Solving inventory routing problem with stochastic demand

This work is motivated by the need to solve the inventory routing problem when implementing a business practice called vendor managed inventory replenishment (VMI). With VMI, vendors monitor their customers′ inventories and decide when and how much inventory should be replenished at each customer. The inventory routing problem attempts to coordinate inventory replenishment and transportation in such a way that the cost is minimized over the long run. We formulate a Markov decision process model of the stochastic inventory routing problem and propose approximation methods to find good solutions with reasonable computational effort. We indicate how the proposed approach can be used for other Markov decision processes involving the control of multiple resources.

In this work we introduce a green inventory routing problem termed the Stochastic Inventory Routing Problem on Electric Roads (S-IRP-ER), in which a hybrid vehicle navigates a road network with charging opportunities in some road sections, to cover the non-stationary stochastic demand of a single product for a set of retailers in the network. We model the problem using isochrone graphs to represent the real road network. In an isochrone graph nodes are located such that the time to travel any arc is constant all over the network. This allows for tracking the battery level of the vehicle serving retailers, as it charges and discharges continuously while travelling. We formulate a mathematical programming heuristics and prove its effectiveness. We use our model on a realistic instance of the problem, showcasing the different strategies that a vehicle may follow depending on fuel costs in relation to the costs of electricity.

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 Stochastic Demand Inventory Routing Problem (SDIRP) is a kind of typical NP-hard problem. Considering the coordination and optimization problem of inventory and distribution in the supply chain is the key to implementing vendor managed inventory (VMI) and is one of the most active directions in the OR realm. This paper studies the stochastic demand IRP with hard time windows (SDIRPHTW), and decomposes it into two sub-problems: stochastic inventory problem and routing schedule problem with time windows restriction. Then a heuristic algorithm based Markov Decision Process (MDP) and modified C-W algorithm is presented. Finally, the efficiency of the algorithm is analyzed through a numerical example.

In this paper, we introduce a simulation-based algorithm for solving the single-period Inventory Routing Problem (IRP) with stochastic demands. Our approach, which combines simulation with heuristics, considers different potential inventory policies for each customer, computes their associated inventory costs according to the expected demand in the period, and then estimates the marginal routing savings associated with each customer-policy entity. That way, for each customer it is possible to rank each inventory policy by estimating its total costs, i.e., both inventory and routing costs. Finally, a multi-start process is used to iteratively construct a set of promising solutions for the IRP. At each iteration of this multi-start process, a new set of policies is selected by performing an asymmetric randomization on the list of policy ranks. Some numerical experiments illustrate the potential of our approach.

This paper addresses the inventory routing problem (IRP) with a many-to-one distribution network, consisting of a single depot, an assembly plant, and geographically dispersed suppliers where a capacitated homogeneous vehicle delivers a distinct product from the suppliers to fulfill the demand specified by the assembly plant over the planning horizon. The inventory holding cost is assumed to be product specific and only incurred at the assembly plant. Two metaheuristics comprise of artificial bee colony (ABC) and scatter search (SS) algorithms are proposed to solve the problem. Computational testing on instances which represents small, medium, and large data sets show that the ABC algorithm performs slightly better when compared the SS overall except for fifty suppliers problems.

It presents a practical modeling and solution approach for VMI cyclic inventory routing problem (IRP) under constant customer demand rates. In VMI, the supplier takes the responsibility for replenishing his customers' inventories based on their consumption data, with the aim of optimizing the overall distribution and inventory costs throughout the supply chain. The objective of this IRP problem is to determine a distribution plan that minimizes average distribution and inventory costs without causing any stockout at the customers. Deterministic constant customer demand rates are assumed and therefore, a long-term cyclical approach is adopted, integrating fleet sizing, vehicle routing, and inventory management. Further, realistic side-constraints such as limited storage capacities, driving time restrictions and constant replenishment intervals are taken into account. A heuristic solution approach is proposed, analyzed and evaluated against a comparable heuristic. The heuristic solution approach is well capable of finding the appropriate cost trade-off under varying circumstances. Furthermore, when fleet sizing is not considered, the heuristic outperforms an existing heuristic in finding the two-way trade-off between distribution and inventory costs.

The inventory routing problem with stochastic demand includes the inventory control, product transportation and scheduling decisions, considering an estimation of customer demands. This problem appears in several real situations, playing a fundamental role in reducing costs and improving the efficiency and reliability of the service. In practice, there are often restrictions on the window, which corresponds to a certain period of the day on which deliveries can be made. Despite the great relevance of this type of constraint, there are no results in the literature that combine stochastic demand and time window constraints. In this work, we propose a system, using advanced techniques of operational research, to solve the inventory routing problem with stochastic demand, considering time window constraints, as well as additional constraints of maximum inventory capacities in both the client and the depot and individual confidence level of the customer service.

