As exploration in space increases through the use of larger telescopes, more sophisticated structures, and physical exploration, the use of autonomous robots will become instrumental to build and maintain the infrastructures required for this exploration. These systems must be autonomous to deal with the infeasibility of teleoperation due signal delay and task complexity. The reality of using robots in the real world without direct human input will require the autonomous systems to have the capability of responding to errors that occur in an assembly scenario on their own. As such, a system must be in place to allow for the sequencing and allocation of tasks to the robotic workforce autonomously, giving the ability to re-plan in real world stochastic environments. This work presents four contributions towards a system allowing for the autonomous sequencing and allocation of tasks for in-space assembly problems. The first contribution is the development of the Stochastic Assembly Problem Definition (SAPD) to articulate all of the features in an assembly problem that are applicable to the task sequencing and allocation. The second contribution is the formulation of a mixed integer program to solve for assembly schedules that are optimal or a quantifiable measurement from optimal. This contribution is expanded through the development of a genetic algorithm formulation to utilize the stochastic information present in the assembly problem. This formulation extends the state-of-the-art techniques in genetic algorithms to allow for the inclusion of new constraints required for the in-space assembly domain. The third contribution addresses how to estimate a robot's ability to complete a task if the robot must be assigned to a task it was previously not expected to work on. This is accomplished through the development of four metrics and analyzed through the use of screw theory kinematics. The final contribution focuses on a set of metrics to guide the selection of a good scheduling method for different assembly situations. The experiments in this work demonstrate how the developed theory can be utilized and shows the scheduling systems producing the best or close to the best schedules for assemblies. It also shows how the metrics used to quantify and estimate robot ability are applied. The theory developed in this work provides another step towards autonomous systems that are capable of assembling structures in-space without the need for human input. / Doctor of Philosophy / As space exploration continues to progress, autonomous robots are needed to allow for the necessary structures to be built in-space, on Mars, and on the Lunar surface. Since it is not possible to plan for every possible thing that could go wrong or break, the robots must be able to figure out how to build and repair structures without human input. The work presented here develops a framework that allows this in-space assembly problem to be framed in a way the robots can process. It then provides a method for generating assembly schedules that describe very good, if not the best way to complete the assembly quickly while still taking into account randomness that may be present. Additionally, this work develops a way to quantify and estimate how good robots will be at a task they have not attempted before. Finally, a set of considerations are proposed to aid in determining what scheduling method will work best for different assembly scenarios. The experiments in this work demonstrate how the developed theory can be used and shows the scheduling systems producing the best or close to the best schedules for assemblies. It also shows how the methods used to define robot ability are applied. The work developed here provides another step towards autonomous systems that are capable of assembling structures in-space without the need for human input.

Massive infrastructure networks such as electric power, natural gas, or water systems play a pivotal role in everyday human lives. Development and operation of these networks is extremely capital-intensive. Moreover, security and reliability of these networks is critical. This work identifies and addresses a diverse class of computationally challenging and time-critical problems pertaining to these networks. This dissertation extends the state of the art on three fronts. First, general proofs of uniqueness for network flow problems are presented, thus addressing open problems. Efficient network flow solvers based on energy function minimizations, convex relaxations, and mixed-integer programming are proposed with performance guarantees. Second, a novel approach is developed for sample-efficient training of deep neural networks (DNN) aimed at solving optimal network dispatch problems. The novel feature here is that the DNNs are trained to match not only the minimizers, but also their sensitivities with respect to the optimization problem parameters. Third, control mechanisms are designed that ensure resilient and stable network operation. These novel solutions are bolstered by mathematical guarantees and extensive simulations on benchmark power, water, and natural gas networks. / Doctor of Philosophy / Massive infrastructure networks play a pivotal role in everyday human lives. A minor service disruption occurring locally in electric power, natural gas, or water networks is considered a significant loss. Uncertain demands, equipment failures, regulatory stipulations, and most importantly complicated physical laws render managing these networks an arduous task. Oftentimes, the first principle mathematical models for these networks are well known. Nevertheless, the computations needed in real-time to make spontaneous decisions frequently surpass the available resources. Explicitly identifying such problems, this dissertation extends the state of the art on three fronts: First, efficient models enabling the operators to tractably solve some routinely encountered problems are developed using fundamental and diverse mathematical tools; Second, quickly trainable machine learning based solutions are developed that enable spontaneous decision making while learning offline from sophisticated mathematical programs; and Third, control mechanisms are designed that ensure a safe and autonomous network operation without human intervention. These novel solutions are bolstered by mathematical guarantees and extensive simulations on benchmark power, water, and natural gas networks.

