Multi-period Inventory Routing Problem Research Articles

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.

A bi-objective green multi-period inventory-routing problem with multi-speed vehicles

Vendor-managed inventory becomes an essential trend in logistics. Inventory routing problem (IRP) is one of the most critical problems in this context. In practice, any distribution plan in an IRP ...

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.

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.

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.

Modelling and solving the multiperiod inventory-routing problem with stochastic stationary demand rates

The inventory-routing problem (IRP) is a typical logistics optimisation problem that supply chains, implementing vendor managed inventory (VMI), are confronted with. It combines inventory control and vehicle routing. The main objective of the IRP is to jointly determine optimal quantities of the product to be delivered to the retailers, delivery periods and optimal vehicle routes for the shipment of these quantities. This paper considers a multiperiod inventory-routing problem with stochastic stationary demand rates (MP-SIRP). The problem is first formulated as a linear mixed-integer stochastic program for which we propose a deterministic equivalent approximation model (MP-DAIRP). This latter model can be decomposed into two well-know subproblems: an inventory allocation subproblem and a vehicle routing subproblem. The stochastic aspect of the demand is accounted for in the inventory allocation subproblem. The vehicle routing subproblem is solved as a deterministic mixed-integer problem. Lagrangian relaxation is used to determine close to optimal feasible solutions for the MP-DAIRP. Results of the proposed Lagrangian relaxation approach on some numerical examples are reported and thoroughly discussed.

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.

Mixed integer and heuristics model for the inventory routing problem in fuel delivery

This paper presents solution approaches for the multi-product multi-period Inventory Routing Problem (IRP) in fuel delivery. A homogeneous fleet of vehicles with compartments is used for fuel distribution from one depot to a set of petrol stations that have deterministic fuel consumption. The IRP consists of two mutually dependent sub-problems, those of inventory and routing, in a Vendor Management Inventory (VMI) environment in which suppliers determine the quantities and time periods of the deliveries. For solving the IRP, we propose a Mixed Integer Programming (MIP) model and a heuristic approach with and without fleet size costs, to observe the impact of these costs on the solutions that are obtained. The heuristics model is based on constructive heuristics with two Variable Neighborhood Descent (VND) search types: a local intra-period search and a large inter-period neighborhood search. Both of these approaches were tested on numerical examples for which the results, together with the performances of the proposed models, are presented. A combination of good computational time and good quality solutions suggests the use of the proposed heuristics on problems with realistic dimensions where the MIP model cannot find an optimal solution in a reasonable amount of time.

An efficient hybrid genetic algorithm for the multi-product multi-period inventory routing problem

The inventory routing problem (IRP) addressed in this study is a many-to-one distribution network consisting of an assembly plant and many distinct suppliers where each supplies a distinct product. We consider a finite horizon, multi-periods, multi-suppliers and multi-products where a fleet of capacitated homogeneous vehicles, housed at a depot, transport products from the suppliers to meet the demand specified by the assembly plant in each period. The demand for each product is deterministic and time varying. A mathematical formulation of the problem is given and CPLEX 9.1 is run for a finite amount of time to obtain lower and upper bounds. A hybrid genetic algorithm, which is based on the allocation first route second strategy and which considers both the inventory and the transportation costs, is proposed. In addition to a new set of crossover and mutation operators, we also introduce two new chromosome representations. Several medium and small sized problems are also constructed and added to the existing data sets to show the effectiveness of the proposed approach.

Heuristics for a multiperiod inventory routing problem with production decisions

Manufacturers who resupply a large number of retailers on a periodic basis continually struggle with the question of how to formulate a replenishment strategy. This paper presents a comparative analysis of a series of heuristics for an inventory routing problem (IRP) that arises in a manufacturing supply chain. The IRP is formulated as a mixed integer program with the objective of maximizing the net benefits associated with making deliveries in a specific time period to a widely dispersed set of customers. It is assumed that inventory can accumulate at the customer sites, but that all demand must be met without backlogging. Because optimal solutions were not within reach of exact methods, a two-step procedure was developed that first estimates daily delivery quantities and then solves a vehicle routing problem for each day of the planning horizon. As part of the methodology, a linear program is used to determine which days it is necessary to make at least some deliveries to avoid stockouts. The IRP is investigated in the context of an integrated production–inventory–distribution–routing problem (PIDRP). The full model takes into account production decisions and inventory flow balance in each period. For the computations, a previously developed branch-and-price algorithm is used that requires the solution of multiple IRPs (one in each period) to generate columns for the master problem. Testing showed that PIDRP instances with up to eight time periods and 50 customers can be solved within 1 h. This level of performance could not be matched by either CPLEX or an exact version of the branch-and-price algorithm.