Swarm intelligence is briefly defined as the collective behavior of decentralized and self-organized swarms. Self-organization and labor division are the two key components of swarm intelligence. Artificial Bee Colony (ABC) algorithm is one of the most recent swarm intelligence-based algorithms. The behavior of bees in ABC algorithm satisfies the self-organization features, but there is no specific labor division mechanism in ABC algorithm. In this work, we propose an improved ABC algorithm called labor division artificial bee colony (LDABC) algorithm by incorporating the labor division mechanism into ABC algorithm, which is achieved by individual specialization and role plasticity. We specify three different search methods for employed bees, onlooker bees and scout bees to realize individual specialization, these search methods are related to food source quality, enable bees to maximize exploitation of food source. Role plasticity is achieved by combining with cellular automata, where the roles of bees are not static but vary with their surrounding environment, enable bees not to limit to one search method. The different search modes and the flexibility of the search behaviors make our algorithm achieve a better balance between exploration and exploitation. The experimental results tested on 13 benchmark functions and CEC-2013 test functions demonstrate a competitive performance.

The artificial bee colony (ABC) algorithm is an important branch of evolutionary algorithms and has been shown to be competitive with other algorithms for solving optimisation problems. However, there are always some insufficiencies in ABC algorithm such as lower convergence speed and easily get trapped in the local optima. To increase depth search capabilities of onlooker bees and ensure scout bees do not discard the current optimal solution, we proposed a modified ABC algorithm (denoted as ORABC) based on the optimisation strategy and retained strategy of the best individual in this paper. Compared with ABC algorithm, ABC* (added retained strategy to ABC) and ORABC algorithm, experiments are conducted on a set of numerical benchmark functions. The numerical simulation results demonstrate that ORABC algorithm improves the convergence characteristics of ABC algorithm and provides very remarkable performance in solving complex numerical optimisation problems compared to original algorithm.

A solution approach to the inventory routing problem in a three-level distribution system

In today's business landscape, demand variability plays a crucial role in determining the success of companies across various industries. This article explores the concept of demand variability, encompassing both deterministic and stochastic demand patterns. We delve into the differences between these demand types and their implications for businesses. The article emphasizes the significance of accurate demand forecasting and its role in strategic decision-making. Deterministic demand, characterized by predictable patterns, allows businesses to forecast with certainty. On the other hand, stochastic demand introduces uncertainty, requiring statistical methods and probability theory for estimation and management. Furthermore, we explore the distinction between stochastic stationary demand and stochastic nonstationary demand. While the former maintains consistent statistical properties over time, the latter experiences fluctuations in its characteristics due to external factors. We highlight the challenges faced by businesses in forecasting and managing nonstationary demand and the need for adaptive forecasting methods. To successfully navigate today's dynamic market, companies must embrace advanced analytics and data-driven approaches. By leveraging historical data, statistical models, and forecasting techniques, businesses can gain valuable insights into demand patterns, optimize inventory management, and make informed strategic decisions. Ultimately, understanding and managing demand variability is paramount for businesses seeking to improve customer satisfaction, optimize operations, and enhance their competitive advantage. This article aims to provide a comprehensive understanding of demand variability and equip readers with insights and strategies to tackle the challenges posed by an ever-changing market landscape.

INTRODUCTION: The artificial bee colony (ABC) algorithm is a nature-inspired technique used for solving different optimization problems. This paper presents a multi-hive ABC algorithm for solving constrained benchmark functions of CEC2006. The CEC2006 data set contains the global benchmark functions with different design variables, number and type of constraints. OBJECTIVES: The objective of the proposed work is to design and apply the GPGPU based multi-hive ABC algorithm to solve constrained optimization problems. METHODS: The proposed approach is a multi-population coarse-grained system implemented using General Purpose Graphics Processing Unit (GPGPU). The performance of the proposed approach is compared with the serial ABC algorithm for eleven benchmark functions and results in the literature. The multi-hive ABC algorithm has multiple hives, each running separate ABC algorithm on different cores of GPGPU. RESULTS: The proposed approach provides global best solutions in significantly reduced time for all benchmark functions. The speed-up obtained is approximately 7X to 9X. The GPGPU device utilization is approximately 57% to 91%. CONCLUSION: The GPGPU based multi-hive ABC algorithm is a found good with respect to best results, speed up factor and GPU utilization to solve constrained optimization problems.

This paper presents a detailed study concerning the importance of the planning horizon when solving inventory routing problems (IRPs). We evaluate the quality of decisions obtained by solving a finite‐horizon IRP. We also discuss the relevance of explicitly considering profit maximization models rather than the traditional cost minimization variant. As a means to this end, we describe four classes of the IRP corresponding to different types of markets. Two of them lead to nonlinear models, which are linearized. Furthermore, we provide a deterministic simulator to evaluate the long‐term effects arising from using planning horizons of varying lengths when solving the IRP. A computational study is performed on cases generated from benchmark data instances. The results confirm that the long‐term performance of the IRP decisions is, in part, contingent on the length of the selected planning horizon. They also show that considering profit maximization instead of cost minimization leads to different decisions, generating considerably more revenue and profits, albeit not nearly as much as suggested by individual solutions to static IRPs with short planning horizons.

A practical solution approach for the cyclic inventory routing problem