The primary aim of this thesis is to develop effective solution techniques for large-scale maritime inventory routing problems that possess a core substructure common in many real-world applications. We use the term “large-scale” to refer to problems whose standard mixed-integer linear programming (MIP) formulations involve tens of thousands of binary decision variables and tens of thousands of constraints and require days to solve on a personal computer. Although a large body of literature already exists for problems combining vehicle routing and inventory control for road-based applications, relatively little work has been published in the realm of maritime logistics. A major contribution of this research is in the advancement of novel methods for tackling problems orders of magnitude larger than most of those considered in the literature. Coordinating the movement of massive vessels all around the globe to deliver large quantities of high value products is a challenging and important problem within the maritime transportation industry. After introducing a core maritime inventory routing model to aid decision-makers with their coordination efforts, we make three main contributions. First, we present a two-stage algorithm that exploits aggregation and decomposition to produce provably good solutions to complex instances with a 60-period (two-month) planning horizon. Not only is our solution approach different from previous methods discussed in the maritime transportation literature, but computational experience shows that our approach is promising. Second, building on the recent successes of approximate dynamic programming (ADP) for road-based applications, we present an ADP procedure to quickly generate good solutions to maritime inventory routing problems with a long planning horizon of up to 365 periods. For instances with many ports (customers) and many vessels, leading MIP solvers often require hours to produce good solutions even when the planning horizon is limited to 90 periods. Our approach requires minutes. Our algorithm operates by solving many small subproblems and, in so doing, collecting and learning information about how to produce better solutions. Our final research contribution is a polyhedral study of an optimization problem that was motivated by maritime inventory routing, but is applicable to a more general class of problems. Numerous planning models within the chemical, petroleum, and process industries involve coordinating the movement of raw materials in a distribution network so that they can be blended into final products. The uncapacitated fixed-charge transportation problem with blending (FCTPwB) that we study captures a core structure encountered in many of these environments. We model the FCTPwB as a mixed-integer linear program and derive two classes of facets, both exponential in size, for the convex hull of solutions for the problem with a single consumer and show that they can be separated in polynomial time. Finally, a computational study demonstrates that these classes of facets are effective in reducing the integrality gap and solution time for more general instances of the FCTPwB.

In this thesis, we propose novel optimization and spatial queueing models that expand the currently existing methods by allowing multiple servers to be located at the same station and multiple servers to be dispatched to a single call. In particular, a mixed integer linear programming (MILP) model is introduced that determines how to locate and dispatch ambulances such that the coverage level is maximized. The model allows multiple servers to be located at the same station and balances the workload among them while maintaining contiguous first priority response districts. We also propose an extension to the approximate Hypercube queueing model by allowing multi-server dispatches. Computational results suggest that both models are effective in optimizing and analyzing the emergency systems. We also introduce the M[G]/M/s/s queueing model as an extension to the M/M/s/s model which allows for multiple servers to be assigned to a single customer.

