231 research outputs found

    A newsvendor model with service and loss constraints

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    Actual performance measurement systems do not only consider financial measures like costs and profits but also non-financial indicators with respect customer service, quality and flexibility. Using the newsvendor model we explore the influence of possibly conflicting performance measures on important operations decisions like the order quantity and the selling price of a product. For price-independent as well as price-dependent demand distribution like in the classical newsvendor model the objective is to maximise the expected profit. But the optimal decisions are computed with respect to a service constraint - a lower bound for the level of product availability - and to a loss constraint - an upper bound for the probability of resulting in loss. For the price-independent model a condition for the existence of an optimal order quantity and its structure is presented. For the price-setting newsvendor the admissible region of the order quantity and the selling price is characterised for the additive and the multiplicative model. Furthermore, it is shown that higher variability of demand leads to a smaller admissible region of the decision variables thereby easing the computation of the optimal decisions.Constrained Newsvendor Model, Price-Setting Newsvendor

    Deep Neural Newsvendor

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    We consider a data-driven newsvendor problem, where one has access to past demand data and the associated feature information. We solve the problem by estimating the target quantile function using a deep neural network (DNN). The remarkable representational power of DNN allows our framework to incorporate or approximate various extant data-driven models. We provide theoretical guarantees in terms of excess risk bounds for the DNN solution characterized by the network structure and sample size in a non-asymptotic manner, which justify the applicability of DNNs in the relevant contexts. Specifically, the convergence rate of the excess risk bound with respect to the sample size increases in the smoothness of the target quantile function but decreases in the dimension of feature variables. This rate can be further accelerated when the target function possesses a composite structure. Compared to other typical models, the nonparametric DNN method can effectively avoid or significantly reduce the model misspecification error. In particular, our theoretical framework can be extended to accommodate the data-dependent scenarios, where the data-generating process is time-dependent but not necessarily identical over time. Finally, we apply the DNN method to a real-world dataset obtained from a food supermarket. Our numerical experiments demonstrate that (1) the DNN method consistently outperforms other alternatives across a wide range of cost parameters, and (2) it also exhibits good performance when the sample size is either very large or relatively limited

    Supplier Choice: Market Selection under Uncertainty.

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    Suppliers and Manufacturers generally have some say in which subset of all possible demand they will meet. In some cases that choice is implicit through pricing decisions and feature selection. Other times it is made explicitly by choosing only specific regions to stock a product in. This thesis includes models using both approaches and incorporates random demands. We present several methods for choosing a subset of all candidate customers given uncertain demands. In this thesis we consider four models of demand selection. The first two research problems consider market selection, which has been studied in the literature. The Selective Newsvendor Problem (SNP) looks at a decision maker choosing a subset of candidate markets to serve, and then receiving revenues and paying newsvendor-type costs based on the selected collection. In this thesis we consider a generalization with normally distributed demands which includes a multi-period problem as a special case and develop both exact and heuristic algorithms to solve it. When demands are not normally distributed, the problem is considerably more complex and is in general NP-hard. We develop an approximation algorithm using sample average approximation and a rounding approach to efficiently solve the problem. In addition to the work on market selection, we propose two other models for demand selection. We study auctions as a tool for a supplier with a fixed capacity to allocate the limited supply to retailers with newsvendor-type costs. Finally, we present a model for a supplier who must ensure demand is met in all markets, but has the option to work with subsidiary suppliers to meet that demand.PhDIndustrial and Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120864/1/zstrinka_1.pd

    Prescriptive Analytics in Electricity Markets

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    Electricity markets are a clear example of a sector in which decision making plays a crucial role in its daily activity. Moreover, uncertainty is intrinsic to electricity markets and affects most of the tasks that agents operating in them must carry out. Many of these tasks involve decisions characterized by low risk and being addressed periodically. In this thesis, we refer to these tasks as iterative decisions. This thesis applies the aforementioned innovative frameworks for decision making under uncertainty using contextual information in iterative decision making tasks faced daily by electricity market agents.Decision making is critical for any business to survive in a market environment. Examples of decision making tasks are inventory management, resource allocation or portfolio selection. Optimization, understood as the scientific discipline that studies how to solve mathematical programming problems, can help make more efficient decisions in many of these situations. Particularly relevant, because of their frequency and difficulty, are those decisions affected by uncertainty, i.e., in which some of the parameters that precisely determine the optimization problem are unknown when the decision must be made. Fortunately, the development of information technologies has led to an explosion in the availability of data that can be used to assist decisions affected by uncertainty. However, most of the available historical data do not correspond to the unknown parameter of the problem but originate from other related sources. This subset of data, potentially valuable for obtaining better decisions, is called contextual information. This thesis is framed within a new scientific effort that seeks to exploit the potential of data and, in particular, of contextual information in decision making. To this end, in this thesis, we have developed mathematical frameworks and data-driven optimization models that exploit contextual information to make better decisions in problems characterized by the presence of uncertain parameters

