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Reducing the computational workload by simplifying the analysis of karst foundations into a plane strain problem can yield significant advantages. Yet, such an approach fails in reproducing the engineering situation in a rigorous manner. In this regard, this paper proposes an upper-bound method that can effectively analyze the bearing capacity of three-dimensional karst foundations. This method is utilized to investigate the impact of various pile diameters, the ratio of roof thickness to pile diameter, and the ratio of cave width to pile diameter on the stability of karst foundations. The validity of this method is established through an illustrative example. The outcomes illustrate that when subjected to both tensile and compressive horizontal stresses if the maximum horizontal stress surpasses the tensile strength of the rock mass, the roof rock mass may suffer damage. Increasing the ratio of roof thickness to pile diameter can bring down the horizontal stress value. The stability factor is largely influenced by the ratio of roof thickness to pile diameter. The most prominent growth trend of the stability factor is observed when the ratio is less than 3. If the ratio of the roof thickness to pile diameter exceeds 3, the prediction of the bearing capacity estimation for the karst foundation in three-dimensional circumstances is more conservative than that in two-dimensional circumstances.

Розглянуто найбільш поширені методи оптимізації, що трапляються під час розв’язання практичних та наукових задач у різних галузях. Наведено основні положення задач аналітичної й чисельної оптимізації та математичного програмування як задач дослідження операцій та алгоритми методів їх комп’ютерного розв’язання. Значну увагу приділено комп’ютерній реалізації розглянутих методів. До кожного розділу надано комплекти завдань для самоконтролю, велику кількість прикладів та контрольні запитання, що сприятиме кращому сприйняттю та засвоєнню матеріалу підручника. Для студентів спеціальності «Автоматизація та комп’ютерно-інтегровані технології», які вивчають дисципліну «Комп’ютерне моделювання систем і процесів». Може бути використаний під час вивчення дисциплін, що пов’язані з комп’ютерним моделюванням та оптимізацією, а також для наукової роботи студентів, аспірантів, інженерів та вчених. The most common methods of optimization that occur when solving practical and scientific tasks in various fields are considered. The main provisions of the issues of analytical and numerical optimization and mathematical programming as tasks of operations research and the algorithms of the methods of their computer solution are presented. Considerable attention is paid to the computer implementation of the considered methods. For each chapter, sets of tasks for self-control, a large number of examples and control questions are provided, which will contribute to a better perception and assimilation of the textbook material. For students majoring in "Automation and computer-integrated technologies" studying the discipline "Computer modeling of systems and processes". It can be used during the study of disciplines related to computer modeling and optimization, as well as for the scientific work of students, postgraduates, engineers and scientists.

Hydrogen network management has economic appeal due to its importance in oil refineries. It has become genuinely relevant due to the restrictions of sulfur content in fuels, which need hydrogen to be removed. Mathematical programming can be used as a tool for optimizing hydrogen networks, and the efficient management of hydrogen within the refineries can be achieved through a material balance of the units that make up the hydrogen network. In this work, an optimization model Mixed-Integer Linear Programming (MILP) and Mixed-Integer Nonlinear Programming (MINLP) for hydrogen networks was applied to minimize the operating costs. The optimization model was developed in GAMS, and it was validated using a literature case study and a real case study from a Brazilian Refinery. The operation cost was reduced by 10% and 19.6% with MILP and 9.7% and 31.5% with MINLP, for example 1 and 2, respectively. Comparing the results, both achieve significant savings in operating costs. The MILP model, which is easier to solve, has proved to be an efficient tool for optimizing hydrogen networks. However, optimization via MINLP, although not guaranteeing the optimal solution, resulted in lower operating and capital costs. The design of the optimized hydrogen networks was also detailed, and other extra restrictions were imposed on the problem.

AV subnetworks is a way to deal with automated traffic and its technological need that will likely increase during the AVs deployment period. This strategy carries many benefits, yet some inconveniences are worth to mention. One of them relies on the fact that the design of AV subnetworks is often in practice focused on mitigating congestion in the peak-hours. However, designing for the most congested hour can be quite delicate when such a strategy is fixed throughout the day. The remaining part of the day involves different mobility patterns and shifting trips patterns throughout the day, i.e., different Origin-Destination pairs. When such O-D pairs are inside these AV subnetworks, CV owners cannot drive, and therefore a new mode of transport is necessary. This paper focuses on the lower-level decision problem, i.e., the traffic distribution during the transition period while AVs are being deployed in urban areas and AV subnetworks are expanding. A nonlinear mathematical programming model is presented to perform the trip distribution, where walking appears as an alternative. The main objective of this paper is to study the impacts of AV subnetworks from a CV owners’ perspective. A novel formulation guarantees that CV trips starting inside AV subnetworks throughout the day aren’t ignored – this means an alternative mode of transport, in this case, walking. This paper evaluates throughout the day when such situations would likely occur in a case study of the city of Delft, in the Netherlands, in two scenarios with AV subnetworks. The experiments revealed that walking is somehow inevitable when AVs reach 75% of the vehicle fleet – increasing travel costs up to 26.0% and 43.8%.

