An effective heuristic for solving a combined cargo and inventory routing problem in tramp shipping

In this paper a vendor managed inventory (VMI) service in tramp shipping is considered. VMI takes advantage of introducing flexibility in delivery time and cargo quantities by transferring inventory management and ordering responsibilities to the vendor which in this case is a shipping company. A two-phase heuristic is proposed to determine routes and schedules for the shipping company. The heuristic first converts inventories into cargoes, thus turning the problem into a classic ship routing and scheduling problem. It then uses adaptive large neighborhood search to solve the resulting cargo routing and scheduling problem. The heuristic iteratively changes the cargoes generated to handle the customer’s inventories, based on the information obtained from an initial solution. Computational results are presented, discussed and compared with exact solutions on large realistic instances. The results reveal the potential savings from converting traditional contracts of affreightment to an integrated VMI service. The factors that influence the benefits obtainable through VMI are also analyzed.     

Scheduling activities at oil wells with resource displacement

Before promising locations at petroliferous basins become productive oil wells, it is necessary to complete development activities at these locations. The scheduling of such activities must satisfy several conflicting constraints and attain a number of goals. Moreover, resource displacements between wells are important and must also be taken into account. The problem is NP‐hard, as can be seen by a simple poly‐time reduction from the Job Shop problem. This paper describes Greedy Randomized Adaptive Search Procedures (GRASPs) for the scheduling of oil well development activities with resource displacement. The heuristics were tested on real instances from a major oil company, recognized for its expertise in offshore oil exploration. Computational experiments over real instances revealed that the GRASP implementations are competitive, outperforming the software currently being used by the company.     

A maritime inventory routing problem with stochastic sailing and port times

This paper describes a stochastic short sea shipping problem where a company is responsible for both the distribution of oil products between islands and the inventory management of those products at consumption storage tanks located at ports. In general, ship routing and scheduling is associated with uncertainty in weather conditions and unpredictable waiting times at ports. In this work, both sailing times and port times are considered to be stochastic parameters. A two-stage stochastic programming model with recourse is presented where the first stage consists of routing, loading and unloading decisions, and the second stage consists of scheduling and inventory decisions. The model is solved using a decomposition approach similar to an L-shaped algorithm where optimality cuts are added dynamically, and this solution process is embedded within the sample average approximation method. A computational study based on real-world instances is presented.     

A Tabu Search Heuristic for the Inland Container Transportation Problem

The Inland Container Transportation Problem describes the movement of full and empty containers among a number of terminals, depots and customers in a hinterland region. A trucking company with a homogeneous fleet of trucks has to serve customers which either receive goods by inbound containers or ship goods by outbound containers. While keeping given hard time constraints the total operating time of all trucks has to be minimized. A comprehensive mathematical formulation which considers vehicle routing and scheduling and empty container repositioning simultaneously is defined. The problem is solved by an efficient Tabu Search Heuristic. Computational experiments carried out on small- and large-sized instances indicate that the proposed algorithm performs well with respect to effectiveness and efficiency.     

A large neighbourhood search heuristic for ship routing and scheduling with split loads

The purpose of this paper is to present and solve a new, important planning problem faced by many shipping companies dealing with the transport of bulk products. These shipping companies are committed to carrying some contract cargoes and will try to derive additional revenue from optional spot cargoes. In most of the literature on ship routing and scheduling problems a cargo cannot be transported by more than one ship. By introducing split loads this restriction is removed and each cargo can be transported by several ships. In this paper we propose a large neighbourhood search heuristic for the ship routing and scheduling problem with split loads. Computational results show that the heuristic provides good solutions to real-life instances within reasonable time. It is also shown that introducing split loads can yield significant improvements.     

Multi-objective optimization of the maritime cargo routing and scheduling problem

This paper addresses the multi-objective maritime cargo routing and scheduling problem, in which the delivery of bulk products from pickup to delivery ports is served by a heterogeneous fleet of vessels. A mixed integer linear programming (MILP) model is formulated to simultaneously minimize total operation costs, the scheduling makespan, and delays in selected deliveries. The model accounts for several real features, such as time windows, capacity of the vessel's compartments, and ports requirements. A fuzzy weighted max–min method was applied to solve the problem. Two heuristics were developed to effectively handle the complex generated MILP models during the solution process. Experiments were conducted to evaluate the optimization approach using real-life instances provided by a fertilizer company. Finally, a case study shows that the developed model and algorithmic framework are flexible and effective in coping with real problems, incorporating specific business rules from different companies.     

