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Aspects such as production, expansion and transport of different types of coal are considered. Burning fossil fuels such as coal negatively impacts the environment, and is controlled by strict emission regulations and allowances. Consequently, the emission allowance trading market is integrated and the model allows for installation and use of abatement technologies under economic constraints. Further aspects considered in the model are power plant expansion and the power transmission network. The outstanding aspect of the model developed is its unique granularity in different areas.
First, coalfired power plants are not modeled as a whole but rather each single boiler is considered separately. Second, although the general time horizon of the model is one year, single decisions are made on more granular time frames within this year. The extension of the model to a multi-year model enables forecasts of a sequence of years. Finally, the possibility that each coal class can be used in every coal-fired unit without any artificial limitations is of outstanding value. Such limitations would anticipate decisions and thereby shorten optimization possibilities. The clearly structured and fully 70 Award Winner Presentations flexible database as well as the attained solving time do not limit the model usage to just the near future.
It may be preferable to select more sophisticated criteria that also reflect variability-risk features of the problem. In this talk we focus attention on risksensitive optimality criteria in discrete-time Markov decision chains, i. Under some unichained assumptions this problem can be studied as a classical Markov decision process on condition that the transition probabilities are replaced by general non-negative matrices.
We suggest policy and value iteration algorithms generating lower and upper bounds on optimal values converging monotonously to the optimal values and show the connections between risk-sensitive and standard optimality criteria. When there is a call for service a patrol unit has to travel to the scene, perform on-scene service, deal with administration afterwards or perhaps go directly to a next call. If all phases are lumped together during analysis, outcomes may be invalid and some policies can not be investigated reliably. Emergency services are typically also subject to non-stationary cyclic arrival patterns.
It is known that even mild fluctuations in this pattern can greatly invalidate outcomes when average rates are used. But service processes may be non-stationary as well, even may depend on the state of the system. Such a service policy may state that no administration a phase is executed at given times or when the system is in a certain state to improve availability and thus performance.
The methodology is based on time discretisation and forward recurrence. We develop an effective method to obtain time-varying system statistics that help administrators to identify unwanted peaks or lows in system performance and give insight in how to develop time- and state-dependent policies to improve service. We test the model on several cases under various system settings to assess feasibility and accuracy of the procedure. According to the generalized processor sharing discipline, each request in the system receives a fraction of the capacity of one processor which depends on the actual number of requests in the system.
We derive systems of ordinary differential equations for the LST and for the moments of the conditional waiting time of a request with given required service time as well as a fast recursive algorithm for the LST of the second moment of the conditional waiting time, which in particular yields the second moment of the unconditional waiting time.
The proposed scheme utilizes the scenario tree from backto-front and obtains the solution of the multi-period stochastic problems related to the subtrees whose root nodes are the starting nodes i. Each subproblem considers the effect of the stochasticity of the uncertain parameters from the periods of the given stage, by using curves that estimate the expected future value EFV of the objective function. Each subproblem is solved for a set of refrence levels of the variables that also have nonzero elements in any of the previous stages besides the given stage.
An appropriate sensitivity analysis of the objective function for each reference level of the linking variables allows to estimate the EFV curves for the scenario groups from the previous stages, until the curves for the first stage are computed. Computational experience is presented. Consequently, it is possible to define multistage stochastic programs as a system of parametric one-stage stochastic programming problems with an inner type of dependence. Evidently, this decomposition can be employed to construct approximate solution scheme.
To this end, evidently first, it is necessary to state assumptions under which the individual constraints sets are nonempty. Furthermore, we introduce the assumptions under which the individual objective functions are finite, convex and Lipschitz. After having presented basic structural properties of these models, we discuss solution methods based on decomposition. Computational results conclude the talk. Its genuine purpose is to help a decision maker to determine a single best decision alternative.
Methodologically we focus on pairwise comparisons of these alternatives which lead to the concept of bipolar-valued outranking digraph. The work is centred around a set of five pragmatic principles which are required in the context of a progressive decision aiding approach. Their thorough study and implementation in the outranking digraph lead us to define a choice recommendation as an extension of the classical digraph kernel concept.
The output lies within the finite subset of floating-point numbers and therefore can not be random real numbers. Classical random number generators produce only a small part of these numbers. Many small numbers are missed and the output can even not be random as floating-point numbers. We give examples of simple simulation studies that lead to wrong results.
But the common empirical tests are not sensitive enough to detect these deficits. By generating mantissa and exponent independently we successfully construct new uniform and exponential random number generators based on a linear congruential generator. The results of the simulation studies are improved. We also develop new simple empirical tests adapted to numbers in the floating-point data format. To do this, first we briefly introduce the concepts of DOB and its applications in decision-making problems.
Then, we explain the way to model a statistical quality control problem by the DOB approach. In this iterative approach, we try to update the belief of the system being out-of-control by taking new observations on the quality characteristic under study. This can be performed using Bayesian rule and previous beliefs. If these beliefs are in specific intervals, we classify the system to be in out-of-control condition or in-control condition.
