A maritime inventory routing problem: Practical approach

Despite of the practicality of the motivation of the inventory routing problem (IRP), there are few successful implementation stories of IRP based decision support systems which utilize optimization algorithms. Besides the fact that the IRP is an extremely challenging optimization problem, simplifications and assumptions made in the definition of typical IRP in the literature make it even more difficult to take advantage of the developed technologies for IRP in practice. This paper introduces a flexible modeling framework for IRP, which can accommodate various practical features. A simple algorithmic framework of an optimization based heuristic method is also proposed. A case study on a practical maritime inventory routing problem (MIRP) shows that the proposed modeling and algorithmic framework is flexible and effective enough to be a choice of model and solution method for practical inventory routing problems.     

A heuristic method for the inventory routing and pricing problem in a supply chain

The inventory routing problem (IRP) in a supply chain (SC) is to determine delivery routes from suppliers to some geographically dispersed retailers and inventory policy for retailers. In the past, the pricing and demand decisions seem ignored and assumed known in most IRP researches. Since the pricing decision affects the demand decision and then both inventory and routing decisions, it should be considered in the IRP simultaneously to achieve the objective of maximal profit in the supply chain. In this paper, a mathematical model for the inventory routing and pricing problem (IRPP) is proposed. Since the solution for this model is an NP (non-polynomial) problem, a heuristic method, tabu search adopting different neighborhood search approaches, is used to obtain the optimal solution. The proposed heuristic method was compared with two other methods considering the IRPP separately. The experimental results indicate that the proposed method is better than the two other methods in terms of average profit.     

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

The 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.     

The exact solution of several classes of inventory-routing problems

In order to be competitive companies need to take advantage of synergistic interactions between different decision areas. Two of these are related to the distribution and inventory management processes. Inventory-Routing Problems (IRPs) arise when inventory and routing decisions must be made simultaneously, which yields a difficult combinatorial optimization problem. In this paper, we propose a branch-and-cut algorithm for the exact solution of several classes of IRPs. Specifically, we solve the multi-vehicle IRP with a homogeneous and a heterogeneous fleet, the IRP with transshipment options, and the IRP with added consistency features. We perform an extensive computational analysis on benchmark instances.     

The Flexible Periodic Vehicle Routing Problem

This paper introduces the Flexible Periodic Vehicle Routing Problem (FPVRP) where a carrier has to establish a distribution plan to serve his customers over a planning horizon. Each customer has a total demand that must be served within the horizon and a limit on the maximum quantity that can be delivered at each visit. A fleet of homogeneous capacitated vehicles is available to perform the services and the objective is to minimize the total routing cost. The FPVRP can be seen as a generalization of the Periodic Vehicle Routing Problem (PVRP) which instead has fixed service frequencies and schedules and where the quantity delivered at each visit is fixed. Moreover, the FPVRP shares some common characteristics with the Inventory Routing Problem (IRP) where inventory levels are considered at each time period and, typically, an inventory cost is involved in the objective function. We present a worst-case analysis which shows the advantages of the FPVRP with respect to both PVRP and IRP. Moreover, we propose a mathematical formulation for the problem, together with some valid inequalities. Computational results show that adding flexibility improves meaningfully the routing costs in comparison with both PVRP and IRP.     

基于改进粒子群算法的异质车队二级IRP优化

针对供货商管理库存（Vendor Managed Inventory,VMI）模式下的二级库存路径问题（Inventory Routing Problem,IRP）,结合需求的波动特征,以二级库存路径问题系统总成本最小化为目标,建立异质车队的二级库存路径问题混合整数规划模型,并设计改进的粒子群算法对模型求解。数值实验分析验证了模型和算法的适用性和有效性,结果显示,使用异质车队不仅可以提高配送车辆的装载率,降低零售商的库存水平,还会减少二级库存路径问题系统总成本;敏感性分析表明,不论需求波动程度怎样变化,使用异质车队时二级库存路径问题系统总成本都会得到降低。     

Variable Neighborhood Search heuristic for the Inventory Routing Problem in fuel delivery

In this paper we observe the extension of the vehicle routing problem (VRP) in fuel delivery that includes petrol stations inventory management and which can be classified as the Inventory Routing Problem (IRP) in fuel delivery. The objective of the IRP is to minimize the total cost of vehicle routing and inventory management. We developed a Variable Neighborhood Search (VNS) heuristic for solving a multi-product multi-period IRP in fuel delivery with multi-compartment homogeneous vehicles, and deterministic consumption that varies with each petrol station and each fuel type. The stochastic VNS heuristic is compared to a Mixed Integer Linear Programming (MILP) model and the deterministic “compartment transfer” (CT) heuristic. For three different scale problems, with different vehicle types, the developed VNS heuristic outperforms the deterministic CT heuristic. Also, for the smallest scale problem instances, the developed VNS was capable of obtaining the near optimal and optimal solutions (the MILP model was able to solve only the smallest scale problem instances).     

