Leandro C. Coelho

Thirty Years of Inventory Routing

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.

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.

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.

Optimal joint replenishment, delivery and inventory management policies for perishable products

In this paper we analyze the optimal joint decisions of when, how and how much to replenish customers with products of varying ages. We discuss the main features of the problem arising in the joint replenishment and delivery of perishable products, and we model them under general assumptions. We then solve the problem by means of an exact branch-and-cut algorithm, and we test its performance on a set of randomly generated instances. Our algorithm is capable of computing optimal solutions for instances with up to 30 customers, three periods, and a maximum age of two periods for the perishable product. For the unsolved instances the optimality gap is always small, less than 1.5% on average for instances with up to 50 customers. We also implement and compare two suboptimal selling priority policies with an optimized policy: always sell the oldest available items first to avoid spoilage, and always sell the fresher items first to increase revenue.

A branch-and-cut algorithm for the multi-product multi-vehicle inventory-routing problem

The combined operation of distribution and inventory control achieved through a vendor-managed inventory strategy creates a synergetic interaction that benefits supplier and customers. Inventory-Routing Problems (IRPs) arise when inventory and routing decisions must be taken simultaneously, which yields a difficult combinatorial optimisation problem. While most IRP research deals with a single product, there are often several products involved in distribution activities. In this paper, we propose a branch-and-cut algorithm for the solution of IRPs with multiple products and multiple vehicles. We formally define and model the problem, and we solve it exactly. We also consider the inclusion of consistency features that are meaningful in a multi-product environment and help improve the quality of the service offered.

Heuristics for dynamic and stochastic inventory-routing

The combination of inventory management and vehicle routing decisions yields a difficult combinatorial optimization problem called the Inventory-Routing Problem (IRP). This problem arises when both types of decisions must be made jointly, which is the case in vendor-managed inventory systems. The IRP has received significant attention in recent years, with several heuristic and exact algorithms available for its static and deterministic versions. In the dynamic version of the IRP, customer demands are gradually revealed over time and planning must be made at the beginning of each of several periods. In this context, one can sometimes take advantage of stochastic information on demand through the use of forecasts. We propose different heuristic policies to handle the dynamic and stochastic version of the IRP. We perform an extensive computational analysis on randomly generated instances in order to compare several solution policies. Amongst other conclusions we show that it is possible to take advantage of stochastic information to generate better solutions albeit at the expense of more computing time. We also find that the use of a longer rolling horizon step does not help improve solutions. Finally, we show that ensuring consistent solutions over time increases the cost of the solutions much more under a dynamic environment than in a static setting.

O impacto do compartilhamento de informações na redução do efeito chicote na cadeia de abastecimento

The objective of this paper is to emphasize the importance of sharing data in a supply chain, as a strategy to reduce the bullwhip effect. To achieve this effect, its causes, the ways it shows itself and the means to avoid it are presented. In order to facilitate the understanding about the damages caused by its influence, a hypothetical scenario is suggested, in which the components of a supply chain try to align its offer to its demand. Next, based on a bibliographical research, the solution - the strategic alignment and the information sharing - are shown, thus creating the synergy needed for developing competitive advantage for the company and/or for the chain. Finally, to support this solution, we created an indicator based on a supply chain, simulated several times in the classroom using software, which demonstrated the positive effects of sharing data.

Flexibility and consistency in inventory-routing

In many contexts, logistics is used to enable competitive advantages and cost savings. For some companies, logistics itself is its core competency (i.e., logistics providers). In this context, vendor-managed inventory (VMI) systems are one of the most up-to-date strategies allowing companies to reach a superior performance. Under a VMI strategy, the replenishment and distribution making process is centralized at the supplier’s level, leading to an overall reduction of logistics costs. In order to operate a VMI system, an Inventory-Routing Problem (IRP) has to be solved, simultaneously making inventory management and routing decisions over several periods. Our purpose is to introduce two new concepts, called flexibility and consistency, within the context of the IRP. Flexibility will be added through the possibility of sharing inventory among locations, making the concept of transshipment available within inventory-routing. It is also useful to react quickly to changes in the demand in a dynamic and stochastic environment. Transshipment problems are typically characterized by movements of goods among entities of the same level, such as customers. They allow the system to share stockout risks and to increase the flexibility of the decision maker by increasing the number of sources from which goods can be transferred. We then introduce the Inventory-Routing Problem with Transshipment (IRPT), a problem in which the decision maker has the option to plan transshipment movements so as to minimize the total system cost. This problem arises, for instance, when solving stochastic Inventory-Routing Problems (SIRP) in a rolling horizon framework where one uses demand forecasts for the next time periods as approximations of the unknown demand. We present a formulation that allows transshipments, either from the supplier to customers or between customers. We develop a branch-and-cut algorithm capable of solving small and medium size instances. We also propose an adaptive large neighborhood search heuristic to solve larger instances. 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 maxi-

A Comparison of Several Enumerative Algorithms for Sudoku

Sudoku is a puzzle played of an n × n grid where n is the square of a positive integer m. The most common size is n=9. The grid is partitioned into n subgrids of size m × m. The player must place exactly one number from the set N={1, …, n} in each row and each column of as well as in each subgrid. A grid is provided with some numbers already in place, called givens. In this paper, some relationships between Sudoku and several operations research problems are presented. We model the problem by means of two mathematical programming formulations. The first one consists of an integer linear programming model, while the second one is a tighter non-linear integer programming formulation. We then describe several enumerative algorithms to solve the puzzle and compare their relative efficiencies. Two basic backtracking algorithms are first described for the general Sudoku. We then solve both formulations by means of constraint programming. Computational experiments are performed to compare the efficiency and effectiveness of the proposed algorithms. Our implementation of a backtracking algorithm can solve most benchmark instances of size 9 within 0.02 s, while no such instance was solved within that time by any other method. Our implementation is also much faster than an existing alternative algorithm.