Heuristic algorithms for a three-dimensional loading capacitated vehicle routing problem in a carrier

In this paper, we present heuristic algorithms for a three-dimensional loading capacitated vehicle routing problem arising in a real-world situation. In this problem, customers make requests of goods, which are packed in a sortment of boxes. The objective is to find minimum cost delivery routes for a set of identical vehicles that, departing from a depot, visit all customers only once and return to the depot. Apart of the usual 3D container loading constraints which ensure that the boxes are packed completely inside the vehicles and that the boxes do not overlap each other in each vehicle, the problem also takes into account constraints related to the vertical stability of the cargo and multi-drop situations. The algorithms are based on the combination of classical heuristics from both vehicle routing and container loading literatures, as well as two metaheuristic strategies, and their use in more elaborate procedures. Although these approaches cannot assure optimal solutions for the respective problems, they are relatively simple, fast enough to solve real instances, flexible enough to include other practical considerations, and normally assure relatively good solutions in acceptable computational times in practice. The approaches are also sufficiently generic to be embedded with algorithms other than those considered in this study, as well as they can be easily adapted to consider other practical constraints, such as the load bearing strength of the boxes, time windows and pickups and deliveries. Computational tests were performed with these methods considering instances based on the vehicle routing literature and actual customers’ orders, as well as instances based on a real-world situation of a Brazilian carrier. The results show that the heuristics are able to produce relatively good solutions for real instances with hundreds of customers and thousands of boxes.     

An ILS heuristic for the ship scheduling problem: application in the oil industry

This paper addresses a real‐life rescheduling problem of a pipe‐laying support vessel (PLSV) fleet in charge of subsea oil well connections. The short‐term schedule of these vessels is subject to uncertainties inherent to its operations, resulting in ships idleness or delays in oil production. The objective of this study is to develop methods to support a Brazilian oil and gas company in overcoming impacts caused by operational disruptions, while reaching its planned production level. The PLSV rescheduling problem was treated as an identical parallel machine scheduling problem, where the machines represent the vessels and the jobs are the activities for the subsea well connections. We propose a mathematical programming model and a method based on the iterated local search (ILS) metaheuristic to solve the problem. This paper contributes to this by considering simultaneously setup times, machine eligibility, release dates, due dates, and machine availability. Both methods were applied on 10 instances based on real PLSV data. Taking into account an objective function that measures the operational impact on schedules, the ILS provided an average improvement above 91% in schedules when compared to the initial solution provided by the studied company. The ILS outperformed a mathematical programming model for the problem, in eight instances, within a 30‐minute execution time limit, fitting to the company process.     

Solving the ship inventory routing and scheduling problem with undedicated compartments

This paper presents a ship inventory routing and scheduling problem with undedicated compartments (sIRPSP-UC). The objective of the problem is to find a minimum cost solution while satisfying a number of technical and physical constraints within a given planning horizon. In this problem, we identify four sub-problems that need to be decided simultaneously: route selections, ship selection, loading, and unloading activity procedures. To solve this problem, first, we developed a mixed integer linear programming model. We then developed a one-step greedy heuristic, and then based on this heuristic, we propose a set of heuristics. Each heuristic has a combination of rules for each sub-problem. A number of problem instances are used to compare the solutions of the two approaches. We applied selected good combinations of rules to solve each problem using the heuristic approach. The results show that 8 out 12 of the considered problem instances have no gap with MILP solution solved using LINGO. We also find that the average gap is 1.96%. In contrast when we consistently use the same combination for all iterations, there are no dominant combinations of heuristics that can find good solutions for all the problem instances.     

A travelling salesman problem with allocation, time window and precedence constraints — an application to ship scheduling

A Travelling Salesman Problem with Allocation, Time Window and Precedence Constraints (TSP-ATWPC) is considered. The TSP-ATWPC occurs as a subproblem of optimally sequencing a given set of port visits in a real bulk ship scheduling problem, which is a combined multi-ship pickup and delivery problem with time windows and multi-allocation problem. Each ship in the fleet is equipped with a flexible cargo hold that can be partitioned into several smaller holds in a given number of ways, thus allowing multiple products to be carried simultaneously by the same ship. The allocation constraints of the TSP-ATWPC ensure that the partition of the ship's flexible cargo hold and the allocation of cargoes to the smaller holds are feasible throughout the visiting sequence. The TSP-ATWPC is solved as a shortest path problem on a graph whose nodes are the states representing the set of nodes in the path, the last visited node and the accumulated cargo allocation. The arcs of the graph represent transitions from one state to another. The algorithm is a forward dynamic programming algorithm. A number of domination and elimination tests are introduced to reduce the state space. The computational results show that the proposed algorithm for the TSP-ATWPC works, and optimal solutions are obtained to the real ship scheduling problem.     