    Models for Flexible Supply Chain Network Design

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    Arguably Supply Chain Management (SCM) is one of the central problems in Operations Research and Management Science (OR/MS). Supply Chain Network Design (SCND) is one of the most crucial strategic problems in the context of SCM. SCND involves decisions on the number, location, and capacity, of production/distribution facilities of a manufacturing company and/or its suppliers operating in an uncertain environment. Specifically, in the automotive industry, manufacturing companies constantly need to examine and improve their supply chain strategies due to uncertainty in the parameters that impact the design of supply chains. The rise of the Asian markets, introduction of new technologies (hybrid and electric cars), fluctuations in exchange rates, and volatile fuel costs are a few examples of these uncertainties. Therefore, our goal in this dissertation is to investigate the need for accurate quantitative decision support methods for decision makers and to show different applications of OR/MS models in the SCND realm. In the first technical chapter of the dissertation, we proposed a framework that enables the decision makers to systematically incorporate uncertainty in their designs, plan for many plausible future scenarios, and assess the quality of service and robustness of their decisions. Further, we discuss the details of the implementation of our framework for a case study in the automotive industry. Our analysis related to the uncertainty quantification, and network's design performance illustrates the benefits of using our framework in different settings of uncertainty. Although this chapter is focused on our case study in the automotive industry, it can be generalized to the SCND problem in any industry. We have outline the shortcomings of the current literature in incorporating the correlation among design parameters of the supply chains in the second technical chapter. In this chapter, we relax the traditional assumption of knowing the distribution of the uncertain parameters. We develop a methodology based on Distributionally Robust Optimization (DRO) with marginal uncertainty sets to incorporate the correlation among uncertain parameters into the designing process. Further, we propose a delayed generation constraint algorithm to solve the NP-hard correlated model in significantly less time than that required by commercial solvers. Further, we show that the price of ignoring this correlation in the parameters increases when we have less information about the uncertain parameters and that the correlated model gives higher profit when exchange rates are high compared to the stochastic model (with the independence assumption). We extended our models in previous chapters by presenting capacity options as a mechanism to hedge against uncertainty in the input parameters. The concept of capacity options similar to financial options constitute the right, but not the obligation, to buy more commodities from suppliers with a predetermined price, if necessary. In capital-intensive industries like the automotive industry, the lost capital investment for excess capacity and the opportunity costs of underutilized capacity have been important drivers for improving flexibility in supply contracts. Our proposed mechanism for high tooling cost parts decreases the total costs of the SCND and creates flexibility within the structure of the designed SCNs. Moreover, we draw several insights from our numerical analyses and discuss the possibility of price negotiations between suppliers and manufacturers over the hedging fixed costs and variable costs. Overall, the findings from this dissertation contribute to improve the flexibility, reliability, and robustness of the SCNs for a wide-ranging set of industries.PHDIndustrial & Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145819/1/nsalehi_1.pd

    Analizando los efectos del diseño contractual y estructural en la cadena de suministro del sector salud

