Dynamic Programming Approximations for a Stochastic Inventory Routing Problem

We consider an inventory routing problem with stochastic demand where the demand is expressed in a probabilistic sense and it is dynamic in which the demand is gradually revealed at the end of each period. The problem is known as dynamic and stochastic inventory routing problem (DSIRP). DSIRP distribution network consists of a supplier and a set of retailers is considered. A limited number of single product is assumed to be produced by the supplier and a holding cost per unit product is incurred at both the supplier. The demand is assumed to follow the binomial probability distribution. We adopt an order-up-to level inventory policy and each unit of positive inventory at the retailer is incurred a holding cost, while the unmet demand (stock-out) is penalized. We assumed that the transportation of the product from supplier to the retailers is handled by a third party. The aim of DSIRP is to minimize the total expected cost which includes the inventory cost at supplier, inventory cost at retailers, stockout cost at retailers and transportation cost. The DSIRP is modeled as a Markov decision process (MDP) where the state in period t is represented as the inventory level for all retailers. A hybrid rollout algorithm where a Mixed Integer Linear Programming of the problem is used to obtain the control in each state. We also proposed an Artificial Bee Colony (ABC) algorithm to obtain a feasible and better controls. Computational experiments is conducted using an existing benchmark problem.

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 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.

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.

PurposeThis study aims to design a supply chain network in an uncertain environment while exists two options for distribution of the perishable product and production lot-sizing is concerned.Design/methodology/approachOwing to the complexity of the mathematical model, a solution approach based on a Lagrangian relaxation (LR) heuristic is developed which provides good-quality upper and lower bounds.FindingsThe model output is discussed through various examples. The introduction of some enhancements and using some heuristics results in better outputs in the solution procedure.Practical implicationsThis paper covers the modeling of some real-world problems in which demand is uncertain and managers face making some concurrent decisions related to supply chain management, transportation and logistics and inventory control issues. Furthermore, considering the perishability of product in modeling makes the problem more practically significant as these days there are many supply chains handling dairy and other fresh products.Originality/valueConsidering uncertainty, production, transshipment and perishable product in the inventory-routing problem makes a new variant that has not yet been studied. The proposed novel solution is based on the LR approach that is enhanced by some heuristics and some valid inequalities that make it different from the current version of the LR used by other studies.

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.

A genetic algorithm-Taguchi based approach to inventory routing problem of a single perishable product with transshipment

This work proposes a multi-objective extension of a real-world inventory routing problem (IRP), a generalisation of the classical vehicle routing problem (VRP) with vendor managed inventory (VMI) replenishment. While many mathematical formulations and solution models already exist, this study incorporates business-related and risk considerations that makes it unique. It is known that a significant volume of hazardous materials travels every day. Consideration of risks arising from the transportation of hazardous materials as a criterion for selecting distribution routes could potentially reduce the likelihood of accidents and/or the expected consequences of accidents.

In this study, a two phase hybrid heuristic approach was proposed to solve the multi-depot multi-vehicle inventory routing problem (MDMVIRP). Inventory routing problem (IRP) is one of the major issues in the supply chain networks that arise in the context of vendor managed systems (VMI) The MDMVIRP combines inventory management and routing decision. We are given on input a fleet of homogeneous vehicles, in which any of these vehicles have a capacity and a fixed cost. Also, a set of distribution centers with restricted capacities are responsible to serve the customer’s demands, which are known for distributer at beginning of each period. The problem consists of determining the delivery quantity to the customers at each period and the routes to be performed to satisfy the demand of the customers. The objective function of this problem is to minimize sum of the holding cost at distributer centers and the customers, and of the transportation costs associated to the preformed routes. In the proposed hybrid heuristic method, after a Construction phase (first phase) a modified variable neighborhood search algorithm (VNS), with distinct neighborhood structures, is used during the improvement phase (second phase). Moreover, we use simulated annealing (SA) concept to avoid that the solution remains in a local optimum for a given number of iterations. Computational results on benchmark instances that adopt from the literature of IRP indicate that the proposed algorithm is capable to find, within reasonable computing time, several solutions gained by the approaches that applied in the previous published studies.

This study considers a stochastic inventory relocation problem for a one-way, station-based car-sharing system that utilises electric vehicles (EV), where customers' rental demands and rented vehicles' travel distances are uncertain and temporal-spatial imbalance. Workers are hired to relocate vehicles between stations. To maximise the total expected profits that can be collected by the system, a worker must determine whether to relocate an EV, which vehicle to choose, and which station to move the EV to upon their arrival at a rental station. The problem is formulated as a Markov decision process (MDP). A reinforcement learning algorithm is proposed to develop dynamic policies for the problem. The reinforcement learning algorithm uses an approximate value iteration (AVI) algorithm to overcome the computational challenges arising from the extensive state and action space. Action-space restriction and state-space aggregation schemes are developed to enhance the performance of the AVI algorithm. The effectiveness of the proposed modelling and solution methodologies is demonstrated through a comparison of the dynamic policies against benchmark solutions. Additionally, sensitivity analyses are conducted to investigate whether parameter configurations will impact the performance of the dynamic policies.

We consider an inventory routing problem (IRP) in the liquefied natural gas (LNG) supply chain, called the LNG-IRP. Here, an actor is responsible for the LNG production and inventory management at the liquefaction plants, the routing and scheduling of a heterogeneous fleet of LNG ships, as well as the inventories and sales at the regasification terminals. Furthermore, all ports have a limited number of berths available for loading and unloading. The LNG-IRP is more complicated than many other maritime inventory routing problems because a constant rate of the cargo evaporates in the tanks each day and is used as fuel during transportation. In addition, a variable number of tanks are unloaded at the regasification terminals. We introduce a new path flow formulation for this problem arising from a novel decomposition scheme based on parts of a ship schedule, called duties. A ship schedule for the entire planning horizon can be divided into duties consisting of a visit to a liquefaction plant, then one or two visits to a regasification terminal before ending in a liquefaction plant. The solution method suggested is based on a priori generation of duties, and the formulation is strengthened by valid inequalities. The same problem was previously solved by a branch-price-and-cut algorithm for a schedule-based formulation. Computational results show that the new formulation provides tighter bounds than the previous schedule-based formulation. Furthermore, on a set of 27 benchmark instances, the proposed algorithm clearly outperforms the previous branch-price-and-cut algorithm both with regard to computational time and the number of problems solved within a 10-h time limit.

Modelling and comparison of stability metrics for a re-optimisation approach of the Inventory Routing Problem under demand uncertainty

A matheuristic solution approach for the production routing problem with visit spacing policy

CARE: Heuristics for two-stage multi-product inventory routing problems with replenishments

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.