The inventory-routing problem (IRP) dates back 30 years. It can be described as the combination of vehicle-routing and inventory management problems, in which a supplier has to deliver products to a number of geographically dispersed customers, subject to side constraints. It provides integrated logistics solutions by simultaneously optimizing inventory management, vehicle routing, and delivery scheduling. Some exact algorithms and several powerful metaheuristic and matheuristic approaches have been developed for this class of problems, especially in recent years. The purpose of this article is to provide a comprehensive review of this literature, based on a new classification of the problem. We categorize IRPs with respect to their structural variants and the availability of information on customer demand.

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Thirty Years of Inventory Routing

A review on recent sizing methodologies of hybrid renewable energy systems

Rich vehicle routing problems: From a taxonomy to a definition

https://www.cirrelt.ca/DocumentsTravail/CIRRELT-2013-49.pdf

The production routing problem

The inventory routing problem (IRP) and the production routing problem (PRP) are two difficult problems arising in the planning of integrated supply chains. These problems are solved in an attempt to jointly optimize production, inventory, distribution, and routing decisions. Although several studies have proposed exact algorithms to solve the single-vehicle problems, the multivehicle aspect is often neglected because of its complexity. We introduce multivehicle PRP and IRP formulations, with and without a vehicle index, to solve the problems under both the maximum level (ML) and order-up-to level (OU) inventory replenishment policies. The vehicle index formulations are further improved using symmetry breaking constraints; the nonvehicle index formulations are strengthened by several cuts. A heuristic based on an adaptive large neighborhood search technique is also developed to determine initial solutions, and branch-and-cut algorithms are proposed to solve the different formulations. The results show tha...

Formulations and Branch-and-Cut Algorithms for Multivehicle Production and Inventory Routing Problems

This paper introduces a robust inventory routing problem where a supplier distributes a single product to multiple customers facing dynamic uncertain demands over a finite discrete time horizon. The probability distribution of the uncertain demand at each customer is not fully specified. The only available information is that these demands are independent and symmetric random variables that can take some value from their support interval. The supplier is responsible for the inventory management of its customers, has sufficient inventory to replenish the customers, and distributes the product using a capacitated vehicle. Backlogging of the demand at customers is allowed. The problem is to determine the delivery quantities as well as the times and routes to the customers, while ensuring feasibility regardless of the realized demands, and minimizing the total cost composed of transportation, inventory holding, and shortage costs. Using a robust optimization approach, we propose two robust mixed integer programming (MIP) formulations for the problem. We also propose a new MIP formulation for the deterministic (nominal) case of the problem. We implement these formulations within a branch-and-cut algorithm and report results on a set of instances adapted from the literature.

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Robust Inventory Routing Under Demand Uncertainty

We address a vendor-managed inventory-routing problem where a supplier (vendor) receives a given amount of a single product each period and distributes it to multiple retailers over a finite time horizon using a capacitated vehicle. Each retailer faces external dynamic demand and is controlled by a deterministic order-up-to level policy requiring that the supplier raise the retailer's inventory level to a predetermined maximum in each replenishment. The problem is deciding on when and in what sequence to visit the retailers such that systemwide inventory holding and routing costs are minimized. We propose a branch-and-cut algorithm and a heuristic based on an a priori tour using a strong formulation. To the best of our knowledge, this study is the first to consider a strong formulation for the inventory replenishment part of inventory-routing problems. Computational results reveal that the new branch-and-cut algorithm and heuristic perform better than those noted in the literature.

A Branch-and-Cut Algorithm Using a Strong Formulation and an A Priori Tour-Based Heuristic for an Inventory-Routing Problem

Optimal sizing of stand-alone photovoltaic systems in residential buildings

This paper proposes an optimization model to determine the optimal tank size of a single residential housing unit for rainwater harvesting and storage. Taking into account the site specific data such as the rainfall profile, the roof area of the building, the water consumption per capita and the number of residents, an integrated optimization model based on linear programming is proposed to decide on the size of rainwater storage tank to build such that the net present value of the total tank construction costs and freshwater purchase costs is minimized. The proposed model was tested on a case study from Northern Cyprus, the results of which emphasized the feasibility of rainwater harvesting as a sustainable supplement to the depleting aquifers in the region. The study also offers managerial insights on the impact of various parameters such as the number of residents, roof area, discount rate, water consumption per capita, unit cost of building the rainwater tank, and rainfall characteristics on the optimal tank size and on the net financial benefit gained from rainwater harvesting through detailed sensitivity analysis.

Optimal sizing of storage tanks in domestic rainwater harvesting systems: A linear programming approach

The production-routing problem can be seen as a combination of two well known combinatorial optimization problems: the lotsizing and the vehicle routing problems. The variant considered in this paper consists in designing a production schedule for an uncapacitated plant, replenishment schedules for multiple customers, and a set of routes for a single uncapacitated vehicle starting and ending at the plant. The aim of the problem is to fulfill the demand of the customers over a finite horizon such that the total cost of distribution, setups, and inventories is minimized. This paper introduces a basic mixed integer linear programming formulation and several strong reformulations of the problem. Two families of valid inequalities, 2-matching and generalized comb inequalities, are introduced to strengthen these formulations, and they are used within a branch-and-cut algorithm. Computational results on a large set of randomly generated instances are presented. Instances with up to 40 customers and 15 time periods or with 80 customers and 8 periods have been solved to optimality within a two-hour limit. The tests clearly indicate the effectiveness of the new formulations and of the valid inequalities. In addition, an uncoordinated approach is considered to demonstrate the benefits of the simultaneous optimization of production and distribution planning. The total cost increases on average by 47% when employing such an uncoordinated approach. Finally, a heuristic algorithm, based on defining an a priori tour for the vehicle routing part, is investigated. The heuristic algorithm shows an excellent performance. The average CPU time is less than 1% of the CPU time for the optimal solution, whereas the average cost increase is only 0.33%.

Oğuz Solyalı

Papers

Robust Inventory Routing Under Demand Uncertainty

A Branch-and-Cut Algorithm Using a Strong Formulation and an A Priori Tour-Based Heuristic for an Inventory-Routing Problem

Optimal sizing of stand-alone photovoltaic systems in residential buildings

Optimal sizing of storage tanks in domestic rainwater harvesting systems: A linear programming approach

Efficient Formulations and a Branch-and-Cut Algorithm for a Production-Routing Problem