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.     

A coordinated approach to hedge the risks in stochastic inventory-routing problem

The inventory routing problem (IRP) studied in this research involves repeated delivery of products from a depot to a set of retailers that face stochastic demands over a long period. The main objective in the IRP is to design the set of routes and delivery quantities that minimize transportation cost while controlling inventory costs. Traditional IRP focuses on risk-neutral decision makers, i.e., characterizing replenishment policies that maximize expected total net present value, or equivalently, minimize expected total cost over a planning horizon. In this research, for incorporating risk aversion, a hedge-based stochastic inventory-routing system (HSIRS) integrated with Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model and Forward Option Pricing (FOP)model based on Black-Scholes model, from hedge point of view, is proposed to solve the multi-product multi-period inventory routing problem with stochastic demand. Computational results demonstrate the importance of this approach not only to risk-averse decision makers, but also to maximize the net present value at an acceptable service level. As a result, an optimal portfolio (R, s, S) system of product group can be generated to maximize the net present value under an acceptable service level in a given planning horizon. Meanwhile, the target group needed to be served and the relative transportation policy also can be determined accordingly based on the time required to be served as a priori partition to minimize the average transportation costs; hence, the routing assignment problem can be successfully optimized through a Predicting Particle Swarm Optimization algorithm.     

The inventory-routing problem with transshipment

This paper introduces the Inventory-Routing Problem with Transshipment (IRPT). This problem arises when vehicle routing and inventory decisions must be made simultaneously, which is typically the case in vendor-managed inventory systems. Heuristics and exact algorithms have already been proposed for the Inventory-Routing Problem (IRP), but these algorithms ignore the possibility of performing transshipments between customers so as to further reduce the overall cost. We present a formulation that allows transshipments, either from the supplier to customers or between customers. We also propose an adaptive large neighborhood search heuristic to solve the problem. This heuristic manipulates vehicle routes while the remaining problem of determining delivery quantities and transshipment moves is solved through a network flow algorithm. Our approach can solve four different variants of the problem: the IRP and the IRPT, under maximum level and order-up-to level policies. We perform an extensive assessment of the performance of our heuristic.     

Considering lost sale in inventory routing problems for perishable goods

This paper presents a mathematical model for an inventory routing problem (IRP). The model is especially designed for allocating the stock of perishable goods. It is assumed that the age of the perishable inventory has a negative impact on the demand of end customers and a percentage of the demand is considered as lost sale. The proposed model balances the transportation cost, the cost of inventory holding and lost sale. In addition to the usual inventory routing constraints, we consider the cost of lost sale as a linear or an exponential function of the inventory age. The proposed model is solved to optimality for small instances and is used to obtain lower bounds for larger instances. We have also devised an efficient meta-heuristic algorithm to find good solutions for this class of problems based on Simulated Annealing (SA) and Tabu Search (TS). Computational results indicate that, for small problems, the average optimality gaps are less than 10.9% and 13.4% using linear and exponential lost sale functions, respectively. Furthermore, we show that the optimality gaps found by CPLEX grow exponentially with the problem size while those obtained by the proposed meta-heuristic algorithm increase linearly.     

基于多代理系统方法的存贮路径问题研究

在分析现有研究成果的基础上,运用智能化的多代理技术建模方法,将问题抽象映射成为4类自治的Agent,构造存贮路径问题（Inventory Routing Problem,IRP）的多代理模型,通过Agent间的通信与协作完成问题的求解,为该问题的处理探索一条新的途径。     

Iterated local search and simulated annealing algorithms for the inventory routing problem

This paper addresses the inventory routing problem (IRP), which consists in defining the customer visit schedule, the delivery quantities, and the vehicle routing plan to meet the demands of a set of customers over a given time horizon. We consider the variant with a single item, a single supplier, multiple vehicles, and a finite multiperiod planning horizon, minimizing the sum of inventory and travel costs. In addition, we address an alternative objective function that minimizes the logistic ratio, defined as the total travel cost divided by the total quantity delivered to customers. This second objective function, while more realistic in some logistics settings, poses a challenge for integer programming models and exact methods because of its nonlinearity. To our knowledge, no heuristic method has been proposed to address this objective in the IRP variant addressed in this paper. To solve this problem with each of these objective functions, we propose effective metaheuristic algorithms based on iterated local search and simulated annealing. Computational experiments show that these algorithms provide reasonably high‐quality solutions in relatively short running times for both objective functions when compared to other methods for well‐known instances from the literature. Moreover, the algorithms produce new best solutions for some of these instances.     

