Inventory Routing Problem Research Articles

Enhancing efficiency in delivering petroleum products: optimizing the deteriorating inventory-routing problem with heterogeneous multi-compartment vehicles

Enhancing efficiency in delivering petroleum products: optimizing the deteriorating inventory-routing problem with heterogeneous multi-compartment vehicles

A novel mixed-integer linear programming formulation for continuous-time inventory routing

Inventory management, vehicle routing, and delivery scheduling decisions are simultaneously considered in the context of the inventory routing problem. This paper focuses on the continuous-time version of this problem where, unlike its more traditional discrete-time counterpart, the distributor is required to guarantee that inventory levels are maintained within the desired intervals at any moment of the planning horizon. In this work, we develop a compact mixed-integer linear programming formulation to model the continuous-time inventory routing problem. We further discuss means to expedite its solution process, including the adaptation of well-known rounded capacity inequalities to tighten the formulation in the context of a branch-and-cut algorithm. Through extensive computational studies on a suite of 90 benchmark instances from the literature, we show that our branch-and-cut algorithm outperforms the state-of-the-art approach. We also consider a new set of 63 instances adapted from a real-life dataset and show our algorithm’s practical value in solving instances with up to 20 customers to guaranteed optimality.

Joint optimization of recyclable inventory routing problem under uncertainties in an incentive-based recycling system

Due to the value of resource recovery and the development of a circular economy, waste recycling has gathered global attention. Recently, many emerging cities designed new systems like an incentive-based recycling system (IBRS). In such systems, recyclables are collected through community recycling nodes by offering incentives, then transported to street recycling stations and sorted before being finally recycled. The increased recycling nodes and the incentives enhance the convenience and residents’ enthusiasm for waste recycling, but also intensify the uncertainty of recycling quantities and the complexity of the recycling operation management. Poor recycling operation management may result in increased recycling costs or greater loss of recyclables, which discourages residents from participating in recycling. Based on an existing IBRS, this study investigates the joint optimization problem of the recyclable inventory management at each community recycling node and the vehicle routing from the recycling nodes to the recycling station. A two-stage dual-objective multi-period stochastic programming model is established to minimize the loss of recyclables and logistics costs, which is further reformulated using the weighting method and transportation cost approximation parameters. To solve the reformulated model, a three-phase iterative algorithm is designed by combining the progressive hedging algorithm and route splitting algorithm based on the Lin-Kernighan heuristic. A case study is conducted using data from Shanghai’s IBRS. The proposed joint decision model is superior to separate decisions and the three-phase iterative algorithm can reduce the average total cost by up to 42.12% compared to the genetic algorithm and the Iteration-Move-Search method in the literature. Additionally, a sensitivity analysis is conducted to provide managerial insights.

Stability metrics for a maritime inventory routing problem under sailing time uncertainty

We study a multi-product maritime inventory routing problem (MIRP) with sailing time uncertainty. We explicitly consider the replanning that happens after uncertainty is revealed. The objective is to determine the stability of the adjusted plans after the occurrence of an uncertain event and to evaluate the effect of incorporating different stability metrics in the rescheduling process. Five stability metrics are introduced, and mathematical formulations of the MIRP incorporating each metric are presented. A reoptimization framework is then used to analyze the impact of each stability metric. Calculations are performed using 360 instances. The main result is that adjustments to the original plan occur at no additional cost almost 50% of the time. If decision makers want a more stable plan, they should accept a 5% cost deterioration, resulting in 20% more stable solutions.

An integrated inventory and order pick-up model considering the vendor's capacities and the vehicle trips' duration for the MVSB system

Purpose: This research develops a model integrating inventory with order pick-up that considers both the vendor’s capacities and the pick-up time for the multi-vendor single-buyer (MVSB) system.Design/methodology/approach: A model of integrating inventory with pick-up of order considering both the vendor’s capacities and the pick-up time for the MVSB’s system is formulated as a mixed integer non-linear programming, and a heuristic-metaheuristic algorithm is proposed to solve the problem. This model applies a decomposition approach to minimize total relevant costs, which consist of the buyer’s ordering, vendor’s set-up, vendor’s and buyer’s holding, and pick-up.Findings: This research proposes an inventory model integrated with the pick-up of orders, considering both the capacity of the vendor and the pick-up time for the MVSB system. This research also proposes a hybrid heuristic-metaheuristic algorithm that can obtain a solution in realistic computational time. Originality/value: This paper proposes a mathematical model for the inbound inventory routing problem, considering both the capacities of vendors and the pick-up time for the MVSB system.