Les travaux de cette thèse sont les fruits de collaboration depuis 2008 entre l’ICL et le Centre Ingénierie et Santé (CIS) de l'Ecole des Mines de Saint Etienne. CIS et ICL sont tous deux membres de l'Institut Fédératif de Recherche en Science, Ingénierie et Santé (IFRESIS) et participent tous deux aux travaux du Cancéropôle Lyon Auvergne Rhône-Alpes (CLARA) dont Franck Chauvin animait l'axe IV sur Epidémiologie, SHS, Information du Patient et Organisation des Soins. Cette thèse a été initiée avec la volonté de développer une recherche originale sur l'optimisation de la production de soins en cancérologie.Nous nous intéressons à différentes problématiques de la gestion de soins des patients dans un hôpital de jour en cancérologie. Nous visons à équilibrer au mieux les besoins journaliers en lits tout en prenant en compte l'adhérence aux protocoles de soins, les contraintes des oncologues et les aléas des flux de patients. Pour un hôpital de jour en oncologie, nous avons identifié et étudié les décisions suivantes : I. Le planning médical une fois par an afin de déterminer les périodes de travail des oncologues dans une semaine. Nous avons proposé une formulation originale sous forme d'un modèle de programmation linéaire en nombres mixtes (MIP) et une approche en 3-étapes. II. L’affectation des nouveaux patients qui détermine le jour de la chimiothérapie pour chaque patient entrant. Nous avons présenté trois stratégies de planification et nous avons décrit un algorithme de simulation pour évaluer ces stratégies de planification. Les stratégies de planification proposées exploitent les informations contenues dans les protocoles de soins des patients et utilisent l’optimisation Monte Carlo III. La planification des rendez-vous. Nous avons présenté deux méthodes pour la résolution de ce problème : une approche basée sur la relaxation Lagrangienne et une heuristique basée sur une optimisation par recherche localeIV. La planification des jours fériés : permet de remédier au problème des semaines comportant des jours fériés. Nous avons développé un modèle en programmation linéaire en nombres mixtes permettant de répartir rapidement la charge du jour férié sur les jours en amont et en aval sans trop dégradé l’efficacité du traitement, ni surcharger le travail de l’HDJ. / This research is performed in close collaboration with the cancer center ICL. The « Institut de Cancérologie de la Loire » (Loire Cancer Institute), a.k.a. ICL, is a French public comprehensive cancer center providing oncology.This thesis addresses the problem of determining the work schedule, called medical planning, of oncologists for chemotherapy of oncology patients at ambulatory care units. A mixed integer programming (MIP) model is proposed for medical planning in order to best balance bed capacity requirements under capacity constraints of key resources such as beds and oncologists. The most salient feature of the MIP model is the explicit modeling of specific features of chemotherapy such as treatment protocols. The medical planning problem is proved to be NP-complete. A three-stage approach is proposed for determining good medical planning in reasonable computational time.

Sistemas dutoviários desempenham um papel fundamental na cadeia de suprimento da indústria de petróleo. Este tipo de sistema é responsável pelo transporte da maior parte do volume de petróleo e seus derivados. Sistemas de dutos transportam uma grande quantidade de diferentes tipos de petróleo e seus derivados a custo mais baixo que outros tipos de modais. Dutos interligam campos de produção de petróleo, portos, refinarias, centros de distribuição (ou depósitos), e mercado consumidor. O problema estudado neste trabalho é baseado em um sistema que é composto por uma refinaria que pode transferir vários produtos para um terminal (depósito) através de um único duto. Os produtos são conjuntos de derivados de petróleo que devem ser transferidos da refinaria para o terminal ou do terminal para a refinaria. Ambos, refinaria e terminal estão conectados a outras refinarias, terminais e mercados consumidores e com isto formam uma complexa rede de dutos. Por outro lado há um conjunto de demandas externas e internas. Esta última demanda decorre da necessidade de processamento de produtos intermediários que são misturas compostas de várias correntes intermediárias, tais como diluentes de óleos combustíveis, propano intermediário, e diesel intermediário. Com o objetivo de obter vantagens sobre a estrutura da rede de transporte, torna-se benéfica e mesmo necessária a operação do duto em ambas as direções para atender tanto à demanda externa quanto à interna. O objetivo deste trabalho é desenvolver um modelo matemático para a programação de um sistema de poliduto. A formulação para a programação deve considerar a possibilidade de trocar o sentido do poliduto. Neste contexto, a programação de um poliduto envolve decisões tais como sentido de operação, quantidade, temporização e seqüências de produtos, com objetivo de obter uma solução ótima, considerando todas as restrições de demanda, perfil de produção, estoques e custos. O modelo de programação é baseado em uma representação de tempo discreto e composto da área de tancagem da refinaria, um terminal, e um poliduto. Além disto o duto é dividido em segmentos de volumes iguais como em Rejowski Jr e Pinto (2003). As principais variáveis de decisão são a direção da movimentação