The production routing problem: A review of formulations and solution algorithms

The production routing problem (PRP) combines the lot-sizing problem and the vehicle routing problem, two classical problems that have been extensively studied for more than half a century. The PRP is solved in an attempt to jointly optimize production, inventory, distribution and routing decisions and is thus a generalization of the inventory routing problem (IRP). Although the PRP has a complicated structure, there has been a growing interest in this problem during the past decade in both academia and industry. This article provides a comprehensive review of various solution techniques that have been proposed to solve the PRP. We attempt to provide an in-depth summary and discussion of different formulation schemes and of algorithmic and computational issues. Finally, we point out interesting research directions for further developments in production routing.     

近年来库存路径问题研究动态及展望

在概括总结2009年之前IRP研究成果的基础上,从IRP问题类型、求解算法、国内外研究差异、研究重点、研究特点、主要成就等方面分析了2009以来库存路径问题(IRP)国内外研究状况。总结了2009年以来IRP研究在问题层级数和行业应用方面的不足,指出以行业具体需求为导向的多层级IRP深入细化研究是未来发展的趋势。     

A multi-start algorithm to design a multi-class classifier for a multi-criteria ABC inventory classification problem

In this paper we deal with the problem of designing a classifier able to learn the classification of existing units in inventory and then use it to classify new units according to their attributes in a multi-criteria ABC inventory classification environment. To solve this problem we design a multi-start constructive algorithm to train a discrete artificial neural network using a randomized greedy strategy to add neurons to the network hidden layer. The process of weights’ searching for the neurons to be added is based on solving linear programming formulations. The computational experiments show that the proposed algorithm is much more efficient when the dual formulations are used to find the weights of the network neurons and that the obtained classifier has good levels of generalization accuracy. In addition, the proposed algorithm can be straight applied to other multi-class classification problems with more than three classes.     

具单周期特性的短生命周期产品随机IRP及算法

为优化企业物流系统,针对单周期,短生命周期产品的特点,将库存控制与配送路径安排决策集成,考虑随机需求、缺货成本、积压贬值成本、配送成本等,建立一个具有单周期特性的短生命周期产品随机IRP离散模型,目标是合理确定各零售门店的订购数量及配送路线使得系统成本最小。该问题属于NP-hard问题。对此,采用“报童模型”和差分法求解最佳订购量,将模型予以转化,并设计了一种遗传算法进行求解。算例结果表明所提算法能在较短时间内求解出不同客户数目组合的满意解。结论是：门店订购量宜采用组合选择方式;系统成本与单位行程运价正相关;车容量增大有助于降低系统成本。     

Integrated Inventory Control and Facility Location Decisions in a Multi-Echelon Supply Chain Network with Hubs

This paper develops mathematical models to coordinate facility location and inventory control for a four-echelon supply chain network consisting of multiple suppliers, warehouses, hubs and retailers. The hubs help in reducing transportation costs by consolidating products from multiple warehouses and directing the larger shipments to the retailer. The integrated models studied in this paper simultaneously determines three types of decisions: (i) facility location—the number and location of warehouses and hubs, (ii) allocation—assignment of suppliers to located warehouses and retailers to located warehouses via the location hubs, and (iii) inventory control decisions at each located warehouse. The goal is to minimize the facility location, transportation and the inventory costs. A mixed integer nonlinear programming formulation is first presented. The nonlinear integer programming formulation is then transformed into a conic mixed integer program and a novel and compact conic mixed integer programming formulation. Computational runs are conducted using commercial solvers to compare the performance of the different formulations. The compact conic mixed integer programming formulation was found to significantly outperform the other formulations by achieving significant computational savings. The results demonstrate that large scale instances of certain multi-echelon supply chain network design problems can be solved using commercial solvers through intelligent reformulation of the model.     

基于IRP的高校教育信息管理系统集成研究*

IRP新技术是对信息从采集、处理、传输到使用的全面规划。把其应用于高校教育信息管理系统中并与实践相结合,解决信息孤岛,实现信息共享。本文从IRP的理论体系入手,分析了IRP应用技术,基于IRP技术规划了高校教育信息管理系统的实施步骤,初步提出了数据的整合集成等方案,为现有系统的集成改造提供了新的方法。     

Multi-period Vehicle Routing Problem with Due dates

In this paper we study the Multi-period Vehicle Routing Problem with Due dates (MVRPD), where customers have to be served between a release and a due date. Customers with due dates exceeding the planning period may be postponed at a cost. A fleet of capacitated vehicles is available to perform the distribution in each day of the planning period. The objective of the problem is to find vehicle routes for each day such that the overall cost of the distribution, including transportation costs, inventory costs and penalty costs for postponed service, is minimized. We present alternative formulations for the MVRPD and enhance the formulations with valid inequalities. The formulations are solved with a branch-and-cut algorithm and computationally compared. Furthermore, we present a computational analysis aimed at highlighting managerial insights. We study the potential benefit that can be achieved by incorporating flexibility in the due dates and the number of vehicles. Finally, we highlight the effect of reducing vehicle capacity.