Multi-period Inventory Routing Research Articles

Design of Multi-Period Inventory Routing Problem Considering Road Rehabilitation Plans in Post-Disaster

Design of Multi-Period Inventory Routing Problem Considering Road Rehabilitation Plans in Post-Disaster

A Single-Product Multi-Period Inventory Routing Problem under Intermittent Demand

Demand fluctuations and uncertainty bring challenges to inventory management, and intermittent demand patterns increase the risk of inventory backlogs and raise inventory holding costs. In previous studies on inventory routing problems, different variants have been proposed to cope with complicated industrial scenarios. However, there are few studies on inventory routing problems with intermittent demand patterns. To solve this problem, we introduce a lateral transshipment strategy and build a single-product multi-period inventory routing mixed integer programming model to reduce customers’ inventory backlogs, balance regional inventory, reduce inventory holding costs, and improve inventory management efficiency. Furthermore, we design an adaptive large-neighborhood search algorithm with new operators to improve the solving efficiency. The experimental results show that an appropriate transshipment price can reduce the share of distribution costs. Another finding is that higher-capacity vehicles lead to higher revenue. Our findings not only expand the scope of the IRP domain but also provide actionable management insights for business practitioners.

Dual-Sourcing Inventory Routing Problem with Route-Dependent Lead Times in Rolling Horizon Framework

Traditional inventory routing problems ignore the time consumption in transportation. In this paper, an inventory routing problem with air–land transportation and route-dependent lead times is studied. The model is based on the rolling horizon framework which can serve as a “here-and-now” approximation for multi-period inventory routing problems. A planning horizon crossing strategy is proposed to consider the effect of the single-period decision on long-term planning. The box uncertainty set is used to depict demands. A tractable closed-form robust solution for optimal replenishment quantity is derived. An adaptive variable neighborhood search algorithm is developed for this problem. A novel shaking phase is proposed, and the performance of shaking operators is evaluated in numerical experiments. Results also validate the effectiveness of the robust solution and the planning horizon crossing strategy.

A multi-period inventory routing problem with procurement decisions: a case in China

A multi-period inventory routing problem with procurement decisions: a case in China

A modified adaptive genetic algorithm for multi-product multi-period inventory routing problem

Recent developments in urbanization and e-commerce have pushed businesses to deploy efficient systems to decrease their supply chain cost. Vendor Managed Inventory (VMI) is one of the most widely used strategies to effectively manage supply chains with multiple parties. VMI implementation asks for solving the Inventory Routing Problem (IRP). This study considers a multi-product multi-period inventory routing problem, including a supplier, set of customers, and a fleet of heterogeneous vehicles. Due to the complex nature of the IRP, we developed a Modified Adaptive Genetic Algorithm (MAGA) to solve a variety of instances efficiently. As a benchmark, we considered the results obtained by Cplex software and an efficient heuristic from the literature. Through extensive computational experiments on a set of randomly generated instances, and using different metrics, we show that our approach distinctly outperforms the other two methods. In this way, we created a decision support and computer-based approach to assist policy and decision-makers in the pathway of constructing a sustainable society.

A green multi-period inventory routing problem with pickup and split delivery: A case study in flour industry

In this study, we proposes a multi-period inventory routing problem with pickup and split delivery for distributing flour among bakeries. This study aims to determine the routes for heterogeneous vehicles with different loading capacity and, at the same time, decrease the cost of the system by enabling the pickup and split delivery at customer nodes. Also, we incorporate the environmental aspects into our modeling framework to reduce the adverse effect of transportation operations. We formulate the problem as a bi-objective multi-period inventory routing problem with pickup and split delivery. The proposed framework incorporates different strategical and operational decisions to optimize the supply chain network. We evaluate the performance of the model with and without the pickup option through an illustrative example. From the algorithm perspective, we implemented a priori method to solve the proposed formulation. We performed numerous experiments on real instances to showcase the application of the proposed framework on real-world problems. Finally, we provided the Pareto solution set for decision-makers to choose the best solutions based on their preference.