do duto (da refinaria para terminal ou do terminal para refinaria) e o que está sendo movimentado a cada intervalo. Estas decisões são formuladas através de uma representação disjuntiva. As disjunções são transformadas em uma formulação baseada em programação matemática mista-inteira, a partir da representação Convex-hull. A função objetivo considera os custos de estocagem, movimentação e interface de produtos. O modelo é aplicado inicialmente a um caso protótipo e posteriormente aplicado a um sistema real composto pelos terminais de São Sebastião e Guararema e o poliduto OSPLAN. Neste caso ao todo quatro famílias de produtos são transportadas: gasolina, querosene, nafta e diesel. A programação é gerada para o período de uma semana. / Pipeline systems play a major role in the supply chain of the petroleum industry. These systems are responsible for the transportation of most of the crude oil and petroleum derivatives. Pipeline systems transfer large amounts of different petroleum types and their products at a lower cost than any other transportation mode. Pipelines interconnect oil fields, ports, refineries, distribution centers (or depots), and consumer markets. The problem addressed is this work is based on a system that is composed by an oil refinery that must transfer multiple products through a single pipeline connected to one depot. The products are a set of petroleum derivatives that must be either transported from the refinery to the depot or from the depot to the refinery. Both depot and refinery also connect other refineries as well as other depots and customers, thus forming a complex transportation network. On the other hand, there are several demands that arise either from external customers or from refineries. The latter demand is due from the need of processing intermediate streams with components mixtures such as diluents, propane and diesel. In order to take advantage of the structure of the transportation network, it becomes beneficial and even necessary to operate the pipeline in both directions so that internal and external demands are satisfied. The objective of this work is to develop a mathematical model for the short term scheduling of a multiproduct pipeline system. The scheduling formulation must account for the bidirectionality of the multiproduct pipeline. In this context, the scheduling a multiproduct pipeline involves the from-to decision, the product amounts, their sequence and timing, in the optimal sense, considering all constrains on demands, production rates, inventories, and costs. The scheduling model is based on a discrete time representation and is composed by one refinery tank farm, one depot and one multiproduct pipeline. Moreover, the pipeline is divided into segments of equal volume, as in Rejowski Jr and Pinto (2003). The main decisions variables are the directions of transfer (refinery to depot or depot to refinery) and the types of products at each time interval. These decisions are formulated with a disjunctive representation. The disjunctions are represented in mixed integer formulation based on the convex-hull approach. The objective function involves inventory, transfer and product interface costs. The model is first applied to a prototype case and after applied to a real-world system that is composed of the São Sebastião and Guararema depot and the OSPLAN pipeline. Overall four families of products are transported: gasoline, kerosene, naphtha and oil diesel. These are scheduled over a period of one week.

Neste trabalho, apresentamos um estudo sobre o problema de dimensionamento de lotes com múltiplas plantas, múltiplos itens e múltiplos períodos. As plantas têm capacidade de produção limitada e a fabricação de cada produto incorre em tempo e custo de preparação de máquina. Nosso objetivo é encontrar um plano de produção que satisfaça a demanda de todos os clientes, considerando que a soma dos custos de produção, de estoque, de transporte e de preparação de máquina seja a menor possível. Este trabalho tem duas contribuições centrais. Primeiramente, propomos a modelagem do problema de dimensionamento de lotes com múltiplas plantas utilizando o conceito de localização de facilidades. Para instâncias de pequena dimensão, os testes computacionais mostraram que a resolução do problema remodelado apresenta, como esperado, resultados melhores que o modelo original. No entanto, seu elevado número de restrições e de variáveis faz com que as instâncias de maiores magnitudes não consigam ser resolvidas. Para trabalhar com instâncias maiores, propomos um método híbrido (math-heurística), que combina o método relax-and-fix, com a restrição de local branching. Testes computacionais mostram que o método proposto apresenta soluções factíveis de boa qualidade para estas instâncias / In this work, we present a study about the multi-plant, multi-item, multi-period lot-sizing problem. The plants have limited capacity, and the production of each item implies in setup times and setup costs. Our objective is to find a production plan which satisfies the demand of every client, considering that the sum of the production, stocking, transport and setup costs is the lowest possible. This work has two main contributions. Firstly, we propose the multi-plant lot-sizing problem modeling using the facility location concept. For small dimension problems, computational tests showed that the remodeled problem resolution presents, as expected, better results than the original model. However, the great number of restrictions and variables make bigger instances to be intractable. To work with the bigger dimension instances, we propose a hybrid method (math-heuristic), which combines the relax-and-fix method and the local branching restriction. Computational tests show that the proposed math-heuristic presents good quality feasible solutions for these instances

