A two-phase algorithm for the cyclic inventory routing problem

A convex optimization approach for solving the single-vehicle cyclic inventory routing problem

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.

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.

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.

This paper presents a tractable approximation method for reliably finding near-optimal solutions to the cyclic inventory routing problem (IRP) without requiring the specialised modelling skills and computing technology to deploy more exact solution approaches. Together with simultaneously attaining high solution quality and efficiency, the method's contribution to the IRP literature stems from modelling transportation cost in a way that parsimoniously captures (a) complexities of estimating vehicle requirements and (b) the heretofore ignored phenomenon of possible correlation between customer locations and demands. An extensive set of computational settings to test the method's performance indicated that vis-à-vis a well-founded benchmark from the literature, the average gap in cost is just slightly above 1%, with a worst-case gap of 4.8% across all settings.

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

In This Issue

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.

The choice of a suitable time representation plays a major role in designing a computationally efficient planning/scheduling framework. For the time representation to be effective, it needs to capture the nuances of the actual process, while ensuring that the resultant model is tractable and computationally efficient. In this paper, a novel time representation scheme, titled hybrid time discretization, which combines both continuous- and discrete-time representations in a single framework, is proposed and used to solve a complex multiproduct maritime inventory routing problem (MIRP) with undedicated compartments. Several continuous- and discrete-time-based frameworks have been proposed to solve the MIRP over the years. While single-/multigrid discretized frameworks do efficiently capture the time-sensitive nuances of the problem (such as active/inactive jetty hours and hourly/daily variations in the demands), they struggle to solve larger problem instances to the required optimality gap in a reasonable time. This is primarily due to the large disparities among the timings of different task components in the model. On the other hand, continuous-time representation can significantly reduce the problem size and computational effort; however, modeling the entire problem using the continuous-time-based framework could have problems in representing some time-sensitive intricacies in the demands and jetty/port activities. To allay the above-mentioned drawbacks, in this paper, a novel hybrid time representation is proposed, which combines a continuous-time representation with a multigrid discrete-time framework. The proposed novel framework is cast in a rolling horizon strategy and tested on various scenarios generated for the above-mentioned maritime transportation problem, which are shown to be significantly more complex than those presented in the literature. The proposed MILP framework is able to solve most of the test cases to the required optimality in a reasonable time without the need for heuristic or meta-heuristic assists. The proposed hybrid time representation could find significant utility in other lateral applications such as batch scheduling and inventory routing problems.

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

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.

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.

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

A practical solution approach for the cyclic inventory routing problem

In this paper, a special case of inventory routing problem, in which a distribution centre as the supplier distributes a single product to a set of sales-points using economic order quantity policy to manage inventories, is investigated. A fleet of homogeneous vehicles, each with a given capacity, is available for delivery of inventory to the sales-points served by a vehicle in a cyclical manner in such a way that at no moment a stock-out occurs. Demand rates at the sales-points are constant and known to the supplier. The proposed model in this paper extends the concept of vehicle multi-tours considering the inventory costs of the supplier; in other words, the objective is to minimise total ordering and inventory holding costs of the supplier coordinately with fleet operating, sales-points inventory holding and distribution costs during a given planning horizon. The frequency and routes by which each sales-point is to be served and the type of vehicles for this purpose are determined by this model. We have developed a tabu search-based heuristic to solve the problem. Because of the novelty of the model, a set of numerical examples is designed and solved in order to assess the performance of the model.