Inventory Routing Problem in Supply Chain of Perishable Products under Cost Uncertainty

This paper presents a multi-objective, multi-period inventory routing problem in the supply chain of perishable products under uncertain costs. In addition to traditional objectives of cost and greenhouse gas (GHG) emission minimization, a novel objective of priority index maximization has been introduced in the model. The priority index quantifies the qualitative social aspects, such as coordination, trust, behavior, and long-term relationships among the stakeholders. In a multi-echelon supply chain, the performance of distributor/retailer is affected by the performance of supplier/distributor. The priority index measures the relative performance index of each player within the supply chain. The maximization of priority index ensures the achievement of social sustainability in the supply chain. Moreover, to model cost uncertainty, a time series integrated regression fuzzy method is developed. This research comprises of three phases. In the first phase, a mixed-integer multi-objective mathematical model while considering the cost uncertainty has been formulated. In order to determine the parameters for priority index objective function, a two-phase fuzzy inference process is used and the rest of the objectives (cost and GHG) have been modeled mathematically. The second phase involves the development of solution methodology. In this phase, to solve the mathematical model, a modified interactive multi-objective fuzzy programming has been employed that incorporates experts’ preferences for objective satisfaction based on their experiences. Finally, in the third phase, a case study of the supply chain of surgical instruments is presented as an example. The results of the case provide optimal flow of products from suppliers to hospitals and the optimal sequence of the visits of different vehicle types that minimize total cost, GHG emissions, and maximizes the priority index.

Modeling and Solving a Multi-Period Inventory Fulfilling and Routing Problem for Hazardous Materials

Any potential damage may be severe once an accident occurs involving hazardous materials. It is therefore important to consider the risk factor concerning hazardous material supply chains, in order to make the best inventory routing decisions. This paper addresses the problem of hazardous material multi-period inventory routing with the assumption of a limited production capacity of a given manufacturer. The goal is to achieve the manufacturer’s production plan, the retailer’s supply schedule and the transportation routes within a fixed period. As the distribution of hazardous materials over a certain period is essentially a multiple travelling salesmen problem, the authors formulate a loading-dependent risk model for multiple-vehicle transportation and present an integer programming model to maximize the supply chain profit. An improved genetic algorithm considering two dimensions of chromosomes that cover the aforementioned period and supply quantity is devised to handle the integer programming model. Numerical experiments carried out demonstrate that using the proposed multi-period joint decision-making can significantly increase the overall profit of the supply chain as compared to the use of single period decision repeatedly, while effectively reducing its risk.

Agri-food supply chains with stochastic demands: A multi-period inventory routing problem with perishable products

This paper considers an agri-food supply chain with a single fresh food supplier, who owns a central warehouse that serves several retail centers. Retail centers carry a certain amount of inventory of the fresh product, which is prone to deterioration. The supplier makes both inventory and routing decisions to minimize the inventory, transportation, food-waste, and stock-out costs in the face of stochastic customer demand and perishable products that need to be delivered to each retail center. This inventory routing problem is known as perishable inventory routing problem (PIRP) with stochastic demands in the literature. We model it using a mixed integer program and propose a simheuristic algorithm, which integrates Monte Carlo simulation within an iterated local search, to solve it. Our experiments show that the proposed algorithm can improve the initial solution with reasonable computational times. The resulting procedure is easy to implement and is applicable to other domains where a multi-period PIRP with stochastic demands may appear.

Inventory Routing Problem with Carbon Emission Consideration

Inventory Routing Problem (IRP) has been continuously developed and improved due to pressure from global warming issue particularly related to greenhouse gases (GHGs) emission. The burning of fossil fuel for transportations such as cars, trucks, ships, trains, and planes primarily emits GHGs. Carbon dioxide (CO2) from burning of fossil fuel to power transportation and industrial process is the largest contributor to global GHGs emission. Therefore, the focus of this study is on solving a multi-period inventory routing problem (MIRP) involving carbon emission consideration based on carbon cap and offset policy. Hybrid genetic algorithm (HGA) based on allocation first and routing second is used to compute a solution for the MIRP in this study. The objective of this study is to solve the proposed MIRP model with HGA then validate the effectiveness of the proposed HGA on data of different sizes. Upon validation, the proposed MIRP model and HGA is applied on real-world data. The HGA is found to be able to solve small size and large size instances effectively by providing near optimal solution in relatively short CPU execution time.

Considering Production Planning in the Multi-period Inventory Routing Problem with Transshipment between Retailers

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 show that the solutions yielded by the heuristic method have high efficiency.