A construction and improvement heuristic for a liquefied natural gas inventory routing problem

We present a large scale ship routing and inventory management problem for a producer and distributor of liquefied natural gas (LNG). The problem contains multiple products, inventory and berth capacity at the loading port and a heterogeneous fleet of ships. The goal is to create an annual delivery program to fulfill the producer’s long-term contracts at minimum cost, while maximizing the revenue from selling LNG in the spot market. To solve this problem we have developed a construction and improvement heuristic (CIH).The CIH is a multi-start local search heuristic that constructs a set of solutions using a greedy insertion procedure. The solutions are then improved using either a first-descent neighborhood search, branch-and-bound on a mathematical formulation, or both. Tests on real-life instances show that the CIH provides good solutions in a short amount of time.     

Multi-start iterated local search for the periodic vehicle routing problem with time windows and time spread constraints on services

In the field of high-value shipment transportation, companies are faced to the malevolence problem. The risk of ambush increases with the predictability of vehicle routes. This paper addresses a very hard periodic vehicle routing problem with time windows, submitted by a software company specialized in transportation problems with security constraints. The hours of visits to each customer over the planning horizon must be spread in the customer's time window. As the aim is to solve real instances, the running time must be reasonable. A mixed integer linear model and a multi-start iterated local search are proposed. Results are reported on instances derived from classical benchmarks for the vehicle routing problem with time windows, and on two practical instances. Experiments are also conducted on a particular case with a single period, the vehicle routing problem with soft time windows: the new metaheuristic competes with two published algorithms and improves six best known solutions.     

Multiscale production routing in multicommodity supply chains with complex production facilities

In this work, we introduce the multiscale production routing problem (MPRP), which considers the coordination of production, inventory, distribution, and routing decisions in multicommodity supply chains with complex continuous production facilities. We propose an MILP model involving two different time grids. While a detailed mode-based production scheduling model captures all critical operational constraints on the fine time grid, vehicle routing is considered in each time period of the coarse time grid. In order to solve large instances of the MPRP, we propose an iterative MILP-based heuristic approach that solves the MILP model with a restricted set of candidate routes at each iteration and dynamically updates the set of candidate routes for the next iteration. The results of an extensive computational study show that the proposed algorithm finds high-quality solutions in reasonable computation times, and in large instances, it significantly outperforms a standard two-phase heuristic approach and a solution strategy involving a one-time heuristic pre-generation of candidate routes. Similar results are achieved in an industrial case study, which considers a real-world industrial gas supply chain.     

A reactive simheuristic using online data for a real‐life inventory routing problem with stochastic demands

In the context of a supply chain for the animal‐feed industry, this paper focuses on optimizing replenishment strategies for silos in multiple farms. Assuming that a supply chain is essentially a value chain, our work aims at narrowing this chasm and putting analytics into practice by identifying and quantifying improvements on specific stages of an animal‐feed supply chain. Motivated by a real‐life case, the paper analyses a rich multi‐period inventory routing problem with homogeneous fleet, stochastic demands, and maximum route length. After describing the problem and reviewing the related literature, we introduce a reactive heuristic, which is then extended into a biased‐randomized simheuristic. Our reactive approach is validated and tested using a series of adapted instances to explore the gap between the solutions it provides and the ones generated by existing nonreactive approaches.     

Variable neighborhood search based approaches to a vehicle scheduling problem in agriculture

A vehicle scheduling problem (VSP) that arises from sugar beet transportation within minimum working time under the set of constraints reflecting a real‐life situation is considered. A mixed integer quadratically constrained programming (MIQCP) model of the considered VSP and reformulation to a mixed integer linear program (MILP) are proposed and used within the framework of Lingo 17 solver, producing optimal solutions only for small‐sized problem instances. Two variants of the variable neighborhood search (VNS) metaheuristic—basic VNS (BVNS) and skewed VNS (SVNS) are designed to efficiently deal with large‐sized problem instances. The proposed VNS approaches are evaluated and compared against Lingo 17 and each other on the set of real‐life and generated problem instances. Computational results show that both BVNS and SVNS reach all known optimal solutions on small‐sized instances and are comparable on medium‐ and large‐sized instances. In general, SVNS significantly outperforms BVNS in terms of running times.     