We apply stochastic dynamic programming to calculate these intervals. Technology development is often an essential part of the operational strategy, during which deployment or implementation decisions are made. In most cases, companies or agencies have several candidate technologies that they can decide to invest and develop. Each of these technologies requires an uncertain amount of investment, and also has probabilistic returns. Given these uncertainties and resource limitations, the objective of the technology portfolio optimization problem is to determine an investment schedule for a fixed planning period such that the expected total return of the invested technologies over an infinite time horizon is maximized.
Depending on the application, the set of candidate technologies may also have additional attributes. The technology portfolio management problem is a large scale stochastic optimization model, which is not amenable to any specific method. In this study, we develop a multistage stochastic programming model which, however, differs from classical stochastic programming models since the times of realizations in the scenario tree are dependent on the decisions made.
An efficient solution procedure is developed and presented along with computational results. The latter, widely applied in Mathematical Finance, may prevent the node number of the scenario tree to grow exponentially with the number of time stages. We show how this property may be exploited within a non-Markovian framework and under time-coupling constraints.
Being close to the well-established Nested Benders Decomposition, our approach uses the special structure of recombining trees for simultaneous cutting plane approximations. We develop methods and stopping criteria to avoid an exponential growth of the number of subproblem evaluations and present numerical results that show the efficiency of our method. We derive an explicit representation of the optimal consumption and trading strategies using Malliavin calculus.
We also provide an example, where the drift process is modeled as a continuous time Markov chain with finitely many states.premiermoneysource.com/wp-content/como/4006.php
ben10 videos ben 10 season 2 episode 21 the best weapon 225
But the computation of the filter and its Malliavin derivative are numerically difficult in discrete time. Following Clark a robust version of the filter and its Malliavin derivative can be implemented. Moreover we provide another example where the drift is modeled as a mean-reverting Ornstein-Uhlenbeck process.
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The results are applied to historical prices. Niu, Note on inventory model with a mixture of back orders and lost sales, European Journal of Operational Research ] presented the necessary condition of the existence and uniqueness of the optimal solution of Padmanabhan and Vrat [G. Vrat, Inventory model with a mixture of back orders and lost sales, International Journal of Systems Science 21 ]. Also, Chung-Yuan et al. Reconfigure Manufacturing Systems RMS is a new paradigm that focuses on manufacturing a high variety of products at the same system.
In an RMS adapting the production with arrival orders which follow Poisson distribution with different arrival rates is an important issue. It is especially important where there is a possibility of missing orders. In this paper, we introduce a method to estimate the behavior of expected inventory level where arrival orders follow Poisson distribution. To solve this model, we proposed a tabu search based procedure which has three types of moves.
A numerical example is presented to illustrate the procedure. The simply formulation is following. The angler goes to fishing. He buys fishing ticket for a fixed time. There are two places for fishing at the lake. The fishes are caught according to renewal process which is different at both places.
These distributions are different for the first and second fishing place. On each place the angler has another utility functions and another cost functions. For example, on the one place better sort of fish can be caught with bigger probability or one of the places is more comfortable Obviously our angler wants to have as much satisfaction as possible and additionally he have to leave the lake before the fixed moment. Therefore his goal is to find two optimal stopping times in order to maximize his satisfaction. The first time corresponds the moment, when he eventually should change the place and the second time, when he should stop fishing.
These stopping times should be less than the fixed time of fishing. The dynamic programming methods were used to find these two optimal stopping times and to specify the expected satisfaction of the angler at those times. It is supposed that several products can be produced and their demands follow Poisson stream with different rates. The aim of this article is maximizing the adaptation of production outputs to arrival demands.
To achieve this mean a cyclic point of view to production is introduced then a heuristic two-stage model is developed to minimize the inventory holding costs and shortage costs. In first stage, the optimum inventory level of each product at the beginning of each cycle OIL is determined. If in hand inventory level of a product at the beginning of a cycle is equal to determined amount in first stage OIL , the inventory holding and shortage costs of mentioned product will be minimal at that cycle.
In second stage, considering in hand inventory levels of each product at the beginning of a cycle, the optimum combination of products to produce is determined so that firstly, production system parameters are satisfied and secondly, the expected inventory levels at the end of the cycle will be near to OIL as much as possible.
To illustrate a numerical example is described. Moreover, the particularity of this model allows taking account of system state improvement in time course. The estimation of its parameters is considered through maximum likelihood ML and Expectation-Maximisation EM algorithm. Decision tests to choose between a HPP and our model are revealed. Field failures data from an industrial setting are used to fit the model. In order to specify asymptotic properties, a Monte-Carlo simulation is employed, allowing to compare the estimate of our model by ML and EM algorithm.