A presente pesquisa aborda um problema de roteirização e programação de veículos incorporando uma nova restrição operacional: a requisição simultânea de múltiplos veículos para atendimento da demanda. Trata-se de uma característica encontrada em operações de apoio à exploração de petróleo \"offshore\", em que mais de uma embarcação é requerida para executar tarefas de reboque e lançamento de linhas de ancoragem. Esta imposição, somada às restrições de janela de tempo, precedência entre tarefas, autonomia das embarcações e atendimento integral da demanda, configuram este problema. A programação é orientada pela minimização dos custos variáveis da operação e dos custos associados ao nível de serviço no atendimento. Este problema é uma variação do problema clássico de roteirização e programação de veículos com janela de tempo, de classe NP-Difícil. Nesta pesquisa, propõe-se modelar e resolver o problema em escala real por meio do algoritmo \"branch and cut\" acoplado às heurísticas de busca em vizinhança \"local branching\" e \"variable neighborhood search\". Para gerar as soluções iniciais será empregado o método \"feasibility pump\" e uma heurística construtiva. / This research focuses a fleet scheduling problem with new operational constraints: each task requiring multiple types of vehicles simultaneously. This kind of operation occurs in offshore exploitation and production sites, when more than one vessel is needed to accomplish the tugging and mooring of oil platforms. Other constraints are maintained such as time windows, precedence between tasks, route duration and the demand attendance. The solution schedules are cost oriented, which encompasses the routing variable costs and the customer service costs. This is a variation of the classical fleet routing and scheduling, which is an NP-Hard problem. This research aims to solve the real scale problem through a combined use of branch and cut strategy with local search algorithms such as local branching and variable neighborhood search. An efficient heuristic rule will be used in order to generate initial solutions using the feasibility pump method.

Sistemas dutoviários desempenham um papel fundamental na cadeia de suprimento da indústria de petróleo. Este tipo de sistema é responsável pelo transporte da maior parte do volume de petróleo e seus derivados. Sistemas de dutos transportam uma grande quantidade de diferentes tipos de petróleo e seus derivados a custo mais baixo que outros tipos de modais. Dutos interligam campos de produção de petróleo, portos, refinarias, centros de distribuição (ou depósitos), e mercado consumidor. O problema estudado neste trabalho é baseado em um sistema que é composto por uma refinaria que pode transferir vários produtos para um terminal (depósito) através de um único duto. Os produtos são conjuntos de derivados de petróleo que devem ser transferidos da refinaria para o terminal ou do terminal para a refinaria. Ambos, refinaria e terminal estão conectados a outras refinarias, terminais e mercados consumidores e com isto formam uma complexa rede de dutos. Por outro lado há um conjunto de demandas externas e internas. Esta última demanda decorre da necessidade de processamento de produtos intermediários que são misturas compostas de várias correntes intermediárias, tais como diluentes de óleos combustíveis, propano intermediário, e diesel intermediário. Com o objetivo de obter vantagens sobre a estrutura da rede de transporte, torna-se benéfica e mesmo necessária a operação do duto em ambas as direções para atender tanto à demanda externa quanto à interna. O objetivo deste trabalho é desenvolver um modelo matemático para a programação de um sistema de poliduto. A formulação para a programação deve considerar a possibilidade de trocar o sentido do poliduto. Neste contexto, a programação de um poliduto envolve decisões tais como sentido de operação, quantidade, temporização e seqüências de produtos, com objetivo de obter uma solução ótima, considerando todas as restrições de demanda, perfil de produção, estoques e custos. O modelo de programação é baseado em uma representação de tempo discreto e composto da área de tancagem da refinaria, um terminal, e um poliduto. Além disto o duto é dividido em segmentos de volumes iguais como em Rejowski Jr e Pinto (2003). As principais variáveis de decisão são a direção da movimentação do duto (da refinaria para terminal ou do terminal para refinaria) e o que está sendo movimentado a cada intervalo. Estas decisões são formuladas através de uma representação disjuntiva. As disjunções são transformadas em uma formulação baseada em programação matemática mista-inteira, a partir da representação Convex-hull. A função objetivo considera os custos de estocagem, movimentação e interface de produtos. O modelo é aplicado inicialmente a um caso protótipo e posteriormente aplicado a um sistema real composto pelos terminais de São Sebastião e Guararema e o poliduto OSPLAN. Neste caso ao todo quatro famílias