Hybrid Time-Based Framework for Maritime Inventory Routing Problem

• A unified continuous-time framework is developed for enterprise-wide scheduling and planning optimization • Continuous-time representation eliminates the time-scale inconsistencies between planning and scheduling • Three representative continuous-time formulations are systematically evaluated in terms of optimality and computational efficiency • The unit-slot formulation achieves superior efficiency and solution quality Inconsistent continuous-time and discrete-time representations have been a big challenge in achieving the enterprise-wide optimum for integrated crude scheduling and refinery planning problems. This paper proposes a unified continuous-time representation for solving the integrated enterprise-wide optimization problem. Instead of implementing continuous-time slots for the crude scheduling subproblem and discrete-time slots for the refinery planning subproblem in a hybrid way, continuous-time slots are applied to both subproblems and synchronized via the crude distillation units. Such a proposed modeling framework provides a more flexible and consistent time formulation to the integrated problem. Furthermore, three typical continuous-time representations for crude scheduling, namely, unit-slot time representation, event-based time representation, and multi-operation sequence time representation, are investigated with cases adapted from practical complexes. Compared to the traditional integrated problem based on a hybrid continuous-time and discrete-time representation, the proposed unified model framework reveals a better optimization performance. Higher-quality solutions can be obtained for both crude scheduling and planning operations. Moreover, among the three time representations, the model based on the unit-slot time outperforms the other two models. This work provides a promising alternative modeling strategy for achieving enterprise-wide optimality in the petrochemical industry.

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.

We review recent literature pertaining to the maritime inventory routing problem (MIRP), a stimulating, albeit niche, subclass of vendor‐managed inventory problems. MIRPs deal with optimally distributing products with a (typically heterogeneous) vessel fleet between production and consumption ports with inventory tracking and inventory limits. We present two mixed‐integer linear programming models for the MIRP—one based on discrete time, the other based on continuous time—and we discuss the advantages and disadvantages of each of the two modeling approaches. In surveying more than 50 papers spanning the decade 2013–2023, we investigate MIRP variants from many different applications and discuss how these have been modeled and solved. Our purpose is to provide a comprehensive overview of state‐of‐the‐art MIRP research published in this period, collated along multiple dimensions. In addition to providing information about available test instances, we highlight recent trends and interesting avenues for future research. As such, we believe this survey will be useful to students, researchers, and practitioners in this domain.

Improved time representation model for the simultaneous energy supply and demand management in microgrids

To ensure the competitiveness of manufacturing companies in the market, batching and batch scheduling are among the most important tasks. This paper presents a simulation-optimization approach that combines the discrete event simulation (DES) and the genetic algorithm (GA) to solve the batching and batch scheduling problem in a hybrid flow shop (HFS). HFS is widely used for the production of medium and large quantities of different technologically complex products. Based on a real-world manufacturing company, the HFS simulation model was developed using the Tecnomatix Plant Simulation software package. By analysing the influencing factors that represent production costs, a new formulation of the total cost of production was proposed. The purpose of this case study was to ensure timely delivery and minimize production costs by integrating simulation and optimization tools. This research considers sequence-dependent setup times, and availability of manufacturing and transportation equipment. The results of this research showed that the proposed simulation-optimization approach can be applied to solve the problem in many industrial case studies.

A single‐product maritime inventory routing problem (MIRP) is studied in which the production and consumption rates vary over the planning horizon. The problem involves a heterogeneous fleet and multiple production and consumption ports with limited storage capacity. Two discrete time formulations are developed: an original model and a reformulated model that is a pure fixed charge network flow (FCNF) model with side constraints. Mixed integer sets arising from the decomposition of the formulations are identified. In particular, several lot‐sizing relaxations are derived for the formulations and used to establish valid inequalities to strengthen the proposed formulations. Until now, the derivation of models and valid inequalities for MIRPs has mainly been inspired by the developments in the routing community. Here, we have developed a new model leading to new valid inequalities for MIRPs obtained by generalizing valid inequalities from the recent lot‐sizing literature. Considering a set of instances based on real data, a computational study is conducted to test the formulations and the effectiveness of the valid inequalities. The FCNF formulation is generally much stronger than the original formulation. The developed valid inequalities reduce the integrality gap significantly for both formulations. By using a branch‐and‐bound scheme based on the strengthened FCNF formulation, most of our test instances are solved to optimality. © 2013 Wiley Periodicals, Inc. NETWORKS, Vol. 62(4), 297–314 2013

In This Issue

Dynamics of quality improvement programs – Optimal investment policies

Order and inventory variance amplification: The equivalence of discrete and continuous time analyses

