A multi-period multi-product stochastic inventory problem with order-based loan

This paper investigates a multi-product stochastic inventory problem in which a cash-constrained online retailer can adopt order-based loan provided by some Chinese e-commerce platforms to speed up its cash recovery for deferred revenue. We first build deterministic models for the problem and then develop the corresponding stochastic programming models to maximize the retailers' expected profit over the planning horizon. The uncertainty of customer demand is represented by scenario trees, and a scenario reduction technique is used to solve the problem when the scenario trees are too large. We conduct numerical tests based on real data crawling from an online store. The results show that the stochastic model outperforms the deterministic model, especially when the retailer is less cash-constrained. Moreover, the retailer tends to choose using order-based loan when its initial available cash is small or facing long receipt delay length

Coordinación hidrotérmica considerando altas penetraciones de fuentes de energía renovable

Esta tesis se presenta la implementación de un modelo de coordinación hidrotérmica incorporando plantas de energía hidráulica, cadenas hidráulicas, generadores térmicos convencionales, al igual que generadores a partir de fuentes de energía renovable en un sistema reducido equivalente del sistema interconectado colombiano. Este modelo se solucionó usando los métodos de programación lineal entera mixta y progressive hedging en el marco de programación estocástica de dos etapas, implementando un entorno de paralelización. Los resultados muestran las bondades del algoritmo de descomposición progressive hedging frente a problemas de naturaleza estocástica construidos a partir de escenarios, reduciendo los tiempo de computo significativamente (reducciones de hasta 100 veces). Adicionalmente se realizaron simulaciones considerando un numero elevado de escenarios de viento, obteniendo buenos resultados para la aplicación en programación de generación a corto plazoAbstract: In this thesis is presented the implementation of a hydrothermal coordination model incorporating hydraulic plants, hydraulic chains, conventional thermal generators, as well as renewable energy generators, in a reduced equivalent system of Colombian national grid. This model was solved using the mixed integer linear programming and progressive hedging technique in a two step stochastic programming field, implementing a parallel schedule. The results show the advantages of progressive hedging algorithm in problems with stochastic nature, constructed from scenarios, reducing the computation time significantly (around 100 times reductions). Additionally, simulations considering a large number of wind scenarios were conducted, obtaining good results for the application in short term generation schedulingMaestrí

Análise de desempenho de estratégias no algoritmo de Progressive Hedging quando aplicado na solução do problema de planejamento da operação energética

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia Elétrica, Florianópolis, 2013.O Planejamento da Operação Energética no Brasil é um problema de natureza estocástica, devido às incertezas relacionadas às variações climáticas, em virtude do uso da hidroeletricidade como principal fonte de energia do sistema elétrico brasileiro. Com o objetivo de representar adequadamente as incertezas envolvidas no problema, é importante resolver esse problema por meio de técnicas de Otimização Estocástica. O Setor Elétrico Brasileiro usa atualmente os algoritmos baseados na Decomposição de Benders para resolver o problema de Planejamento da Operação Energética. Entretanto, essa técnica não é o único meio existente de se resolver este problema. Outras técnicas de Programação Estocástica podem ser aplicadas, tais como o Progressive Hedging, objeto de estudo deste trabalho. O presente trabalho visa apresentar essa técnica aplicada ao problema de Planejamento da Operação Energética aplicado a Sistemas Hidrotérmicos, na sua forma mais usual e em modelagens que utilizam artifícios matemáticos, com o objetivo de proporcionar melhor desempenho computacional desta técnica de otimização ao problema de Planejamento da Operação Energética Operation Planning in Brazil is a problem of stochastic nature, due to uncertainties related to climate changes, due to the use of hydropower as the main energy source of the Brazilian electrical system. In order to represent the uncertainties involved in the problem adequately, it is important to solve this problem by Stochastic Optimization techniques. Currently, the Brazilian Electricity Sector uses algorithms based on Benders decomposition to solve the problem of Operation Planning. However, this technique is not the only way of solving this problem. Other Stochastic Programming techniques can be applied, such as the Progressive Hedging, focused in this work. This work aims to present this technique when applied to the problem of Operation Planning applied in Hydrothermal Systems, in its most usual shape and modeling using mathematical strategies, with the aim of providing better computational performance of this optimization technique to the problem of Operation Planning