The paper studies packing ellipsoids of revolution in a cylindrical container of minimum volume. Ellipsoids can be continuously rotated and translated. Two nonlinear mathematical programming models are introduced: exact and approximated. The latter uses an optimized multi-spherical approximation of ellisoids. For both models the phi-function technique is employed to describe analytically non-overlapping and containment constraints. Two solution approaches are proposed to solve the packing problem. Computational results for up to 500 ellipsoids are provided to demonstrate efficiency of the proposed approaches.

The Critical Path Method (CPM) has failed practically for scheduling repetitive projects and Line Of Balance (LOB) has emerged as an alternative for scheduling such projects. Because of the size of...

We present a mixed integer nonlinear mathematical programming model, covering a broad range of operations research (OR)-related topics. The case is designed to allow students to use knowledge acqui...

Retraining of staff is a compulsory managerial function in many organisations and often requires planning for a large number of employees. The large scale of this problem and various restrictions on the resultant assignment to classes make this planning challenging. The paper presents a complexity analysis of this problem together with linear and nonlinear mathematical programming formulations. Three different column generation based optimisation procedures and a large neighbourhood search procedure, incorporating column generation, are compared by means of computational experiments. The experiments used data typical to large electricity distributors.

As far as uncertainty is prevalent, financial anomalies increase the complexity of financial decisions. The possible consequence of an anomaly is either an over or underreaction. This paper...

In the pharmaceutical industry, leftover medications that have not been properly disposed not only damage the environment but also might turn into a peril to people׳s health if being redistributed illegally in undeveloped countries. In contrary, if they are returned to the pharmaceutical producer before their expiry dates, they can be sold at subsidized prices or donated in such countries. In this research, we explore the role of providing incentives to customers in order to facilitate leftover returns and improve the sustainability for a real pharmaceutical reverse supply chain (RSC). Moreover, this research investigates the effect of having a proper coordination method between a producer of medications and third-party logistics (3PL) companies, responsible for collecting unwanted medications from customer zones. Finally, a technique is also proposed to share the RSC׳s saving among the producer and the 3PL companies. The experimental results on a real case study indicate that introducing incentives to customers could decrease the amount of uncollected medications from 18% up to 6.5%. Furthermore, having a proper coordination with 3PL companies could guarantee a full medication recovery.

This work presents optimization results obtained for a double-effect H2O-LiBr absorption refrigeration system considering the total cost as minimization criterion, for a wide range of cooling capacity values. As a model result, the sizes of the process units and the corresponding operating conditions are obtained simultaneously. In this paper, the effectiveness factor of each proposed heat exchanger is considered as a model optimization variable which allows (if beneficial, according to the objective function to be minimized) its deletion from the optimal solution, therefore, helping us to determine the optimal configuration. Several optimization cases considering different target levels of cooling capacity are solved. Among the major results, it was observed that the total cost is considerably reduced when the solution heat exchanger operating at low temperature is deleted compared to the configuration that includes it. Also, it was found that the effect of removing this heat exchanger is comparatively more significant with increasing cooling capacity levels. A reduction of 9.8% in the total cost was obtained for a cooling capacity of 16 kW (11,537.2 $·year-1 vs. 12,794.5 $·year-1), while a reduction of 12% was obtained for a cooling capacity of 100 kW (31,338.1 $·year-1 vs. 35,613.9 $·year-1). The optimization mathematical model presented in this work assists in selecting the optimal process configuration, as well as determining the optimal process unit sizes and operating conditions of refrigeration systems. Fil: Mussati, Sergio Fabian. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo y Diseño. Universidad Tecnológica Nacional. Facultad Regional Santa Fe. Instituto de Desarrollo y Diseño; Argentina Fil: Mansouri, Seyed Soheil. Technical University of Denmark; Dinamarca Fil: Gernaey, Krist V.. Technical University of Denmark; Dinamarca Fil: Morosuk, Tatiana. Technishe Universitat Berlin; Alemania Fil: Mussati, Miguel Ceferino. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo y Diseño. Universidad Tecnológica Nacional. Facultad Regional Santa Fe. Instituto de Desarrollo y Diseño; Argentina

We present a mixed integer nonlinear mathematical programming model, covering a broad range of operations research (OR)-related topics. The case is designed to allow students to use knowledge acquired from OR and management science classes to model, analyze, and provide concrete solutions for the considered problem. Because of its high practicality, this exercise is an ideal tool to make the OR domain more accessible and to learn how to balance a problem’s complexity with the availability of algorithms for its solution. The case has been proposed as a competitive challenge and has been assigned both to students pursuing a bachelor’s degree in management engineering and students pursuing a master’s degree in industrial engineering. Students were grouped into working teams, and all teams competed against each other to get the best solution to win the challenge. Both the work-in-team and the challenge settings have been enjoyed by the students. During three lectures of 90 minutes, a brief review of OR-related tools and a detailed description and analysis of the case study have been provided to the students. Successive periodic debriefing meeting sessions have been scheduled to engage and monitor students during project development. Online supplemental files are available at https://doi.org/10.1287/ited.2018.0202ca .