Sustainable solutions analysis of a bi-objective green inventory routing problem with heterogeneous fleet and different types of fuels

Sustainable solutions analysis of a bi-objective green inventory routing problem with heterogeneous fleet and different types of fuels

Towards efficient solutions for vehicle routing problems for oxygen supply chains

This work investigates the integrated production–inventory-routing problem (PIRP) for liquid oxygen supply chains consisting of multiple plants, customers, and heterogeneous vehicles. Solving such a problem is challenging, especially when dealing with large-scale industrial scales. A two-level procedure is adopted that determines decisions regarding production, inventory, and product allocation by simplifying the routing component in the first level. Then, the routing decisions are considered in the lower level for which 3-index mathematical programming formulations are presented. To address the combinatorial complexity of the lower-level decisions, we propose alternative multi-trip heterogeneous vehicle routing problem (MTHVRP) formulations together with a column generation-based solution strategy. A set of test instances and a real-world case study demonstrate the applicability and performance of the formulations and solution methods.

Inventory Routing Problem With Split Delivery and Variable Time Windows for Customers With Small Capacity and Large Sales

Inventory Routing Problem With Split Delivery and Variable Time Windows for Customers With Small Capacity and Large Sales

Fuzzy inventory-routing problem with priority customers

Fuzzy inventory-routing problem with priority customers

Modeling a closed-loop inventory routing problem for returnable transport items under horizontal logistics collaborations and dynamic demand structure

ABSTRACT This paper addresses a closed-loop inventory routing problem with multiple suppliers, products, and periods under horizontal collaboration assumptions. Our problem encompasses various decision aspects, including routing, inventory management, product delivery, returnable transport item collection and cleaning. We analyze various logistics collaboration scenarios. The effects of demand dynamicity are also assessed. The problem has been mathematically defined as a Mixed Integer Linear Programming model. A rolling horizon approach and a hybrid heuristic algorithm are proposed for instances that exceed the computational requirements of solving the exact MILP model. The applicability and potential benefits of the MILP model and the proposed solution methodologies are demonstrated through a base case and additional numerical analyses on larger-sized instances and networks. The results show that supplier collaboration significantly reduces routing costs, while customer collaboration reduces inventory costs. Numerical comparisons reveal that the proposed algorithms outperform the MILP model for large-scale problem instances.

An inventory-routing optimization model for pharmaceutical supply chain with time-dependent travel time on a multi-graph network: a case study

PurposeSpurred by the high turnover in the pharmaceutical industry, locating pharmacies inside urban areas along with the high product perishability in this industry, the pharmaceutical supply chain management has recently gained increasing attention. Accordingly, this paper unveils an inventory-routing problem for designing a pharmaceutical supply chain with perishable products and time-dependent travel time in an uncertain environment.Design/methodology/approachIn this study, mathematical programming is employed to formulate a multi-graph network affected by the traffic volume in order to adapt to real-world situations. Likewise, by transforming the travel speed function to the travel time function using a step-by-step algorithm, the first-in-first-out property is warranted. Moreover, the Box–Jenkins forecasting method is employed to diminish the demand uncertainty.FindingsAn appealing result is that the delivery horizon constraint in the under-study multi-graph network may eventuate in selecting a longer path. Our analysis also indicates that the customers located in the busy places in the city are not predominantly visited in the initial and last delivery horizon, which are the rush times. Moreover, it is concluded that integrating disruption management, routing planning and inventory management in the studied network leads to a reduction of costs in the long term.Originality/valueApplying the time-dependent travel time with a heterogeneous fleet of vehicles on the multi-graph network, considering perishability in the products for reducing inventory costs, considering multiple trips of transfer fleet, considering disruption impacts on supply chain components and utilizing the Box–Jenkins method to reduce uncertainty are the contributions of the present study.

Simultaneous Pickup-and-Delivery Production-Routing Problem in closed-loop supply chain with remanufacturing and disassembly consideration

In a context of Closed-Loop Supply Chain, Production-Routing Problem with Pickup and Delivery is presented. In its basic form, Production-Routing Problem (PRP) attempts to solve jointly Dynamical Lot-Sizing and Inventory-Routing Problems. In this paper, a novel PRP model seeking to minimize the total cost of manufacturing, remanufacturing, disassembly, inventory, and routing by taking into account the remanufacturing and disassembly processes of End-of-Life returned products is provided. Novel hybrid heuristics based on Two-Phase Iterative and Relax-and-Fix heuristics were developed and outperform Branch-and-Cut algorithm for large size instances with a small vehicle capacity. Main insights derived from sensitivity analyses are (i) managers can use the model to trade off the cost saving resulting from the integration of forward and reverse flows, on the one hand, and any additional cost incurred by the organizational changes related to the integration, on the other hand, (ii) a high level of remanufacturing rate for returned products is not necessarily profitable, and managers should develop a return policy that leads to the appropriate level of remanufacturing rate, and (iii) investing in expanding the remanufacturing or the disassembly capacities can significantly reduce the total cost until a threshold level, beyond which any further investment is not beneficial.