Algorithms for Stochastic Integer Programs Using Fenchel Cutting Planes

This dissertation develops theory and methodology based on Fenchel cutting planes for solving stochastic integer programs (SIPs) with binary or general integer variables in the second-stage. The methodology is applied to auto-carrier loading problem under uncertainty. The motivation is that many applications can be modeled as SIPs, but this class of problems is hard to solve. In this dissertation, the underlying parameter distributions are assumed to be discrete so that the original problem can be formulated as a deterministic equivalent mixed-integer program. The developed methods are evaluated based on computational experiments using both real and randomly generated instances from the literature. We begin with studying a methodology using Fenchel cutting planes for SIPs with binary variables and implement an algorithm to improve runtime performance. We then introduce the stochastic auto-carrier loading problem where we present a mathematical model for tactical decision making regarding the number and types of auto-carriers needed based on the uncertainty of availability of vehicles. This involves the auto-carrier loading problem for which actual dimensions of the vehicles, regulations on total height of the auto-carriers and maximum weight of the axles, and safety requirements are considered. The problem is modeled as a two-stage SIP, and computational experiments are performed using test instances based on real data. Next, we develop theory and a methodology for Fenchel cutting planes for mixed integer programs with special structure. Integer programs have to be solved to generate a Fenchel cutting plane and this poses a challenge. Therefore, we propose a new methodology for constructing a reduced set of integer points so that the generation of Fenchel cutting planes is computationally favorable. We then present the computational results based on randomly generated instances from the literature and discuss the limitations of the methodology. We finally extend the methodology to SIPs with general integer variables in the second-stage with special structure, and study different normalizations for Fenchel cut generation and report their computational performance

Subgradient-based Decomposition Methods for Stochastic Mixed-integer Programs with Special Structures

The focus of this dissertation is solution strategies for stochastic mixed-integer programs with special structures. Motivation for the methods comes from the relatively sparse number of algorithms for solving stochastic mixed-integer programs. Two stage models with finite support are assumed throughout. The first contribution introduces the nodal decision framework under private information restrictions. Each node in the framework has control of an optimization model which may include stochastic parameters, and the nodes must coordinate toward a single objective in which a single optimal or close-to-optimal solution is desired. However, because of competitive issues, confidentiality requirements, incompatible database issues, or other complicating factors, no global view of the system is possible. An iterative methodology called the nodal decomposition-coordination algorithm (NDC) is formally developed in which each entity in the cooperation forms its own nodal deterministic or stochastic program. Lagrangian relaxation and subgradient optimization techniques are used to facilitate negotiation between the nodal decisions in the system without any one entity gaining access to the private information from other nodes. A computational study on NDC using supply chain inventory coordination problem instances demonstrates that the new methodology can obtain good solution values without violating private information restrictions. The results also show that the stochastic solutions outperform the corresponding expected value solutions. The next contribution presents a new algorithm called scenario Fenchel decomposition (SFD) for solving two-stage stochastic mixed 0-1 integer programs with special structure based on scenario decomposition of the problem and Fenchel cutting planes. The algorithm combines progressive hedging to restore nonanticipativity of the first-stage solution, and generates Fenchel cutting planes for the LP relaxations of the subproblems to recover integer solutions. A computational study SFD using instances with multiple knapsack constraint structure is given. Multiple knapsack constrained problems are chosen due to the advantages they provide when generating Fenchel cutting planes. The computational results are promising, and show that SFD is able to find optimal solutions for some problem instances in a short amount of time, and that overall, SFD outperforms the brute force method of solving the DEP

Operational model for empty container repositioning

Ph.DDOCTOR OF PHILOSOPH