Please read the abstract in the section 00front of this document. / Thesis (PhD)--University of Pretoria, 2010. / Industrial and Systems Engineering / unrestricted

We consider a continuous time dynamic pricing model where a seller needs to sell a single item over a finite time horizon. Customers arrive in accordance with a Poisson process. Upon arrival, a customer either purchases the item if the posted price is lower than his/her reservation price, or leaves empty-handed. After purchasing the item, some customers, however, will return the item to the seller at an exponential rate for a full refund. We assume that a returned item is in mint condition and the seller can resell it to future customers. The objective of the seller is to dynamically adjust the price in order to maximize the expected total revenue when the sale horizon ends. We formulate the dynamic pricing problem as a dynamic programming model and derive the structural properties of the optimal policy and the optimal value function. For cases in which the customer's reservation price is exponentially distributed, we derive the optimal policy in a closed form. For general reservation price distribution, we consider an approximation of the original model by discretizing both time and the allowable price set. We then present an algorithm for numerically computing the optimal policy in this discrete time model. Numerical examples show that if the discrete price set is carefully chosen, the expected total revenue is nearly the same as that when the allowable price set is continuous. / Master of Science

We study simulation optimization methods for the stochastic economic lot scheduling problem. In contrast to prior research, we focus on methods that treat this problem as a black box. Based on a large-scale numerical study, we compare approximate dynamic programming with a global search for parameters of simple control policies. We propose two value function approximation schemes based on linear combinations of piecewise- constant functions as well as control policies that can be described by a small set of parameters. While approximate value iteration worked well for small problems with three products, it was clearly outperformed by the global policy search as soon as problem size increased. The most reliable choice in our study was a globally optimized fixed-cycle policy. An additional analysis of the response surface of model parameters on optimal average cost revealed that the cost effect of product diversity was negligible. (authors' abstract)

We consider the stochastic economic lot scheduling problem (SELSP) with lost sales and random demand, where switching between products is subject to sequence-dependent setup times. We propose a solution based on simulation optimization using an iterative two-step procedure which combines global policy search with local search heuristics for the traveling salesman sequencing subproblem. To optimize the production cycle, we compare two criteria: minimizing total setup times and evenly distributing setups to obtain a more regular production cycle. Based on a numerical study, we find that a policy with a balanced production cycle leads to lower cost than other policies with unbalanced cycles. (authors' abstract)

Fornecedores necessitam atender a demanda de seus clientes da forma mais adequada possível e mantendo a qualidade de seu serviço, porém em muitos casos essa demanda é desconhecida. Esse problema pode ser modelado como um problema de roteirização e estoque com demanda estocástica o qual inclui o controle de estoque, transporte do produto e decisões de agendamento da entrega. Existem vários trabalhos na literatura para resolver esse problema, porém nenhum deles lida com janela de tempo de atendimento, capacidade máxima de estoque tanto no cliente quanto no depósito e o nível de confiança de atendimento individualizado para cada cliente. O objetivo principal deste trabalho é propor um novo algoritmo baseado em otimização matemática para lidar com esse problema mais realista. Além disso, este trabalho tem como objetivo secundário melhorar o algoritmo de estado da arte baseado em otimização matemática, visando encontrar soluções com um menor tempo computacional e custo. Foram realizados experimentos com instâncias sintéticas com 15 até 50 clientes, as quais são geradas aleatoriamente, e com uma instância real, baseada na experiência profissional no mercado empresarial e em cenários reais de distribuição na cidade de São Paulo / Providers need to supply the demand of their clients as optimally as possible and maintaining the quality of their service, however in many cases this demand is unknown. This problem can be modeled as a inventory routing problem with stochastic demand, which includes inventory control, product transportation and delivery scheduling decisions. There are several papers in the literature to solve this problem, but none of them deals with service time window, maximum stock capacity for both the customer and the depot and individualized confidence level for each costumer. The main objective of this work is to propose a new algorithm based on mathematical optimization to deal with this more realistic problem. In addition, this work has as secondary objective to improve the state of the art algorithm based on mathematical optimization, aiming to find solutions with a lower computational time and cost. Experiments were performed with synthetic instances with 15 to 50 clients, which are randomly generated, and with a real instance, based on professional experience in the business market and in real distribution scenarios in the city of São Paulo