Enhancing Supply Chain Efficiency: Implementation of Vendor Managed Inventory in Inventory Routing Problem

Enhancing Supply Chain Efficiency: Implementation of Vendor Managed Inventory in Inventory Routing Problem

Joint optimization of the inventory routing problem considering the recycling of broken bikes in the bike-sharing system

Bike-sharing system has become an indispensable element of sustainable urban transportation, effectively resolving the "last mile" transportation challenge for city dwellers. A major daily operational task in these systems is planning a fleet to rebalance the bikes over time, ensuring the optimal availability of bikes and docks to users. Recycling is also a daily work with the an increase in the number of broken bikes. However, rebalancing or recycling operation is always regarded as an independent tasks. They are separately studied in existing papers. Thus, this paper develops an operational strategy for recycling broken bikes during the rebalancing process, and studies the combination of the station inventory and vehicle routing problems. First, an inventory routing model is constructed with the aim of minimizing the total costs including procurement, expected user loss, inventory and transportation costs. Then, a two-stage iterative algorithm is developed with both exact and heuristic algorithms. We use real-world data from Capital Bikeshare to test our proposed model and approach, which shows the two-stage iterative algorithm is efficient and outperforms existing solutions in reducing total costs. Finally, the sensitivity analysis is performed on key parameters such as the vehicle’s capacity, unit penalty costs for customer dissatisfaction events, unit inventory holding costs and the observation period of rebalancing. It shows that enterprises can reduce the total cost by altering vehicle’s capacity, reducing the unit inventory holding costs or changing the observation period of rebalancing.

Bibliometric Study of Metaheuristics Application for Solving Inventory Routing Problem

Bibliometric Study of Metaheuristics Application for Solving Inventory Routing Problem

Modeling of sustainable integrated supply chains under the consideration of European Union regulations

AbstractThis work introduces a multi-period, multi-commodity, inventory-routing problem with strategic fleet scheduling decisions, under the consideration of speed limits, as well as strict European Union regulations on truck drivers’ working and driving time. To address the new problem, a mixed integer linear programming model was developed. Several artificial but realistic problem instances were randomly generated following relative guidelines from the open literature, to validate and assess the performance of the novel mathematical model. Furthermore, in an effort to produce useful managerial insights, several sensitivity analyses were performed considering different fluctuation rates on key model parameters.

Iterated Local Search Approach to a Single-Product, Multiple-Source, Inventory-Routing Problem

We address an inventory-routing problem that arises in a liquid oxygen-producing company. Decisions must be made for the efficient transport of the product from sources to destinations by means of a heterogeneous fleet of trucks. This combinatorial problem has been stated as a constrained minimization one, whose objective function is the quotient of the operating cost divided by the total amount of delivered product. The operating cost comes from the distances traveled, the drivers’ salary, and the drivers’ overnight accommodation. The constraints include time windows for drivers and destinations, inventory safety levels, lower bounds for the quantity of product delivered to destinations, and maximum driving times. To approximate the optimal solution of this challenging problem, we developed a heuristic algorithm that first finds a feasible solution, and then iteratively improves it by combining the Metropolis criterion with local search. Our results are competitive with the best proposals in the literature.

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.

Cost optimization of shuttle tanker offloading operations

This paper proposes an optimization model accounting for voyage costs, charter costs, and the cost of lost production for scheduling the operation of shuttle tankers that are used to transport the oil from the oil production units in deep water, to onshore terminals. This model introduces the effect of the costs from lost production, which can vastly surpass both voyage and charter costs, improving on previous research on the scheduling of such operations, which has focused solely on the optimization of voyage and charter costs, with the cost of lost production in case of failure of the logistics system being ignored. A simulation-optimization method is proposed, allowing for uncertainty in weather condition and oil production. Given the highly structured nature of the policies governing the underlying inventory routing problem, the problem can be recast as a routing problem, to great computational advantage. A novel efficient voyage-based optimization formulation is proposed, and optimality is achieved for instances with a size much larger than those of previous research. The application of the method is illustrated for Brazil, where problem instance sizes faced in practice are considerably large. Sensitivity analysis shows the considerable impact of costs from lost production on the obtained schedules.

Solving a short sea inventory routing problem in the oil industry

We address an optimization problem related to the minimization of the distribution costs associated with product delivery in the oil industry. Particularly, the problem consists of determining a schedule of shipments from production ports to satisfy demand and desired inventory limits at consumptions ports. Products are transported in vessels, which can be viewed as a set of shared resources. The complexity of the problem derives from the problem structure and the number of decisions that need to be made throughout a planning horizon. The context that we studied belongs to the family of short sea inventory routing problems for which the ports are in the same geographical area. We formulate a mixed-integer programming model that captures the most relevant features of the real system. The main decisions include the selection of the vessels that will be used, the paths that each vessel will follow, and the quantities of each product loaded and unloaded at each port visited during the planning horizon. We test the limits of our mathematical programming formulation and develop a heuristic approach for tackling problem sizes that exceed the capabilities of a commercial solver.