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    Introducción Balancear el acceso a medicamentos necesarios contra el aumento en los costes es uno de los retos fundamentales en el diseño y la reforma de los sistemas de salud. Del año 2000 al 2008, el crecimiento promedio en el gasto per capita en productos farmacéuticos para los países de la Organización para la Cooperación y Desarrollo Económico (OCDE) fue de casi 60 %. La problemática se encuentra especialmente presente en el proceso de introducción de nuevos medicamentos orientados al tratamiento de condiciones crónicas. Aquí los precios de lista propuestos por los productores farmacéuticos tienden a ser altos para recuperar la inversión, en algunas ocasiones contrastando con la falta de evidencia robusta con respecto a la coste-efectividad del tratamiento al momento de la negociación del precio de transferencia. Más aún, tal coste-efectividad puede variar a través de las diferentes indicaciones terapéuticas de un mismo medicamento, i.e., para distintos grupos de pacientes. Como resultado, en los acuerdos tradicionales el pagador de salud (e.g., Sistemas Nacionales de Salud, Organizaciones de Mantenimiento de la Salud, grandes empresas aseguradoras) puede verse atrapado entre restringir el acceso al medicamento o arriesgar el pago de altos precios que pueden no justificarse ex-post debido a la incertidumbre sobre el valor real de la innovación terapéutica del medicamento, la falta de solidez en los resultados presentados por el productor, o la replicabilidad de esos resultados en la práctica clínica. En respuesta a la creciente presión para controlar el gasto en el sector salud, los pagadores de salud han empujado a los productores farmacéuticos a reducir los precios, potencialmente reduciendo los incentivos para invertir en tratamientos innovadores, y continuamente resultando en la (temporal o definitiva) ausencia de un acuerdo entre ambos agentes involucrados con la consecuente pérdida de bienestar para los pacientes potenciales y de benficios financieros para el productor. Lo anterior ha motivado a los productores -particularmente aquellos en los sectores cardiovasculares y de oncología- a explorar acuerdos más sofisticados donde los riesgos puedan ser compartidos de una manera más eficiente. Motivados por la tendencia mencionada, reconocemos que un pagador de salud debe decidir no únicamente si aprobar o no un nuevo medicamento para su (parcial o total) reembolso por consumo para la población de pacientes que sirve, sino también determinar el nivel de servicio (cuál será el volumen adquirido para satisfacer la demanda de los pacientes), el nivel de acceso (cuáles grupos de pacientes estarán cubiertos por el pagador de salud), y las condiciones de reembolso a los productores (los parámetros del contrato). Además reconocemos que un pagador de salud puede tener diferentes prioridades según el ambiente social e industrial donde opere (e.g., maximizar la eficiencia de los recursos versus maximizar el bienestar de los pacientes), así como restricciones (e.g., límite máximo de gastos por periodo de demanda para algún medicamento o innovación terapéutica, y un límite mínimo de coste-efectividad). Con respecto a los productores farmacéuticos, consideramos que: la determinación del precio de transferencia puede ser exógena (a través de precios de referencia externos) o endógena (a través de acuerdos directos con los pagadores de salud); que pueden internalizar (parcial o totalmente) el riesgo de mantener el inventario; y que en algunos casos son capaces de segmentar el mercado a través de la creación de productos o canales distinguibles enfocados a cada grupo de pacientes. Preguntas de Investigación En el contexto descrito donde un medicamento innovador con múltiples aplicaciones terapéuticas busca su introducción al mercado, la presente investigación pretende responder de manera analítica las preguntas mostradas a continuación. -- En un sistema verticalmente integrado, ¿cómo interactúan los niveles de acceso y de servicio en función de las prioridades y restricciones del sistema? -- En una cadena de tipo productor - pagador de salud, ¿qué cambia cuando el precio es determinado de manera exógena (vs. endógena) y el productor está (vs. no está) dispuesto a compartir los riesgos asociados a la incertidumbre en la magnitud de la demanda y en los resultados observados en los pacientes? -- Para un medicamento con múltiples aplicaciones terapéuticas, ¿cómo se refleja la decisión de segmentar vs. consolidar el diseño/canal de distribución, en el nivel de servicio y los incentivos para ejercer esfuerzo orientado a la innovación? -- ¿Cuál es el efecto de todo lo anterior en los beneficios del productor farmacéutico, los gastos del pagador de salud, y el bienestar de los pacientes? De este modo, la investigación espera contribuir a una comprensión más amplia del comportamiento del sistema, y así eventualmente orientar el diseño de la estructura y los contratos en las cadenas de suministro del sector salud, de modo que exista una mejor alineación con los objetivos de los agentes involucrados. Metodología y Suposiciones Fundamentales El procedimiento general para responder a las preguntas anteriores se basa en una modelación matemática de las situaciones previamente descritas utilizando la estructura del modelo del vendedor de periódicos (o newsvendor, como se le conoce normalmente en inglés). Esta elección se debe a: i)los tiempos de espera extensos (aproximadamente 4 meses) para la construcción de capacidad productiva, aprovisionamiento de materias primas, producción, y envío de los medicamentos; ii)la práctica común en la industria de ofrecer precios preferenciales para órdenes de gran tamaño, respaldando la suposición sobre la división de la demanda en periodos largos de tiempo; iii)los altos niveles de utilización que son típicos en la industria, limitando la suposición de una amplia capacidad productiva; y iv)la baja probabilidad de, y las consecuencias negativas en tema de salud asociadas con, retrasar el tratamiento médico de un paciente. La cadena de suministro considerada se compone de un productor farmacéutico que ofrece la venta de un medicamento a un pagador de salud quien está a cargo de la disponibilidad de dicho medicamento para la población de pacientes. Se asume que existe heterogeneidad de pacientes de modo que al menos dos grupos de pacientes pueden verse beneficiados al recibir el medicamento, donde se espera que cada grupo obtenga beneficios clínicos diferentes entre sí al consumir el mismo medicamento. Analizamos el problema de optimización con restricciones para el productor, el pagador de salud, o el sistema integrado (según sea el caso en cuestión), utilizando conceptos de teoría de juegos para caractrizar la solución de equilibrio en la toma de decisiones tanto simultáneas como secuenciales. Contribución Teórica En su artículo seminal, Arrow (1963)1 sostiene que la incertidumbre tanto en la incidencia de la enfermedad (i.e., el tamaño de la demanda) como en la eficacia del tratamiento (i.e., el ingreso/beneficio clínico por unidad de tratamiento) genera adaptaciones que limitan el poder descriptivo del modelo tradicional de competencia y sus implicaciones para la eficiencia económica. Tomando esto en cuenta, la disertación contribuye primordialmente a tres vertientes de investigación. Primeramente, la literatura en economía de la salud se concentra sea en la determinación del nivel de acceso dada la heterogeneidad en las características de los pacientes y la incertidumbre en la eficacia del tratamiento (e.g., Barros, 20112; Zaric, 20083), o en la decisión binaria de incluir un medicamento en la lista de tratamientos reembolsables por un pagador de salud dada la incertidumbre en la demanda (e.g., Zhang et al., 20114). En constraste, la tesis analiza de manera simultánea el problema del nivel de acceso e incertidumbre en la demanda, bajo las características específicas del sector. Tal situación es similar al problema planteado en administración de operaciones donde el precio de venta y la cantidad de inventario disponible son determinadas de manera simultánea en la presencia de demanda aleatoria y dependiente del precio. La disertación contribuye a tal línea de investigación (e.g.,., Petruzzi et al., 19995; Salinger et al., 20116) al analizar dicha interacción de decisiones según diferentes diseños de contratos entre el productor y el pagador de salud, bajo una combinación de objetivos y restricciones. Adicionalmente, contribuye a los trabajos en coordinación de la cadena de suministro (e.g.,., Bernstein et al., 20057; Cachon et al., 20058) al permitir que el "ingreso" por unidad "vendida" , i.e., los beneficios clínicos, sea un valor no determinístico, limitando además el espacio de los posibles "precios de venta" a un subconjunto de valores discretos, siendo estos una función del nivel de acceso seleccionado. Finalmente, se contribuye a la literatura de agregación de inventarios (e.g., Eppen, 1979)9 al incorporar la heterogeneidad de pacientes en un sistema de primeras-llegadas primeros-servicios sin posibilidad de reserva, demostrando resultados contrastantes con respecto a las preconcepciones sobre los beneficios generales de la agregación