Fornecedores necessitam atender a demanda de seus clientes da forma mais adequada possível e mantendo a qualidade de seu serviço, porém em muitos casos essa demanda é desconhecida. Esse problema pode ser modelado como um problema de roteirização e estoque com demanda estocástica o qual inclui o controle de estoque, transporte do produto e decisões de agendamento da entrega. Existem vários trabalhos na literatura para resolver esse problema, porém nenhum deles lida com janela de tempo de atendimento, capacidade máxima de estoque tanto no cliente quanto no depósito e o nível de confiança de atendimento individualizado para cada cliente. O objetivo principal deste trabalho é propor um novo algoritmo baseado em otimização matemática para lidar com esse problema mais realista. Além disso, este trabalho tem como objetivo secundário melhorar o algoritmo de estado da arte baseado em otimização matemática, visando encontrar soluções com um menor tempo computacional e custo. Foram realizados experimentos com instâncias sintéticas com 15 até 50 clientes, as quais são geradas aleatoriamente, e com uma instância real, baseada na experiência profissional no mercado empresarial e em cenários reais de distribuição na cidade de São Paulo / Providers need to supply the demand of their clients as optimally as possible and maintaining the quality of their service, however in many cases this demand is unknown. This problem can be modeled as a inventory routing problem with stochastic demand, which includes inventory control, product transportation and delivery scheduling decisions. There are several papers in the literature to solve this problem, but none of them deals with service time window, maximum stock capacity for both the customer and the depot and individualized confidence level for each costumer. The main objective of this work is to propose a new algorithm based on mathematical optimization to deal with this more realistic problem. In addition, this work has as secondary objective to improve the state of the art algorithm based on mathematical optimization, aiming to find solutions with a lower computational time and cost. Experiments were performed with synthetic instances with 15 to 50 clients, which are randomly generated, and with a real instance, based on professional experience in the business market and in real distribution scenarios in the city of São Paulo

Cette thèse porte sur l’optimisation de l’approvisionnement dans les zones géographiquement lointaines. Au moment de planifier des approvisionnements de matières premières ou de composants dans des pays lointains, la longue distance géographique entre l’acheteur et le fournisseur devient un enjeu essentiel à prendre en compte. Puisque le transport se fait souvent par la voie maritime, le délai d’approvisionnement est si long que les besoins peuvent évoluer pendant la longue période de livraison, ce qui peut engendrer un risque de rupture élevé. Cette thèse présente des approches adaptatives afin d’élaborer des plans d’approvisionnements lointains d’une manière rentable. Tout d’abord, nous proposons un cadre d’adaptation de la planification des approvisionnements lointains. Il déploie des techniques de prévision de la demande et des méthodes d’optimisation d’approvisionnements à horizon glissant. En utilisant ce cadre, nous transformons le problème de la planification sur l’horizon globale en plusieurs problèmes standards de lotissement avec demandes stochastiques sur des sous-horizons. Ce cadre permet aussi d’évaluer la performance sur une longue période des méthodes utilisées. Nous considérons ensuite la planification optimale d’approvisionnement sur les sous-horizons. Deux hypothèses de ruptures de stocks sont considérées: livraison tardive et vente perdue (ou sous-traitance). Nous développons des approches optimales ou quasi-optimales pour faire des plans d’approvisionnement tout en minimisant les coûts totaux prévus de commande, de stockage et de rupture sur les sous-horizons. Les méthodes proposées peuvent servir de repères pour évaluer d’autres méthodes. Pour chaque hypothèse, nous menons des expériences numériques pour évaluer les algorithmes développés et les approches adaptatives de planification globales. Les résultats expérimentaux montrent bien leur efficacité. / This research discusses procurement planning problems engaged in global sourcing. The main difficulty is caused by the geographically long distance between buyer and supplier, which results in long lead times when maritime transport is used. Customer demands of finished products usually evolve during the shipment, thus extra costs will be produced due to unpredictable overstocks or stockouts. This thesis presents adaptive planning approaches to make adequate long-distance procurement plans in a cost-efficient manner. Firstly, an adaptive procurement planning framework is presented. The framework deploys demand forecasting and optimal planning in a rolling horizon scheme. In each subhorizon, demands are assumed to follow some known distribution patterns, while the distribution parameters will be estimated based on up-to-date demand forecasts and forecast accuracy. Then a portable processing module is presented to transform the sub-horizon planning problem into an equivalent standard lot-sizing problem with stochastic demands.Secondly, optimal or near-optimal procurement planning methods are developed to minimize expected total costs including setup, inventory holding and stockout penalty in subhorizons. Two extreme stockout assumptions are considered: backorder and lost sale (or outsourcing). The proposed methods can serve as benchmarks to evaluate other methods. Numerical tests have validated the high efficiency and effectiveness of both sub-horizon planning methods and the overall adaptive planning approaches.

