Ship Routing with Pickup and Delivery for a Maritime Oil Transportation System: MIP Modeland Heuristics

This paper examines a ship routing problem with pickup and delivery and time windows for maritime oil transportation, motivated by the production and logistics activities of an oil company operating in the Brazilian coast. The transportation costs from offshore platforms to coastal terminals are an important issue in the search for operational excellence in the oil industry, involving operations that demand agile and effective decision support systems. This paper presents an optimization approach to address this problem, based on a mixed integer programming (MIP) model and a novel and exploratory application of two tailor-made MIP heuristics, based on relax-and-fix and time decomposition procedures. The model minimizes fuel costs of a heterogeneous fleet of oil tankers and costs related to freighting contracts. The model also considers company-specific constraints for offshore oil transportation. Computational experiments based on the mathematical models and the related MIP heuristics are presented for a set of real data provided by the company, which confirm the potential of optimization-based methods to find good solutions for problems of moderate sizes

OPERATIONAL PLANNING IN COMBINED HEAT AND POWER SYSTEMS

This dissertation presents methodologies for operational planning in Combined Heat and Power (CHP) systems. The subject of experimentation is the University of Massachusetts CHP system, which is a 22 MWe/640 MBh system for a district energy application. Systems like this have complex energy flow networks due to multiple interconnected thermodynamic components like gas and steam turbines, boilers and heat recovery steam generators and also interconnection with centralized electric grids. In district energy applications, heat and power requirements vary over 24 hour periods (planning horizon) due to changing weather conditions, time-of-day factors and consumer requirements. System thermal performance is highly dependent on ambient temperature and operating load, because component performances are nonlinear functions of these parameters. Electric grid charges are much higher for on-peak than off-peak periods, on-site fuel choices vary in prices and cheaper fuels are available only in limited quantities. In order to operate such systems in energy efficient, cost effective and least polluting ways, optimal scheduling strategies need to be developed. For such problems, Mixed-Integer Nonlinear Programming (MINLP) formulations are proposed. Three problem formulations are of interest; energy optimization, cost optimization and emission optimization. Energy optimization reduces system fuel input based on component nonlinear efficiency characteristics. Cost optimization addresses price fluctuations between grid on-peak and off-peak periods and differences in on-site fuel prices. Emission optimization considers CO2 emission levels caused by direct utilization of fossil fuels on-site and indirect utilization when importing electricity from the grid. Three solution techniques are employed; a deterministic algorithm, a stochastic search and a heuristic approach. The deterministic algorithm is the classical branch-and-bound method. Numerical experimentation shows that as planning horizon size increases linearly, computer processing time for branch-and-bound increases exponentially. Also in the problem formulation, fuel availability limitations lead to nonlinear constraints for which branch-and-bound in unable to find integer solutions. A genetic algorithm is proposed in which genetic search is applied only on integer variables and gradient search is applied on continuous variables. This hybrid genetic algorithm finds more optimal solutions than branch-and-bound within reasonable computer processing time. The heuristic approach fixes integer values over the planning horizon based on constraint satisfaction. It then uses gradient search to find optimum continuous variable values. The heuristic approach finds more optimal solutions than the proposed genetic algorithm and requires very little computer processing time. A numerical study using actual system operation data shows optimal scheduling can improve system efficiency by 6%, reduce cost by 11% and emission by 14%

ALGORITHMS FOR THE LARGE-SCALE UNIT COMMITMENT PROBLEM IN THE SIMULATION OF POWER SYSTEMS

Lo Unit Commitment Problem (UCP) \ue8 un problema di programmazione matematica dove un insieme di impianti termoelettrici deve essere programmato per soddisfare la domanda di energia e altri vincoli di sistema. Il modello \ue8 impiegato da decenni per supportare la pianificazione operazionale di breve termine dei sistemi elettrici. In questo lavoro affrontiamo il problema di risolvere UCP lineari di larga-scala per realizzare simulazioni accurate di sistemi elettrici, con i requisiti aggiuntivi di impiegare capacit\ue0 di calcolo convenzionali, ad esempio i personal computers, ed un tempo di soluzione di poche ore. Il problema, sotto le medesime condizioni, \ue8 affrontato abitualmente dal nostro partner industriale RSE S.p.A. (Ricerche Sistema Energetico), uno dei principali centri ricerche industriali su sistemi energetici in Italia. L\u2019ottimizzazione diretta di queste formulazioni con solutori generici \ue8 impraticabile. Nonostante sia possibile calcolare buone soluzioni euristiche, ovvero con un gap di ottimalit\ue0 sotto il 10%, in tempi ragionevoli per UCP di larga scala, si richiedono soluzioni pi\uf9 accurate, per esempio con gap sotto l\u20191%, per migliorare l\u2019affidabilit\ue0 delle simulazioni ed aiutare gli esperti di dominio, che potrebbero non essere familiari con i dettagli dei metodi di programmazione matematica, a supportare meglio le loro analisi. Tra le idee che abbiamo esplorato i seguenti metodi risultano i pi\uf9 promettenti: una mateuristica per calcolare efficientemente buone soluzioni e due metodi esatti di bounding: column generation e Benders decomposition. Questi metodi decompongono il problema disaccoppiando il commitment degli impianti termoelettrici, rappresentati da variabili discrete, e il loro livello di produzione, rappresentato da variabili continue. I nostri esperimenti dimostrano che il modello possiede propriet\ue0 intrinseche come degenerazione e forma della funzione obbiettivo piatta che ostacolano o impediscono la convergenza in risolutori allo stato dell\u2019arte. Tuttavia, i metodi che abbiamo sviluppato, sfruttando efficacemente le propriet\ue0 strutturali del modello, permettono di raggiungere soluzioni quasi ottime in poche iterazioni per la maggior parte delle istanze.The Unit Commitment Problem (UCP) is a mathematical programming problem where a set of power plants needs to be scheduled to satisfy energy demand and other system-wide constraints. It has been employed for decades to support short-term operational planning of power plants. In this work we tackle the problem of solving large-scale linear UCPs to perform accurate medium-term power systems simulations, with the additional requirements of employing conventional computing power, such as personal computers, and a solution time of a few hours. The problem, under such conditions, is routinely faced by our industry partner, the Energy Systems Development department at RSE S.p.A. (Ricerche Sistema Energetico), a major industrial research centre on power systems in Italy. The direct optimization of these formulations via general-purpose solvers is impractical. While good heuristic solutions, that is with an optimality gap below 10%, can be found for large-scale UCPs in affordable time, more accurate solutions, for example with a gap below 1%, are sought to improve the reliability of the simulations and help domain experts, who may not be familiar with the details of mathematical programming methods, to better support their analysis. Among the ideas we explored, the following methods are the most promising: a matheuristic to efficiently compute good solutions and two exact bounding methods: column generation and Benders decomposition. These methods decompose the problem by decoupling the commitment of thermal plants, represented by discrete variables, and their level of production, represented by continuous variables. Our experiments proved that the model posses inherent properties as degeneracy and objective flatness which hinder or prevent convergence in state-of-the-art solvers. On the other hand, the methods we devised, by effectively exploiting structural properties of the model, allow to reach quasi-optimal solutions within a few iterations on most instances