In this procedure, we discuss two various cases of degradation. The goal of this presentation is to discuss the potential of the XBRL standard to facilitate consolidation of financial statements under International Financial Reporting Standards. In the first place the results of a showcase project investigating general requirements are presented which aim to model the overview of IFRS consolidation processes. Finally the goals for the standardised IFRS consolidation model are outlined. An interactive decision support system built around a specific transportation problem is used to maximize the revenue generated by selling waste paper to paper mills.
Furthermore, the dual variables of the linear program allow the planner to identify upper bounds for setting bid prices to buy waste paper from waste collection companies. Since its introduction in august the system has become an integral part in the planning process of our industry partner. Operational results have shown a significant increase in profit while at the same time the duration of the planning process could be cut by more than half. Particularly, the choice of an adequate criterion for the selection of new districts is important for the acceptance of a new organizational structure and future adjustments.
Because of the typical problem size methods for the exact solution will generally fail. Therefore, we present optimization heuristics and finally show results for several real world scenarios. SWOT-analysis is dynamical decision making process which is aimed to define ratings of internal and environmental factors and to determine the key factors which influence positively or negatively on corresponding organizational or human problem.
Also SWOT-analysis determines balance between factors which influence on the result using computation of summarized overbalance of positive and negative factors. Managerial arrangements can be developed on the base of rating computations and than the decision about their sequence and priority takes. Fuzzy mathematics methods give possibility to develop traditional decision making models.
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These methods give data for decision makers to assess reliability, risks etc. It is accepted to designate decision making models which are built on the basis of fuzzy mathemathics as Soft Models.
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In this paper two fundamental models of soft SWOT-analysis are proposed, which are based on fuzzy expert ratings using. The first model is fuzzy Artificial Intelligence, Business Intelligence and Decision Support TD 81 widening of classic algorithm with straight factors rating fixing. Second model suppose using of fuzzy pair comparisons of factors and proposed by us fuzzy multiplicative critical path method. The nodes of a trading hub are used to calculate a reference price index that can be used by the market participants. The need for such a reference price is due to considerable variability of energy prices at different nodes of the electricity grid at different periods of time.
We consider the hub nodes selection problem in a nonlinear optimization form proposed in . We discuss its connection to a well-known clustering problem and show the NP-hardness of the original formulation  and its modification with a single hub and lower bounded number of nodes. Several heuristic algorithms based on the local search and evolutionary principles were implemented and compared to the linear and nonlinear MIP solvers CPLEX 9.
Some properties of the local optima are discussed. Mathematical and statistical methods are used to explore economic relationships and to forecast the future market development. However, econometric modeling is often limited to a single market. In the age of globalisation markets are highly interrelated and thus, single market analyses are somehow misleading. In this talk we present a new way to model the dynamics of coherent markets.
Our approach is based on recurrent neural networks, which are able to map multiple scales and different sub-dynamics of the coherent market movement. Unlikely to standard econometric methods, small market movements are not treated as noise but as valuable market information. Although scheduling is a well researched area, classical scheduling theory has 82 Artificial Intelligence, Business Intelligence and Decision Support TD been little used in real manufacturing environments due to the assumption that the scheduling environment is static. In a static scheduling environment where the system attributes are deterministic, different analytical tools such as mathematical modelling, dynamic programming, branch-and-bound methods can be employed to obtain the optimal schedule.
However, scheduling environment is usually dynamic in real world manufacturing systems and the schedule developed beforehand may become inefficient in a dynamically changing and uncertain environment. Therefore, a flexible scheduling method that can handle system variation which results from the change of manufacturing conditions, is needed.
Having the ability to learn and generalize for new cases in short time, in recent years, artificial neural networks ANNs have provided a means of tackling dynamic scheduling problems. The objective of this study is to develop a neural network based decision support system for selection of different dispatching rules for a real-time manufacturing system, in order to obtain the desired performance measures given by a user.
A simulation experiment is conducted to collect the training data. There have been many efficiency frontier analysis methods reported in the literature. However, the assumptions made for each of these methods are restrictive. Each of these methodologies has its strength as well as major limitations. This study proposes a non-parametric efficiency frontier analysis methods based on artificial neural network ANN and genetic algorithm GA for measuring efficiency as a complementary tool for the common techniques of the efficiency studies in the previous studies.
The proposed computational methods are able to find a stochastic frontier based on a set of input-output observational data and do not require explicit assumptions about the functional structure of the stochastic frontier. In these algorithms, for calculating the efficiency scores, a similar approach to econometric methods has been used. Moreover, the effect of the return to scale of decision making unit DMU on its efficiency is included and the unit used for the correction is selected by notice of its scale under constant return to scale assumption.
After reviewing different data preprocessing methods, the best method that converts the nonsatationary process to covariance stationary process is selected. A new method for calculating ANN performance is also proposed. Another unique feature of this study is the utilization of principle component analysis PCA to define input variables versus trial and process method.
Due to various seasonal and monthly changes in electricity consumption and difficulties in modeling it with conventional methods, we consider a case study in Iran for electricity consumption estimation. This setting is well known in the literature and several classifiers have been evaluated in empirical experiments.