One of the objectives of disaggregation in hierarchical production planning is to minimize the setup costs incurred when changing production from one family to another. In this research, the setup costs are reduced by determining a production schedule that minimizes the number of setups during the planning horizon. Previous solutions to the disaggregation problem have considered discrete-time, and more recently continuous-time formulations. This research extends the continuous time disaggregation approach by incorporating production schedules allowing backorder. A mathematical formulation and a solution algorithm are presented and the computational complexity and convergence properties of the algorithm are discussed. Experimental results, using both deterministic and stochastic demand patterns, which demonstrate the efficacies of the solution approach are provided.

O aumento da variabilidade da demanda ao longo de uma cadeia de abastecimento é conhecido como Efeito Chicote (EC). A modelagem deste fenômeno é fundamental para a quantificação de sua intensidade, ajudando a reduzir seus impactos negativos sobre o nível de serviço e sobre os estoques em uma cadeia de abastecimento. Esta tese apresenta uma proposta de modelagem do EC que tem por objetivo aumentar a precisão na quantificação deste fenômeno em ambientes com demanda e lead time estocásticos. O novo modelo considera dois elementos que não estão presentes nos principais modelos disponíveis na literatura: a variabilidade no lead time de entrega de pedidos e a incorporação de um ajuste para contemplar uma política adequada de tratamento dos excessos de estoque. Além disso, define de modo mais preciso o papel do coeficiente de variação da demanda na quantificação do EC. A utilização do modelo proposto aumenta a eficiência da gestão de cadeias de abastecimento ao contribuir para atenuar a propagação do EC, elevar o nível de serviço e reduzir os níveis local e global dos estoques. Neste documento, os principais modelos de quantificação do EC são apresentados e analisados, com destaque para os trabalhos de Lee et al. (1997b), Chen et al. (2000), Fransoo e Wouters (2000) e Warburton (2004); nessa análise foram identificadas várias deficiências, capazes de produzir fortes distorções no processo de quantificação do EC. O modelo proposto supre integralmente estas deficiências e apresenta elementos que indicam que a intensidade e o comportamento estocástico e serial do EC só podem ser adequadamente modelados se a variabilidade do lead time for considerada e se os excessos de estoque forem utilizados no cálculo do tamanho dos pedidos. O novo modelo, além de contribuir para o entendimento da dinâmica do EC e para a ampliação do respectivo campo de discussão, representa adequadamente a complexidade das relações entre as variáveis associadas ao EC, o que lhe confere alta capacidade preditiva. Complementarmente, demonstra-se que o modelo de Chen et al. (2000) constitui um caso particular do modelo proposto. / The increase in demand variability as information flows from customers to manufacturers in a supply chain is known as the Bullwhip Effect (BE). Modeling this phenomenon is fundamental in measuring its intensity, aiming at reducing its negative impacts on both service and inventory levels in the supply chain. In this dissertation we propose a new, more precise mathematical model for quantifying the BE in systems with stochastic demand and lead time. The new model takes into account the lead time variability and is adjusted to a more realistic treatment of negative order quantities that may arise in some inventory cycles, two elements not present in the main available models in the literature. In addition, the model enables a more precise assessment of the role that the demand coefficient of variation plays in the quantification of the BE. The use of the proposed model enables an improved management of the supply chain by attenuating the propagation of the BE, increasing the service level and reducing inventory levels both locally and globally. In this dissertation, the main models for quantifying the BE are presented and analyzed, with emphasis in the works of Lee et al. (1997b), Chen et al. (2000), Fransoo and Wouters (2000) and Warburton (2004); in that analysis were identified several deficiencies, able to generate severe distortions in the quantification of the BE. The proposed model fully overcomes these deficiencies and presents elements that indicate that the intensity and stochastical and serial behavior of the BE can only be appropriately modeled if the lead time variability is considered and if inventory excesses are used in the order size calculation. The new model, in addition to contribute to the understanding of the BE dynamics enriching its analysis, represents appropriately the complexity of relationships among variables associated with the BE, contributing to its high predictive capacity. Finally, it is demonstrated that the model in Chen et al. (2000) represents a special case of the proposed model.