We consider a single product maritime inventory routing problem in which the production and consumption rates are constant over the planning horizon. The problem involves a heterogeneous fleet and multiple production and consumption ports with limited storage capacity. Maritime transportation is characterized by high levels of uncertainty, and sailing times can be severely influenced by varying and unpredictable weather conditions. To deal with the uncertainty, this paper investigates the use of adaptable robust optimization where the sailing times are assumed to belong to the well-known budget polytope uncertainty set. In the recourse model, the routing, the order of port visits, and the quantities to load and unload are fixed before the uncertainty is revealed, while the visit time to ports and the stock levels can be adjusted to the scenario. We propose a decomposition algorithm that iterates between a master problem that considers a subset of scenarios and an adversarial separation problem that searches for scenarios that make the solution from the master problem infeasible. Several improvement strategies are proposed aiming at reducing the running time of the master problem and reducing the number of iterations of the decomposition algorithm. An iterated local search heuristic is also introduced to improve the decomposition algorithm. A computational study is reported based on a set of real instances.

The objective of this paper is the development and solution of nonlinear and mixed-integer (MIP) optimization models for real-world planning and scheduling problems in petroleum refineries. Firstly, we present a nonlinear planning model that represents a general refinery topology and allows implementation of nonlinear process models as well as blending relations. The optimization model is able to define new operating points, thus increasing the production of the more valuable products and simultaneously satisfying all specification constraints. The second part addresses scheduling problems in oil refineries, which are formulated as MIP optimization models and rely on both continuous and discrete time representations. Three practical applications closely related to the current refinery scenario are presented. The first one addresses the problem of crude oil inventory management of a refinery that receives several types of crude oil delivered exclusively by a single oil pipeline. Subsequently, two optimization models intended to define the optimal production policy, inventory control and distribution are proposed and solved for the fuel oil and asphalt plant. Finally, the planning model of Moro et al. (1998) is extended in order to sequence decisions at the scheduling level in the liquefied petroleum gas (LPG) area for maximization of the production of petrochemical-grade propane and product delivery.

We present two decomposition algorithms for single product deep-sea maritime inventory routing problems (MIRPs) that possess a core substructure common in many real-world applications. The problem involves routing vessels, each belonging to a particular vessel class, between loading and discharging ports, each belonging to a particular region. Our algorithms iteratively solve a MIRP by zooming out and then zooming in on the problem. Specifically, in the “zoomed out” phase, we solve a first-stage master problem in which aggregate information about regions and vessel classes is used to route vessels between regions, while only implicitly considering inventory and capacity requirements, berth limits, and other side constraints. In the “zoomed in” phase, we solve a series of second-stage subproblems, one for each region, in which individual vessels are routed through each region and load and discharge quantities are determined. Computational experience shows that an integrated approach that combines these two algorithms is vastly superior to solving the problem directly with a commercial mixed-integer programming solver.

A two-phase algorithm for the cyclic inventory routing problem

This paper concerns a real-life production management problem composed of two stages, which includes interdependent batch scheduling problems. Moreover, both stages require setup operations at the beginning and between the subsequent batches. From the optimisation point of view, this production management problem is complying with customers’ deadlines and hence minimising total lateness. To achieve this objective, the production planner must identify optimum or near-optimum batch schedules for both stages. Correspondingly, this paper aims to develop a methodology to manage the related production problem as accurately as possible. We formulate an optimisation model that employs the mathematical programming method in line with this. Afterwards, an algorithmic proposal based on the simulated annealing algorithm is also developed to solve the problem in realistic sizes. The computational capabilities of the developed model and the algorithm are evaluated on the randomly generated problem sets. A direct comparison between the mathematical model and the algorithm shows how efficiently the proposed algorithm solves real-world problems. Also, computational results indicate that the proposed algorithm satisfactorily solves the related real-world batch scheduling problem.

In this paper, we use the genetic algorithms (GA) technique to handle two problems in the manufacturing systems: the formation of manufacturing cell in cellular manufacturing and batch scheduling. In the formation of machine cells, we use multi-objective functions as criteria to form cell. These criteria are to minimise the inter-cell movement, to minimise variation of workload within cells and to maximise the similarity within cells. Results showed that by varying the weights of each criterion, the algorithm produced is flexible to adapt to changes in the manufacturing environment. Unlike traditional methods which merely rearrange the part-incidence matrix, this algorithm incorporates other parameters such as processing times of each part and number of parts required. The batch scheduling problem described in this paper is the problem of scheduling a single-machine with jobs of different due-dates and arrival times. We have developed an algorithm which is not only able to find the optimum or near-optimal sequence of jobs, but also able to determine the number of jobs to be processed in each batch. The objective function used is to minimise total tardiness.