However, due to inconsistent findings regarding the superiority of one classifier over another and the usefulness of metric-based classification in general, the reliability of respective experiments has been questioned. We consider three potential sources for bias which may have caused this lack of convergence: Comparing classifiers over one or only a small number of proprietary data sets, relying on accuracy indicators which are conceptually inappropriate for cross-study comparisons and software defect prediction in general and finally, conservative usage of statistical testing procedure to secure empirical findings.
A framework for comparative software defect prediction experiments is proposed to remedy these problems and applied in a large-scale empirical comparison of nineteen classifiers over ten public domain data sets from the NASA Metrics Data repository. The results indicate that the importance of the selected classifier is less than generally believed as several models do not produce significantly different results. This is caused by the high dimensionality of the input feature vectors in conjunction with the relative sparseness of most empirical data.
Past own work on model combiners for credit scoring data suggest that some improvement might be possible. The literature also reports on possible progress by supplementing the empirical training data with properly selected artificial data points. We report on using such fictious training data in the vicinity of support vectors generated by the SVM models for our credit scoring problems. In this study, the neural networks based on Fuzzy ART is used for clustering part-machine cells.
The implemented method is an efficient alternative decision support tool to solve the cell-formation problem of cellular manufacturing. The study results that, fuzzy art have several advantages, such 84 Artificial Intelligence, Business Intelligence and Decision Support FA as low execution times, solution quality for large scale problems which can not be solved using conventional techniques. The computational experience shows that, fuzzy art is an efficient algorithm and produce good clustering results for the cellular manufacturing problems.
The Fuzzy ART algorithm was applied to five machine-cell formation problem that obtained from studies occured in the literature. Finally, the results obtained from Fuzzy ART algorithm was compared with the results acquired at the studies in the literature. This paper presents an analysis of simple smart structures, which demonstrates the unity of mechanical structure of an object and its intelligence. We consider a uniform beam subjected to an external force and a control forces produced by the actuators. It is requires to find 1 the number and positions, 2 powers of the actuators in dependence on the inner force.
Separately taken, the problems are known as problems of structure design and optimal control. We introduce the set of possible configurations of the system as the image of the set of all control forces and the set of accepted configurations of the system. The original problem is solvable if the intersection of the sets is not empty.
For the beam we construct the sets introduced.
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The problem couples the positions of actuators producing control forces and control instruction for actuators. It is demonstrated that structure design problem and control design problem are two sides of one problem about not empty intersection of the sets. There are numerous analogs of the described model in nature and social events.
The design of a beam with controlled force unit. Electronic Notes in Discrete Mathematics, , 27 69, We describe Optimization Services OS , a unified framework for a new generation of distributed optimization systems that make solvers readily available over the Internet.
OS incorporates XML-based standards for representing and communicating optimization problem information, so that only a single driver is required for each solver. Related languages and libraries handle the passing of options to solvers and the retrieval of results, as well as protocols for facilitating solver registration, client and scheduler discovery, and communication between the various components of the optimization process.
The OS project is intended to have advantages for both developers and users of optimization software. Thus, we report on different combinations of commercial and open source solvers for the solution of MINLPs. Mathematical decision support is highly desirable in this context but leads to very hard problems. Typically one obtains large scale nonlinear mixed integer network 86 Continuous Optimization WC problems with a rich hierarchical structure. We particularly discuss the mathematical aspects of combinatorial constraints and transform them into continuous nonlinear ones.
In this context GAMS made advances in the recent past by introducing new solvers with both academic and commercial background into the system. We discuss requirements for interfacing these solvers. Besides algebraic model information access to a wide range of local solvers increases the reliability of a GO code. Furthermore, we present tools for benchmarking global and local optimization solvers.
The modeling system GAMS provides an efficient and productive way of developing optimization models using state of the art technologies. We will outline several recent developments of GAMS like automatic model reformulations, explicit formulation of soft constraints and extended nonlinear programming problems, grid solution techniques, encryption and compression and enhanced data exchange with other application.
Abweichend von der Vorgehensweise, die Gutmann zur Behandlung der Hilfsfunktionen nutzt, wird ein modifiziertes Verfahren verwendet. Our paper tries to detect and overcome some structural frontiers of our methods applied to the recently introduced gene-environment networks. Based on the experimental data, we investigate the ordinary differential equations having nonlinearities on the right-hand side and a generalized treatment of the absolute shift term which represents the environmental effects. The genetic process is studied by a time-discretization, in particular, Runge-Kutta type discretization.
The possibility of detecting stability and instability regions is being shown by a utilization of the combinatorial algorithm of Brayton and Tong which is based on the orbits of polyhedra. The time-continuous and discrete systems can be represented by means of matrices allowing biological implications, they encode and are motived by our networks.