O aumento da variabilidade da demanda ao longo de uma cadeia de abastecimento é conhecido como Efeito Chicote (EC). A modelagem deste fenômeno é fundamental para a quantificação de sua intensidade, ajudando a reduzir seus impactos negativos sobre o nível de serviço e sobre os estoques em uma cadeia de abastecimento. Esta tese apresenta uma proposta de modelagem do EC que tem por objetivo aumentar a precisão na quantificação deste fenômeno em ambientes com demanda e lead time estocásticos. O novo modelo considera dois elementos que não estão presentes nos principais modelos disponíveis na literatura: a variabilidade no lead time de entrega de pedidos e a incorporação de um ajuste para contemplar uma política adequada de tratamento dos excessos de estoque. Além disso, define de modo mais preciso o papel do coeficiente de variação da demanda na quantificação do EC. A utilização do modelo proposto aumenta a eficiência da gestão de cadeias de abastecimento ao contribuir para atenuar a propagação do EC, elevar o nível de serviço e reduzir os níveis local e global dos estoques. Neste documento, os principais modelos de quantificação do EC são apresentados e analisados, com destaque para os trabalhos de Lee et al. (1997b), Chen et al. (2000), Fransoo e Wouters (2000) e Warburton (2004); nessa análise foram identificadas várias deficiências, capazes de produzir fortes distorções no processo de quantificação do EC. O modelo proposto supre integralmente estas deficiências e apresenta elementos que indicam que a intensidade e o comportamento estocástico e serial do EC só podem ser adequadamente modelados se a variabilidade do lead time for considerada e se os excessos de estoque forem utilizados no cálculo do tamanho dos pedidos. O novo modelo, além de contribuir para o entendimento da dinâmica do EC e para a ampliação do respectivo campo de discussão, representa adequadamente a complexidade das relações entre as variáveis associadas ao EC, o que lhe confere alta capacidade preditiva. Complementarmente, demonstra-se que o modelo de Chen et al. (2000) constitui um caso particular do modelo proposto. / The increase in demand variability as information flows from customers to manufacturers in a supply chain is known as the Bullwhip Effect (BE). Modeling this phenomenon is fundamental in measuring its intensity, aiming at reducing its negative impacts on both service and inventory levels in the supply chain. In this dissertation we propose a new, more precise mathematical model for quantifying the BE in systems with stochastic demand and lead time. The new model takes into account the lead time variability and is adjusted to a more realistic treatment of negative order quantities that may arise in some inventory cycles, two elements not present in the main available models in the literature. In addition, the model enables a more precise assessment of the role that the demand coefficient of variation plays in the quantification of the BE. The use of the proposed model enables an improved management of the supply chain by attenuating the propagation of the BE, increasing the service level and reducing inventory levels both locally and globally. In this dissertation, the main models for quantifying the BE are presented and analyzed, with emphasis in the works of Lee et al. (1997b), Chen et al. (2000), Fransoo and Wouters (2000) and Warburton (2004); in that analysis were identified several deficiencies, able to generate severe distortions in the quantification of the BE. The proposed model fully overcomes these deficiencies and presents elements that indicate that the intensity and stochastical and serial behavior of the BE can only be appropriately modeled if the lead time variability is considered and if inventory excesses are used in the order size calculation. The new model, in addition to contribute to the understanding of the BE dynamics enriching its analysis, represents appropriately the complexity of relationships among variables associated with the BE, contributing to its high predictive capacity. Finally, it is demonstrated that the model in Chen et al. (2000) represents a special case of the proposed model.