Ship routing and scheduling with cargo coupling and synchronization constraints

The purpose of this paper is to introduce and solve a planning problem faced by shipping companies operating in a special segment of tramp shipping called project shipping. Project shipping differs from other more traditional tramp segments because the cargoes are more unique and usually transported on a one-time basis. The special nature of the cargoes complicates the routing and scheduling. For instance, a cargo can be part of a process facility, but the shipping company cannot transport it unless other parts of the same facility are transported as well, even though these parts may have different origins. This creates an additional coupling constraint between the cargoes. In addition, the different parts might require synchronized delivery within some time window. We present a mathematical formulation for the problem and propose three alternative solution methods based on path flow formulations and a priori column generation. In one of the solution methods this is combined with a scheme for relaxing the complicating synchronization constraints and reintroducing them dynamically when needed. Computational results show that we are able to find optimal solutions to problems based on data obtained from a shipping company.     

Variable neighborhood search algorithms for the vehicle routing problem with two‐dimensional loading constraints and mixed linehauls and backhauls

In this paper, we explore a vehicle routing problem with two‐dimensional loading constraints and mixed linehauls and backhauls. The addressed problem belongs to a subclass of general pickup and delivery problems. Two‐dimensional loading constraints are also considered. These constraints arise in many real‐world situations and can improve efficiency since backhaul customers do not need to be delayed in a route when it is possible to load their items earlier and without rearrangements of the items. To tackle this problem, we report extensive computational experiments to assess the performance of different variants of the variable neighborhood search approaches. The initial solution relies on an insertion heuristic. Both shaking and local search phases resort to 10 neighborhood structures. Some of those structures were specially developed for this problem. The feasibility of routes is heuristically obtained with a classical bottom‐left based method to tackle the explicit consideration of loading constraints. All the strategies were implemented and exhaustively tested on instances adapted from the literature. The results of this computational study are discussed at the end of this paper.     

Considering lost sale in inventory routing problems for perishable goods

This paper presents a mathematical model for an inventory routing problem (IRP). The model is especially designed for allocating the stock of perishable goods. It is assumed that the age of the perishable inventory has a negative impact on the demand of end customers and a percentage of the demand is considered as lost sale. The proposed model balances the transportation cost, the cost of inventory holding and lost sale. In addition to the usual inventory routing constraints, we consider the cost of lost sale as a linear or an exponential function of the inventory age. The proposed model is solved to optimality for small instances and is used to obtain lower bounds for larger instances. We have also devised an efficient meta-heuristic algorithm to find good solutions for this class of problems based on Simulated Annealing (SA) and Tabu Search (TS). Computational results indicate that, for small problems, the average optimality gaps are less than 10.9% and 13.4% using linear and exponential lost sale functions, respectively. Furthermore, we show that the optimality gaps found by CPLEX grow exponentially with the problem size while those obtained by the proposed meta-heuristic algorithm increase linearly.     

A computational study of Benders decomposition for the integrated aircraft routing and crew scheduling problem

The integrated aircraft routing and crew scheduling problem consists in determining a minimum-cost set of aircraft routes and crew pairings such that each flight leg is covered by one aircraft and one crew, and side constraints are satisfied. While some side constraints involve only crews or aircraft, linking constraints impose minimum connection times for crews that depend on aircraft connections. We propose an enhanced model incorporating robustness to handle these linking constraints and compare two Benders decomposition methods—one with the aircraft routing problem as the master problem and one with the crew pairing problem. We also study the impact of generating Pareto-optimal cuts on the speed of convergence of these methods. Computational experiments performed on test instances provided by two major airlines show that the proposed approach yields high-quality solutions in reasonable computing times.     

Heuristics for tactical time slot management: a periodic vehicle routing problem view

In this study, we consider a tactical problem where a time slot schedule for delivery service over a given planning horizon must be selected in each zone of a geographical area. A heuristic search evaluates each schedule selection by constructing a corresponding tactical routing plan of minimum cost based on demand and service time estimates. At the end, the schedule selection leading to the best tactical routing plan is selected. The latter can then be used as a blueprint when addressing the operational problem (i.e., when real customer orders are received and operational routes are constructed). We propose two heuristics to address the tactical problem. The first heuristic is a three‐phase approach: a periodic vehicle routing problem (PVRP) is first solved, followed by a repair phase and a final improvement phase where a vehicle routing problem (VRP) with time windows is solved for each period of the planning horizon. The second heuristic tackles the problem as a whole by directly solving a PVRP with time windows. Computational results compare the two heuristics under various settings, based on instances derived from benchmark instances for the VRP with time windows.