    Demand Modeling And Capacity Planning For Innovative Short Life-Cycle Products

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    This dissertation focuses on demand modeling and capacity planning for innovative short life-cycle products. We first developed a new model in the class of stochastic Bass formulations that addresses the shortcomings of models from the extant literature. The proposed model considers the common fact that the market potential of a product is not fixed and might change during a life-cycle due to exogenous (e.g., economic- or competitors-related) or endogenous (e.g., quality-related) factors. Allowing this parameter (market potential in the Bass model) to follow a geometric random walk, we have showed that the future demand of a product in each period follows a lognormal distribution with specific mean and variance. We also developed a novel stochastic capacity expansion model that can be used by a make-to-order manufacturer, who faces stochastic stationary/non-stationary demand, in order to optimally determine policies for specifying the sizes of capacity procurement. In addition to the cost of expansion decisions, the proposed risk-neutral expansion model considers procurement lead-times, irreversibility of investments, and the costs associated with lost sales and unutilized capacity. We provide necessary and sufficient conditions for the derived optimal policy. We then present an exact solution method, which is more efficient than classical recursive methods. Additionally, three extensions of the proposed expansion model that can address more complicated settings are presented. The first extension increases the capability of the model in order to tackle capacity planning for a multi-sourcing scenario. Multi-sourcing is a case in which the manufacturer can procure capacity from two supply modes whose marginal expansion costs and lead-times are complementary. The second extension addresses a scenario in which an installed capacity can be used for producing future generations of a product. The last extension accounts for salvage value of the installed capacity in the model and provides the necessary and sufficient conditions for the optimal policy. Finally, using the proposed stochastic Bass model, we present the results and managerial insights gathered from numerical experiments that have been conducted for the stochastic capacity expansion models
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