A specific contribution of this paper consists in a careful but rigorous integration of the environment into modeling and dynamics, using generalized semi-infinite optimization. Relations to the parameter estimation within modeling, especially, by using optimization, are indicated, and future research is addressed. A special module implemented into this study is the TEM model on CO2 emission reduction and its control. This practically motivated and theoretically elaborated work is devoted for a contribution to better health care, progress in medicine, a better education and more healthy living conditions.
Due to the high competition in Brazilian banking market, it is relevant for each popular bank to identify with precision variables that may impact market share. It is taken as Input the number of employees, fixed assets, leverage and delinquency rate, and as Output the intermediation financial results and profitability. The compared methods are relevant to increase the precision of market analysis. The results of both methods are compared in order to distinguish their advantages and inconveniencies. As for inefficient banks, the work identifies directives and benchmarks to be met in order to reverse situation.
In particular, we consider the case where the side constraints non-network constraints are 88 Continuous Optimization TA convex. This kind of problems can be solved by means of primal-dual methods, as the minimization of nonlinear network flow problems without side constraints can be efficiently done by exploiting the network structure. In this work the dual problem is solved with the help of approximate subgradient methods. Besides, the dual function is estimated by minimizing approximately a Lagrangian function, which includes the side constraints and is subject to network constraints only.
This work analyzes the influence of some parameters over the performance of some approximate subgradient methods. Moreover, the implementation of these methods gives rise to the code PFNRN05 and its efficiency over nonlinear-network convex problems is compared with that of other well-known codes. Numerical results appear promising. Here we require that the images of a matrix function are K-copositive where the parameter K is a convex cone.
This unified approach makes it possible to investigate simultaneously two important fields of optimization. The dual cone is presented for the ordering cone of K-copositive matrices. Necessary and sufficient optimality conditions in KKT form are derived for this general problem class. Duality results are given for generalized convex problems and applied to linear problems. Least squares is so popular because it is so easily computed. It does, however, suffer from several shortcomings: For example, in order to apply least squares, the user needs to specify which variables are the independent variables, and which one is the response variable.
A change in this setting will lead to a completely different least squares estimate. In practice, however, a distinction between dependent and independent variables is not always so easy. Another deficiency of least squares fitting is an assumption in the underlying model that may be unrealistic in many situations: Multiple Neutral Data Fitting is an approach that avoids these shortcomings. The basic idea is that a different criterion is chosen as objective of the optimization problem: Instead of minimizing the sum of the squares of the residuals, we consider the deviations for each variable and multiply them.
This leads to a more complicated, global optimization problem. The Multiple Neutral Data Fitting approach has beeen alluded to by several statisticians throughout the last century. Some properties of the resulting regression line have been shown, but generally speaking, the method has been discarded because of the difficulties in solving the optimization. In this talk, we analyse Multiple Neutral Data Fitting as a global optimization problem and propose an algorithm to solve it.
We use the number of vertices explored by the algorithm as a performance measure. We prove that the sum, over all coordinates, of numbers of different values that may be taken by corresponding components of a vertex is an upper bound on the amount of vertices explored by our algorithm. For some special cases, as 0,1 -polytopes, this proves the algorithm to explore polynomially many vertices. More explicitly, one wishes that under weak assumptions a nonempty and compact feasible set can be approximated arbitrarily well by a level set of a single smooth function with certain regularity properties.
For problems with the appropriate structure, there should also be a correspondence between KarushKuhn-Tucker points of the original and of the smoothed problem, along with their Morse indices. After discussing why standard smoothing approaches from finite optimization cannot be transferred to semi-infinite optimization problems, we present a new smoothing method which works for finite as well as for standard semi-infinite optimization. It is based on the mollification of the so-called lower level optimal value function, and it adheres to all the above mentioned criteria.
This talk is based on a joint paper with Hubertus Th. Telecommunication, air transport, cargo, postal delivery services are among those well-know applications of HLP. In this talk, a new integer programming model for HLP focusing on public transport PT applications is proposed. Although, this model inherits some fundamental features of classical HLP models, it also tries to relax some classical assumptions of HLPs to realize the PT applicability. HLPs are composed of a hub-level network and a routing problem at the same time. By exploiting this trivial decomposable structure of HLPs, we propose a solution method based on benders decomposition.
A multi-cut scheme based on inter-decomposition of sub-problem dual is also considered. Moreover, other variants of HLP which resulted from modifications on the hub-level network can be solved with same algorithm applied over all kind of these problems without changing the generality of algorithm. Our computational results show that this is a promising solution approach which in presence of existing hardware restriction is capable of solving problem instances of considerably larger size than those which are directly solved by CPLEX.
Its LP-relaxation can be solved in polynomial time. These results are the theoretical basis for a column generation algorithm to solve large-scale track allocation problems. Computational results for the Hanover-Kassel-Fulda area of the German long distance railway network involving up to trains are reported. It can be modeled as a multi-commodity-flow problem in which line and passenger paths are constructed.
