Mathematical Programming Methods for Logistics Planning.

The petroleum industry's extensive use of LP-based operations planning models is well known and often cited as a major triumph of applied operations research. However, few people outside of the petroleum industry realize the degree to which mathematical programming concepts and techniques have penetrated all facets of the oil business from strategic planning through process control. Mathematical programming techniques have been developed and applied, decade by decade, from the 1940s to the present and hold even greater potential for the 1990s.

For capacitated multi-item lot sizing problems, we propose a predictive search method that integrates machine learning/advanced analytics, mathematical programming, and heuristic search into a single framework. Advanced analytics can predict the probability that an event will happen and has been applied to pressing industry issues, such as credit scoring, risk management, and default management. Although little research has applied such technique for lot sizing problems, we observe that advanced analytics can uncover optimal patterns of setup variables given properties associated with the problems, such as problem attributes, and solution values yielded by linear programming relaxation, column generation, and Lagrangian relaxation. We, therefore, build advanced analytics models that yield information about how likely a solution pattern is the same as the optimum, which is insightful information used to partition the solution space into incumbent, superincumbent, and nonincumbent regions where an analytics-driven heuristic search procedure is applied to build restricted subproblems. These subproblems are solved by a combined mathematical programming technique to improve solution quality iteratively. We prove that the predictive search method can converge to the global optimal solution point. The discussion is followed by computational tests, where comparisons with other methods indicate that our approach can obtain better results for the benchmark problems than other state-of-the-art methods. Summary of Contribution: In this study, we propose a predictive search method that integrates machine learning/advanced analytics, mathematical programming, and heuristic search into a single framework for capacitated multi-item lot sizing problems. The advanced analytics models are used to yield information about how likely a solution pattern is the same as the optimum, which is insightful information used to divide the solution space into incumbent, superincumbent, and nonincumbent regions where an analytics-driven heuristic search procedure is applied to build restricted subproblems. These subproblems are solved by a combined mathematical programming technique to improve solution quality iteratively. We prove that the predictive search method can converge to the global optimal solution point. Through computational tests based on benchmark problems, we observe that the proposed approach can obtain better results than other state-of-the-art methods.

A parallel implementation of the TSSP + 1 decomposition for the capacity-constrained vehicle routing problem

Traditional vehicle routing problems implicitly assume that only one crew operates a vehicle for the entirety of its journey. However, this assumption is violated in many applications arising in humanitarian and military logistics. This paper considers a joint vehicle and crew routing and scheduling problem in which crews are able to interchange vehicles, resulting in space and time interdependencies between vehicle routes and crew routes. The problem is formulated as a mixed integer programming (MIP) model and a constraint programming (CP) model that overlay crew routing constraints over a standard vehicle routing problem. The constraint program uses a novel optimization constraint to detect infeasibility and to bound crew objectives. This paper also explores methods using large neighborhood search over the MIP and CP models. Experimental results indicate that modeling the vehicle and crew routing problems jointly and supporting vehicle interchanges for crews may bring significant benefits in cost reduction compared with a method that sequentializes these decisions.

Solving 2D rolling problems using the NORM–TANG iteration and mathematical programming

This paper is concerned with the economic generation dispatch problem. It is a well-known fact that practical aspects of power plant equipment, as well as the objectives to be met, may result in a nonconvex, nondifferentiable model that poses difficulties to conventional mathematical programming methods. This paper proposes the use of metaheuristic Teaching-Learning-Based Optimization to overcome such difficulties. This metaheuristic is well known for requiring a few parameters and, most importantly, it does not require the tuning of problem-dependent parameters. The algorithm proposed in this work is parameter-free; that is, the few parameters required by the Teaching-Learning-Based Optimization method are set automatically based on the power system’s data. In addition, the handling of constraints, such as generators’ prohibited zones and the generator-load-loss power balance, is performed in a very efficient way. Simulation results are shown for power systems containing 3 to 40 generation units, and the results provided by the proposed method are shown and discussed based on comparisons with other metaheuristics and a mathematical programming technique.

In recent years, the integration of sustainable principles into the Vehicle Routing Problem (VRP) for efficient waste management has gained significant attention. This paper provides an overview of advancements in multi-objective mathematical programming (MP) models and the optimization techniques for sustainable waste management practices within the VRP framework. Sustainable waste management practices in the context of the VRP involve optimizing routes and schedules aim to reduce the environmental impact of waste collection. It investigates the integration of multi-objectives with sustainability criteria, including social, economic, and environmental considerations. Furthermore, it surveys various optimization methodologies applied in waste management to enhance efficiency and sustainability practices. The Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) statement was employed as a formal systematic review guideline for data gathering. Data was obtained from studies conducted between 2017 and 2023. The analysis included a total of 18 papers from online sources and databases. Based on the literature review, it has been observed that the majority of the research focused on employing Mixed-Integer Linear Programming (MILP) models to tackle the optimization problem for waste management. The literature survey demonstrated significant contributions in computational performance, cost-effectiveness, operational efficiency, and utilization of real-world data by improving the solution approaches, aiming to prioritize economic, social, and environmentally friendly solutions. The paper aims to serve as a convenient reference for researchers and practitioners seeking information on using the MP model and solution approaches to optimize VRP for waste management.