Fuel Consumption Optimization Model for the Multi-Period Inventory Routing Problem

In the traditional multi-period inventory routing problem (MIRP), traveling distance is considered as the only measurement of vehicles’ variable transportation cost; however, it is in fact the fuel consumption cost, not the distance, which is the greater concern. This paper evaluates vehicles’ variable transportation cost by fuel consumption, which is influenced by distance, load, and fuel price. It presents an integer program to formally characterize the fuel consumption considered MIRP (FCMIRP), which can help enterprises obtain a more accurate tradeoff between transportation and inventory costs. It also benefits the environment, because reducing fuel consumption will curb carbon dioxide (CO2) emissions. Valid inequalities are added to strengthen the model and use a branch-and-cut algorithm. Computational tests indicate that the FCMIRP can decrease fuel consumption and total cost over the traditional model. Factors that influence the results of FCMIRP are also discussed.

A variable neighborhood search simheuristic for the multiperiod inventory routing problem with stochastic demands

AbstractThe inventory routing problem (IRP) combines inventory management and delivery route‐planning decisions. This work presents a simheuristic approach that integrates Monte Carlo simulation within a variable neighborhood search (VNS) framework to solve the multiperiod IRP with stochastic customer demands. In this realistic variant of the problem, our goal is to establish the optimal refill policies for each customer–period combination, that is, those individual refill policies that minimize the total expected cost over the periods. This cost is the aggregation of both expected inventory and routing costs. Our simheuristic algorithm allows to consider the inventory changes between periods generated by the realization of the random demands in each period, which have an impact on the quantities to be delivered in the next period and, therefore, on the associated routing plans. A range of computational experiments are carried out in order to illustrate the potential of our simulation–optimization approach.

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

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

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 hybrid heuristic for the inventory routing problem under dynamic regional pricing

Abstract The inventory routing problem (IRP) seeks to meet the demands of customers during consecutive time periods. Because of the geographical distribution of customers and variations in willingness to pay of the consumers in distinct locations and time, regional and time-based pricing are powerful ways to improve profitability. In this study, a quadratic mixed-integer programming model for single product, multi-period Inventory Routing under the dynamic regional pricing problem (IRDRP) has been proposed. A hybrid heuristic approach is developed to solve it. This algorithm comprises five phases: initialization, demand generation, demand adjustment, inventory routing, and neighborhood search, which are embedded in a simulated annealing framework. Experimental results indicate as the problem size increases, the difference between CPLEX and the proposed heuristic algorithm optimality gap exhibits an upward trend and that the heuristic outperforms CPLEX. A sensitivity analysis demonstrates that by intensifying the scarce capacity, approaching an optimal solution will be more difficult.

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.

An incremental approach using local-search heuristic for inventory routing problem in industrial gases

In this paper we solve the inventory routing problem (IRP) occurring in industrial gas distribution where liquefied industrial gases are distributed to customers that have cryogenic tanks to store the gases on-site. We consider a multi-period inventory routing problem with multiple products assuming deterministic demand rates and the proposed model is formulated as a linear mixed-integer program. We propose an incremental approach based on decomposing the set of customers in the original problem into sub-problems. The smallest sub-problem consists of the customer that needs to be delivered most urgently along with a set of its neighbors. We solve each sub-problem with the number of customers growing successively by providing the solution of the previously solved sub-problem as an input. Each sub-problem is then solved with a randomized local-search heuristic method. We also propose an objective function that drives the local-search heuristics toward a long-term optimal solution. The main purpose of this paper is to develop a solution methodology appropriate for large-scale real-life problem instances particularly in industrial gas distribution.

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.

Multi-product multi-period Inventory Routing Problem with a transshipment option: A green approach

This paper addresses a multi-product multi-period Inventory Routing Problem (IRP) where multiple capacitated vehicles distribute products from multiple suppliers to a single plant to meet the given demand of each product over a finite planning horizon.The demand associated with each product is assumed to be deterministic and time varying. In this supply chain, the products are assumed to be ready for collection at the supplier site when the vehicle arrives. A transshipment option is considered as a possible solution to increase the performance of the supply chain and shows the impact of this solution on the environment. A green logistic issue is also incorporated into the model by considering the interrelationship between the transportation cost and the greenhouse gas emission level. The proposed model is a mixed-integer linear program and solved by CPLEX. We provide a numerical study showing the applicability of the model and underlining the impact of the transshipment option on improved supply chain performance.