The talk discusses a branch-and-cut-and-price approach to line planning. The ultimate goal in such an approach would, of course, be to find a proven integer optimum over the entire set of passenger and line paths. This, however, turns out to be extremely difficult. As a step towards the solution of large line planning problems, we present a two-step approach in which we first solve the LP-relaxation of the line planning problem.
In a second step, we select from the LP-solution a pool of lines which we fix in order to construct an optimum integer solution with 92 Discrete and Combinatorial Optimization WB respect to the chosen pool using cutting plane techniques. In this way, we can compute high quality solutions for the line system of the public transport network of the city of Potsdam.
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The objective categories of such a tournament schedule are fairness, fulfillment of team-wishes and maximizing revenues from TV-contracts and spectators. Important side constraints arise from availability of sports stadiums, restrictions from police and European event schedules. Taking setup times and limited time resources into account, the objective is to minimize the sum of setup costs and inventory costs.
The problem model is defined as an extended proportional lot-sizing and scheduling problem PLSP. As known from the PLSP, the planning horizon is divided into several periods with equal capacity, whereas at most one setup activity is completed per period. Furthermore, lot-sizes may be linked over several periods. In industrial production processes, setup activities frequently depend on the production sequence. Moreover, setup times may exceed the capacity of one period defined in the PLSP. In contrast to most approaches in literature, the new model integrates linked setup activities as well as sequence-dependent setup times.
Hence, the available capacity of each period can be used up completely. Note that a complete utilization of capacity is of significant importance for the overall efficiency of the production plan. The approach is applied to an industrial production system. Obtained cost reductions validate its practical relevance. Fontes, Dalila Martins Fontes In this work, we report the development of a decision support system DSS to plan the best assignment for the weekly promotion space of a TV station.
Each product to promote has a given target audience that is best reached at specific time periods during the week.
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The DSS includes an optimizer based on genetic algorithms that aims to maximize the total number of contacts for each product within its target audience while fulfilling a set of constraints defined by the user. The proposed column generation approach is particularly suited for the GVRP as the complexity of the GVRP is embedded in the columns of the set partitioning formulation and the revenues associated to transportation requests can be easily considered when searching for tours with negative reduced costs.
All customers are known in advance, but its demands take place at any instant inside of a time horizon. The problem needs to initiate at each consumer i according to a specific interval of time, done by [ai, bi]. In this paper, we use Ant Colony System ACS metaheuristic to find the problem solutions, due to its more efficient exploitation strategies than others metaheuristics.
During each slot, the problem is similar to a static VRP, but with vehicles with heterogeneous capacities and starting locations. The aim is to minimize the total travel time while trying to serve all the known orders.
The architecture has been developed to run in a centralized fashion, having two main elements: Events Manager and the ACS. The Events Manager is the central structure of the solution architecture. When the orders arrive to it, they are sent to the Static Problem Element, for selecting them according with their time windows. The orders which have time window corresponding to the present slot are sent to the ACS Element. It defines, at each static problem, the number of routes and the sequence of customers to be served. All routes arisen from the ACS Element are dispatched to the Events Manager that will be responsible of designating them to the vehicles.
All the architecture results are feasible and all the time windows are always respected. Some customers may be visited only by a single lorry or by a lorry without its trailer, some may also be visited by a lorry-trailer combination. In addition to the customer locations, there is another relevant type of location, called transshipment location, where trailers can be parked and where a load transfer from a lorry to its trailer can be performed.
This report presents the first exact solution procedure for the problem, a branch-and-price algorithm. The algorithm is based on a new formulation which uses 94 Discrete and Combinatorial Optimization WC resource variables and considers several additional aspects compared to existing formulations. The results of extensive computational experiments are discussed.
The experiments are performed on randomly generated instances structured to resemble real-world situations. We assume the deployment of a mobile communication and information system which provides the permanent connection between the drivers and the dispatching centre as well as allows localizing vehicles on road. In addition, we use the information about the current traffic conditions and explicitly incorporate into our consideration the possibility to react to some dynamic events that arrive in the course of a day.
In response to them we divert a vehicle en route away from its current destination. Therefore, the problem under consideration is dynamic and time dependent. We use the concept of time rolling horizon and decompose the dynamic problem into a series of mixedinteger linear programming models. Each model characterizes a particular static vehicle routing problem with heterogeneous fleet and varying vehicle locations at a specific point of time. Further, we apply the theory of genetic algorithms to solve the problem. We work out and program the procedures of the algorithm and perform complex parameter tuning.
The developed algorithm is initially tested on the set of the well-known benchmarks with the constant travel times. The quality of the received solutions is between The negative values indicate that our solutions are better than the corresponding best known, i. Finally, we test the algorithm in dynamic settings with variable travel times and show that consideration of the real-time data obtained from mobile systems leads to cost savings. Moreover, a restricted number of docking stations or limited processing capacities for incoming goods at the destination depot can be modeled by means of inter-tour resource constraints.