A genetic algorithm/mathematical programming approach to solve a two-level soft drink production problem

The Berth Allocation Problem aims at assigning and scheduling incoming vessels to berthing positions along the quay of a container terminal. This problem is a well-known optimization problem within maritime shipping. For solving it, we propose two POPMUSIC (Partial Optimization Metaheuristic Under Special Intensification Conditions) approaches that incorporate an existing mathematical programming formulation. POPMUSIC is an efficient metaheuristic that may serve as blueprint for matheuristics approaches once hybridized with mathematical programming. In this regard, the use of exact methods for solving the sub-problems defined in the POPMUSIC template highlight an interoperation between metaheuristics and mathematical programming techniques, which provide a new type of approach for this problem. Computational experiments reveal excellent results.KeywordsParticle Swarm OptimizationService TimeProblem InstanceContainer TerminalMathematical Programming FormulationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Coal is the main fuel in the production process at PT PJB UBJ O&M Tenayan. As a raw material, coal needs to be considered in terms of supply to prevent losses (depreciation in caloric content) in case of oversupply. This study aimed to compare four forecasting methods for coal material supply. The four methods of time series forecasting are the moving average method, the weighted moving average, the single exponential smoothing, and the linear regression. Forecasting error calculations used the smallest MAD, MSE, and MAPE error parameters, whereas the tracking signal was used to monitor the forecasting results. The data required were coal supply and demand. Based on the data processing obtained, results of this study show that the best method is linear regression with the results of the MAD value of 13,285.63, MSE of 228,778,800, and MAPE of 15.04%. Based on the results of the tracking signal, the forecasting results were within the control limits, which shows that the linear regression method is the best forecasting method that can be applied to control coal supply in the next period.

Ad hoc networks have recently been used as a communications medium on tasks that require high levels of communication and coordination. We study the problem of determining an optimal route for a group of wireless units, such that the total connection time among nodes in the resulting mobile ad hoc network is maximized, subject to a limit on the traveled distance. This problem, called the cooperative communication problem in mobile ad hoc networks (CCPM), is modeled using combinatorial optimization and mathematical programming techniques. Applications occur on the coordination of rescue groups, geographical exploration and recognition, unmanned air vehicles (UAVs), and mission coordination. The problem is shown to be NP-hard, and a dynamic programming algorithm is proposed for the problem. Mathematical programming models are presented and computational experiments performed.

BackgroundMalaria transmission is high in western Kenya and the asymptomatic infected population plays a significant role in driving the transmission. Mathematical modelling and simulation programs suggest that interventions targeting asymptomatic infections through mass testing and treatment (MTaT) or mass drug administration (MDA) have the potential to reduce malaria transmission when combined with existing interventions.ObjectiveThis paper describes the study site, capacity development efforts required, and lessons learned for implementing a multi-year community-based cluster-randomized controlled trial to evaluate the impact of MTaT for malaria transmission reduction in an area of high transmission in western Kenya.MethodsThe study partnered with Kenya’s Ministry of Health (MOH) and other organizations on community sensitization and engagement to mobilize, train and deploy community health volunteers (CHVs) to deliver MTaT in the community. Within the health facilities, the study availed staff, medical and laboratory supplies and strengthened health information management system to monitor progress and evaluate impact of intervention.ResultsMore than 80 Kenya MOH CHVs, 13 clinical officers, field workers, data and logistical staff were trained to carry out MTaT three times a year for 2 years in a population of approximately 90,000 individuals. A supply chain management was adapted to meet daily demands for large volumes of commodities despite the limitation of few MOH facilities having ideal storage conditions. Modern technology was adapted more to meet the needs of the high daily volume of collected data.ConclusionsIn resource-constrained settings, large interventions require capacity building and logistical planning. This study found that investing in relationships with the communities, local governments, and other partners, and identifying and equipping the appropriate staff with the skills and technology to perform tasks are important factors for success in delivering an intervention like MTaT.

It is estimated that about two-thirds of global coal is used for power generation and that, in the next 20 years, over 70% of the demand for coal will come from China and India. Coal accounts for approximately 41% of the world's electricity generation. Demand for thermal coal is influenced by factors that include availability, prices of competing products such as oil, gas and nuclear power, and the demand for electricity. The aim of this article is to provide an exposition of supply chain dynamics within the South African coal mining industry and to argue for a more efficient and collaborative supply chain. The authors attempt to investigate at local and global level, the current trends pertaining to the level of reserves, production and consumption of coal. The article further demonstrates the shortcomings of current logistics in meeting the demand for coal in both domestic and export markets. The article draws from secondary data sourced from academic papers, government and agency documents in the exposition of the coal mining supply chain. The paper concludes by recommending the need for a scientific study on supply chain constraints facing the coal mining industry in South Africa.

Due to the complexity of the manufacturing environment, problems that can be solved by mathematical programming techniques are usually represented with non-linear programming (NP) models instead of linear programming (LP) models. When non-stochastic vagueness exists between the problem description and its corresponding NP model, fuzzy set theory can be applied to the mathematical model for the purpose of vividly representing the problem. This paper discusses the idea of the fuzzy NP model. Fuzzy set concepts are adapted to the NP objective function and constraints. An identical crisp NP model is derived from the fuzzy NP model for solving the problem numerically. Kuhn-Tucker conditions are addressed to determine the existence of a global optimal solution. A fuzzy machining economics model, which attempts to find optimal manufacturing parameters under vague elements of influence, is used to demonstrate the theory of the fuzzy NP model.

Routing problems occur in a wide variety of situations. Due to the heterogeneity of cases we do not yet know how to manage the complexity of addressing all the relevant aspects in logistic planning and solving the variety of different problem types in a cost-efficient way. In the last decade, we have witnessed an emergence of systematic approach into managing variation within a set of related software systems. This paper presents an application of these advances from software engineering into vehicle routing: we suggest the construction of a higher-level (meta-) model of routing problems and the application of a software product line approach. The proposed approach results in a flexible product line for constructing a family of routing systems cost-efficiently.