de produtos são transportadas: gasolina, querosene, nafta e diesel. A programação é gerada para o período de uma semana. / Pipeline systems play a major role in the supply chain of the petroleum industry. These systems are responsible for the transportation of most of the crude oil and petroleum derivatives. Pipeline systems transfer large amounts of different petroleum types and their products at a lower cost than any other transportation mode. Pipelines interconnect oil fields, ports, refineries, distribution centers (or depots), and consumer markets. The problem addressed is this work is based on a system that is composed by an oil refinery that must transfer multiple products through a single pipeline connected to one depot. The products are a set of petroleum derivatives that must be either transported from the refinery to the depot or from the depot to the refinery. Both depot and refinery also connect other refineries as well as other depots and customers, thus forming a complex transportation network. On the other hand, there are several demands that arise either from external customers or from refineries. The latter demand is due from the need of processing intermediate streams with components mixtures such as diluents, propane and diesel. In order to take advantage of the structure of the transportation network, it becomes beneficial and even necessary to operate the pipeline in both directions so that internal and external demands are satisfied. The objective of this work is to develop a mathematical model for the short term scheduling of a multiproduct pipeline system. The scheduling formulation must account for the bidirectionality of the multiproduct pipeline. In this context, the scheduling a multiproduct pipeline involves the from-to decision, the product amounts, their sequence and timing, in the optimal sense, considering all constrains on demands, production rates, inventories, and costs. The scheduling model is based on a discrete time representation and is composed by one refinery tank farm, one depot and one multiproduct pipeline. Moreover, the pipeline is divided into segments of equal volume, as in Rejowski Jr and Pinto (2003). The main decisions variables are the directions of transfer (refinery to depot or depot to refinery) and the types of products at each time interval. These decisions are formulated with a disjunctive representation. The disjunctions are represented in mixed integer formulation based on the convex-hull approach. The objective function involves inventory, transfer and product interface costs. The model is first applied to a prototype case and after applied to a real-world system that is composed of the São Sebastião and Guararema depot and the OSPLAN pipeline. Overall four families of products are transported: gasoline, kerosene, naphtha and oil diesel. These are scheduled over a period of one week.

Esta tese aborda um problema de dimensionamento e sequenciamento de lotes de produção baseado em uma indústria alimentícia brasileira que opera por meio de diversas linhas de produção heterogêneas. Nesse ambiente produtivo, as linhas de produção compartilham recursos escassos, tais como, trabalhadores e máquinas e devem ser montadas (ativadas) em cada período produtivo, respeitando-se a capacidade disponível de cada recurso necessário para ativação das mesmas. Modelos de programação matemática inteira mista são propostos para representação do problema, bem como diversos métodos heurísticos de solução, compreendendo procedimentos construtivos e de melhoramento baseados na formulação matemática do problema e heurísticas lagrangianas. São propostas heurísticas do tipo relax-and-fix explorando diversas partições das variáveis binárias dos modelos e uma heurística baseada na decomposição do modelo para construção de soluções. Procedimentos do tipo fix-and-optimize e matheuristics do tipo iterative MIP-based neighbourhood search são propostas para o melhoramento das soluções iniciais obtidas pelos procedimentos construtivos. Testes computacionais são realizados com instâncias geradas aleatoriamente e mostram que os métodos propostos são capazes de oferecer melhores soluções do que o algoritmo Branch-and-Cut de um resolvedor comercial para instâncias de médio e grande porte. / This doctoral dissertation addresses the simultaneous lot sizing and scheduling problem in a real world production environment where production lines share scarce production resources. Due to the lack of resources, the production lines cannot operate all simultaneously and they need to be assembled in each period respecting the capacity constraints of the resources. This dissertation presents mixed integer programming models to deal with the problem as well as various heuristic approaches: constructive and improvement procedures based on the mathematical formulation of the problem and lagrangian heuristics. Relax-and-fix heuristics exploring some partitions of the set of binary variables of a model and a decomposition based heuristic are proposed to construct solutions. Fix-and-optimize heuristics and iterative MIP-based neighbourhood search matheuristics are proposed to improvement solutions obtained by constructive procedures. Computational tests are performed with randomly instances and show that the proposed methods can find better solutions than the Branch-and-Cut algorithm of a commercial solver for medium and large size instances.