In this presentation, we introduce a generic model for VRPs with inter-tour constraints based on the gianttour representation and resource-constrained paths. Furthermore, solving the model by efficient local search techniques is addressed: Tailored preprocessing procedures and feasibility tests are combined into local-search algorithms, that are attractive from a worst-case point of view and are superior to traditional search techniques in the average case.
In the end, the chapter provides results for some new types of studies where VRPs with time-varying processing capacities are analyzed. Two examples are the routing of automated guided vehicle AGVs in container terminals, and the routing of switching engines at cargo railroads. Typically, many constraints have to be considered like turning restrictions, required orientations of the vehicle, deadlocks, livelocks, and time windows. Collisions are defined on edges and nodes of the underlying graph. The problem is dynamic, as scarce resources e.
In an online situation, one is often forced to use a greedy approach which iteratively schedules one route at a time. Here, each route computation determines a shortest path with time windows and a following readjustment of these time windows. Clearly, this heuristic wastes some optimization potential. In this talk we assess the quality of the iterative routing heuristic by means of a mixed integer program MIP for the simultaneous planning.
Variables correspond to scheduled routes, so the linear programming relaxation of this large MIP is solved by column generation. The resulting pricing problem is again a kind of shortest path with time windows computation. On top of that, there are too many constraints for avoiding collisions, so these are generated dynamically as well. Encouraging computational results on real-life instances are presented. It consists of finding a spanning tree whose nodes do not exceed a given maximum degree and whose total edge length is minimum.
We design a primal branch-and-cut algorithm that solves instances of the problem to optimality. On several instances, the primal branch-and-cut program turns out to be competitive with other methods known in the literature. This shows the potential of the primal method. A graph G is said to be noncrossing plane if its edges have pairwise disjoint interiors. A geometric graph representing an abstract graph with a graph property P is called a geometric graph with 96 Discrete and Combinatorial Optimization WC property P. A geometric k-factor F is a k-regular geometric spanning graph.
A graph G is a geometric complement of graph F if its two vertices are adjacent if and only if they are not adjacent in F. The problem of the existence of a noncrossing subgraph H with the given property P in the geometric graph G is NP-hard in general. In this work we deal with this problem for a plane spanning tree in a geometric complement of 2-factor F. It is already known, a geometric graph, that is a complement of intersecting or disconnected geometric 2-factor F contains a noncrossing spanning tree.
For any vertex v let us denote by ed v the number of vertices w from V for which the straight line wv crosses F at the point v not transversally, i. By representing the infrastructure by a single root node, this problem can be formulated as a 2-root-connected prize- collecting Steiner network problem in which certain customer nodes require two node-disjoint paths to the root, and other customers only a simple path. We present an ILP approach based on directed cuts — something that, up until now, has only been possible for similar problems which only require edge-disjointness.
The validity of our formulation is based on proving a certain orientability of the underlying graph which we can exploit to obtain provable otimal solutions. We show that this formulation is in fact stronger, both from the theoretical and from the practical point of view, than the traditional undirected cut approach. These functions multiply a weight to the cost of fulfilling the demand of a customer which depends on the position of that cost relative to the costs of fulfilling the demand of the other customers.
It is shown that, by using this reformulation, better solution times can be obtained. In addition, the covering model is extended so that ordered median functions with negative weights are feasible as well. A set of facilities and a set of clients are given. Every client should be served exactly by one of the facilities. The profit of serving each client by each facility is given. One should open p facilities and assign clients to them maximizing the total profit.
In this paper we present a hybrid algorithm for solving the mixed integer programming formulation of the p-median problem. The algorithm performs a lexicographical enumeration of the feasible solutions of the problem. To give more accurate estimation of the objective function, the Lagrangian relaxation problem is slightly reformulated to take into account only the points that are lexicographically smaller than the current one. The time of solving the Lagrangian problem is considerably reduced by utilizing the information from the previous iterations.
Generally, Lagrangian relaxation is quite precise, but computationally expensive. Benders constraints play the role of a fast alternative to the Lagrangian relaxation if the latter excludes only few points while solving the problem. Finding the lexicographically maximal solution satisfying the system of Benders constraints is an integer programming problem in common case.
To solve it approximately, we developed a greedy algorithm exploiting some properties of the Benders cuts for the p-median problem. The new formualtion allows to apply some already known tools to this extremely hard problem. We show preliminary computational experiments on a general branch and cut approach to solve the problem. However, in many applications, these costs appear in several forms which are much more complicated than the straightforward single linear term which is usually considered in the literature.
The importance of considering more general assignment costs arises, for instance, when different means of transportation are available for delivering goods from facilities to customers. This is the case when, for example, we have different types of trucks that are available to supply the customers. If more than one truck of each size is available, we obtain a situation with capacitated modular links.
