventory Routing Problem (IRP) literature restrict the usage of the proposed models in current food logistics systems. From this point of view, our interest in this study is to enhance the traditional models for the IRP to make them more useful for the decision makers in food logistics management. Therefore, we present a multi-period IRP model that includes truck load dependent (and thus route dependent) distribution costs for a comprehensive evaluation of CO2 emission and fuel consumption, perishability, and a service level constraint for meeting uncertain demand. A case study on the fresh tomato distribution operations of a supermarket chain shows the applicability of the model to a real-life problem. Several variations of the model, each differing with respect to the considered aspects, are employed to present the benefits of including perishability and explicit fuel consumption concerns in the model. The results suggest that the proposed integrated model can achieve significant savings in total cost while satisfying the service level requirements and thus offers better support to decision makers.

A new hybrid GA-PSO method for solving multi-period inventory routing problem with considering financial decisions

Integration of various logistical components in supply chain management, such as transportation, inventory control and facility location are becoming common practice to avoid sub-optimization in nowadays’ competitive environment. The integration of transportation and inventory decisions is known as inventory routing problem (IRP) in the literature. The problem aims to determine the delivery quantity for each customer and the network routes to be used in each period, so that the total inventory and transportation costs are to be minimized. On the contrary of conventional IRP that each retailer can only provide its demand from the supplier, in this paper, a new multi-period, multi-item IRP model with considering lateral trans-shipment, back-log and financial decisions is proposed as a business model in a distinct organization. The main purpose of this paper is applying an applicable inventory routing model with considering real world setting and solving it with an appropriate method.

Modeling inventory routing problems in supply chains of high consumption products

Given a distribution center and a set of sales-points with their demand rates, the objective of the inventory routing problem (IRP) is to determine a distribution plan that minimizes fleet operating and average total distribution and inventory holding costs without causing a stock-out at any of the sales-points during a given planning horizon. We propose a new model for the long-term IRP when demand rates are stable and economic order quantity-like policies are used to manage inventories of the sales-points. The proposed model extends the concept of vehicle routes (tours) to vehicle multi-tours. To solve the nonlinear mixed integer formulation of this problem, a column generation based approximation method is suggested. The resulting sub-problems are solved using a savings-based approximation method. The approach is tested on randomly generated problems with different settings of some critical factors to compare our model using multi-tours as basic constructs to the model using simple tours as basic constructs.

An integrated model of the periodic delivery problems for vending-machine supply chains

In this paper we present a model and solution procedures of the Inventory Routing Problem (IRP) encountered in vending machine supply chains working under vendor-managed inventory (VMI) scheme. The new IRP model is built based on the existing Periodic Vehicle Routing Problem with Time-windows (PVRPTW). The model will be referred to as the Integrated Inventory and Periodic Vehicle Routing Problem with Time-windows (IPVRPTW). The objective of the IPVRPTW is to minimize the sum of the average inventory holding and traveling costs during a given m-day period. The visit frequency is treated as a decision variable instead of as a fixed parameter. We attempt to optimize the visit frequency of each retailer and to build vehicle tours simultaneously in order to find the best trade-off between the inventory holding and traveling costs. Computational experiments are conducted on some instances taken from the literature to evaluate the performance of the proposed model.