In this paper we consider the case in which the quantities to be shipped are integer. Afterwards, we propose models using discretized binary variables indicating not only whether or not a facility sends some amount to a demand point but also the exact amount being shipped. The formulations proposed are compared in terms of the linear relaxation bound. Computational tests are presented showing the superiority of the discretized models enhanced by the new valid inequalities when a commercial package is considered for solving the problem optimality.
Hamacher In this paper the minimum width annulus problem the single facility equity location problem in networks is introduced. An equivalence of the minimum width annulus problem and the circle location problem is shown. A relation between the minimum width annulus problem and the absolute 1center problem in general undirected networks is considered.
This relation is used to achieve a better complexity for solving the absolute 1-center problem compare to known results. The algorithm runs in O mn expected time assuming that the shortest distance matrix is given. The minimum radius circle location problem and the minimum radius circle location problem with minimum cardinality of the circle are formulated. Therefore, it is a problem with two different components: The location work is done by the firm which locates the plants. If the firm has the control of the allocation process or if the customers know the optimality criterium from the firm and they agree with it, then it is a SPLP situation.
When particular preferences and costs are given, certain known problems may appear as particular cases of the SPLPO, e. In this work, several properties of the SPLPO will be studied and it will be shown how they are applied to solve it in a more efficient way. In a graph, a subset of vertices S is called dominating if every vertex outside S has a neighbor in S. A subset S is called independent if no two vertices of S are adjacent. An independent set S is maximal if no other independent set contains S. An independent dominating set is a vertex subset that is both independent and dominating, or equivalently, is maximal independent.
The problem of finding an independent dominating set of minimum cardinality the independent dominating set problem is known to be NP-hard even for bipartite graphs of maximum degree three. A graph G is called a triangle graph if it satisfies the following triangle condition: Triangle graphs constitute an interesting non-hereditary class, i. We prove that the problem under consideration is NP-complete for triangle graphs with maximum degree six.
Moreover, we consider the problem of approximating the independent domination set problem for triangle graphs. We strengthen this result to some factor depending on e and n, where e is a positive constant and n is the number of vertices in the input triangle graph. This is the first result on the hardness of approximating the independent dominating set problem within non-hereditary classes of graphs. State-of-the-art optimization methods for WDPs are exact algorithms whereas MDKPs are mainly solved using heuristics or metaheuristics such as evolutionary algorithms EAs.
It shows that all currently used WDP test instances can be solved optimally and in a short length of time by exact optimization methods. Thus, these test instances are only of limited usefulness for estimating the performance of optimization methods for more complex instances of the WDP. For typical MDKP instances, exact approaches fail while simple greedy heuristics are very fast and provide high-quality solutions.
The gaps towards optimal solutions are usually only a few percent and decrease with an increasing tightness ratio of the underlying MDKP. Weightcoded EAs significantly improve solution quality of greedy heuristics at the expense of much higher computational effort. However, as the main quality improvement occurs in the very early stages of EA runs, running times observed in the literature can be greatly reduced with only minor effects on the resulting solution quality.
The individuals are subject to some probabilistic operators such as recombination, mutation, and selection in order to evolve the population towards better fitness values. This idea has been used in several population-based metaheuristics such as genetic algorithms, scatter search, and particle swarm optimization PSO. These methods may include some local search component as an important factor for obtaining high quality solutions. The basic idea of PSO is that a particle moves through the search space, thus exploring it and finding new solutions.
The position of a particle is updated depending on locations where good solutions have already been found by the particle itself or other particles in the swarm. Scatter search provides a complementary perspective on PSO, operating on a relatively small number of solutions, called reference set. Some combination of two or more candidates from the reference set creates new solutions, which may be improved by means of local search.
We consider the continuous flow-shop scheduling problem CFSP with flow-time objective. A given set of jobs has to be processed in an identical order on a given number of machines. The CFSP includes no-wait restrictions for the processing of each job, i. We design and analyze different variants of population-based metaheuristics for the CFSP. Solutions for a given problem are constructed by a random walk on a so-called construction graph.
This random walk can be influenced by heuristic information about the problem. In contrast to many successful applications, the theoretical foundation of this kind of metaheuristic is rather weak. Theoretical investigations with respect to the runtime behavior of ACO algorithms have been started only recently for the optimization of pseudo-Boolean functions.
We present the first comprehensive rigorous analysis of a simple ACO algorithms for a combinatorial optimization problem. In our investigations we consider the minimum spanning tree problem and examine the effect of two construction graphs with respect to the runtime behavior. The choice of the construction graph in an ACO algorithm seems to be crucial for the success of such an algorithm.
After that, a more incremental construction procedure is analyzed. It turns out that this procedure is superior to the Broder-based algorithm and produces additionally in a constant number of iterations a minimum spanning tree if the influence of the heuristic information is large enough. The system includes a database, modules of optimization, visualization and others. Also the software can be used for analysis of the produced sketches quality. The experiments show encouraging results. Valid only on your first 2 online payments. Cashback will be credited as Amazon Pay balance within 10 days from purchase.
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