In this paper, we consider a multistage feedback control strategy for producing 1,3-propanediol in microbial continuous fermentation. Both the dilution rate and the concentration of glycerol in the input feed are used as control variables, and these variables are further assumed to be in the form of a linear combination of biomass and glycerol concentrations. Unlike the general form of linear feedback control, the coefficients of linear combination are continuous functions with respect to time. Inspired by the control parameterization method, we use the piecewise-constant functions to approximate the coefficient functions; then we get the multistage feedback control law by solving nonlinear mathematical programming problems. Numerical results indicate the flexibility and effectiveness of our strategy.

This article addresses a job-shop problem with limited output buffers (JS-LOB) with the objective of minimizing the process makespan. An integer nonlinear mathematical programming model is proposed to describe this problem. Based on the model, a two-stage algorithm consisting of obtaining feasible solutions and a local search is proposed to solve the JS-LOB problem. The local search has two operators: the first is a neighbourhood structure based on a disjunctive graph model, and the second is similar to crossover in the genetic algorithm to avoid falling into local optima. Computational results are presented for a set of benchmark tests. The results show the effectiveness of the proposed algorithm and indicate whether the processing time of the job conforms to a uniform distribution. When the proportion between the capacity of the buffer and the number of jobs is larger than 20%, the influence of the buffer becomes very small.

Parameter estimation of semi-empirical models for vapour – liquid equilibrium (VLE) data modelling, plays an important role in the design, optimization, and control of separation units. Conventional optimisation methods are very sensitive to the initial guesses of the unknown parameters and often fail to converge to the global optimum of the parameter estimation nonlinear mathematical programming problems. In this work we present an alternative evolutionary algorithm approach, based on genetic algorithm (GA) technologies, which can solve efficiently the nonlinear parameter estimation problem, finds the global optimum with high probability and most importantly is not sensitive to the initial estimates of the unknown parameters and the tuning parameters of the method. The proposed approach is evaluated and compared with conventional optimisation methods in nine VLE modelling problems of increased complexity. The results illustrate the efficiency and robustness of the proposed method.

The aim of this paper is constructed a new combined fitting index for handling the decision-making problem of medical device under the interval type-2 fuzzy environment. Consider a matter of interval type-2 fuzzy sets geometric measurement with approximate positive and negative ideal, we use elasticity of decision making $\lambda$ -cuts to obtain cutoff points and vectoring it. In contrast to the traditional nonlinear mathematical programming model which combined the common distance formula, this paper directly generates more intuitive geometric measurement formula which described the relationship between interval type-2 fuzzy numbers and approximate positive and negative ideal. Next, this task presents the concept of fitting-index using geometric measurement formula. Meanwhile, by using geometric measurement formula has been constructed to determine the attribute weights based on the minimizing overall uncertainty principle, a novel decision-making approach has been proposed with a comprehensive fitting index, the effectiveness and simplicity of method are reflect by a example analysis of medical device.

We study questions of existence and calculation of directional derivatives of value functions of nonlinear mathematical programming problems depending on parameters. To this end, we use the directional derivatives of the multivalued mappings, defined by the constraints of the problems; this approach was pioneered by Demyanov. We obtain sufficient conditions for existence and explicit formulas for calculating the directional derivatives of the first and second orders, under weaker hypotheses than those traditionally assumed.

Magistrsko delo obravnava optimizacijo gradbenih konstrukcij s teoretičnega in praktičnega vidika. Predstavljene so metode optimiranja s poudarkom na matematičnem programiranju. Za praktični prikaz je za že dimenzioniran jeklen cestni most razpona 50 m izvedeno stroškovno optimiranje glede na ceno jekla, protikorozijske in protipožarne zaščite. Z metodo nelinearnega programiranja je v okolju GAMS optimirana glavna jeklena konstrukcija mostu, ki obsega glavna vzdolžna, vmesna vzdolžna in prečne nosilce mostu. Zaključek dela predstavlja cenovna primerjava osnovne jeklene konstrukcije z optimirano in ocena smiselnosti optimizacije glede na vložen napor in prihranek. This Master thesis deals with the optimization of constructions from theoretical and practical point of view. Presented are optimisation methods with emphasis on mathematical programming and a cost optimisation of already designed road steel bridge with 50 m span. The non-linear programming optimisation conducted in GAMS environment is made for the main steel structure, consisting of main lateral, intermediate lateral and transverse bridge beams. Cost optimisation is based on the price of steel, anti-corrosion protection and fire protection coatings. At the end, the optimisation results are compared to the costs of initial construction and the value of optimisation is reviewed based on the savings and work done.

This paper addresses part scheduling problems (CPS problems) in the context of the need for exceptional parts to visit machines among cells and to be transferred via an automated guided vehicle (AGV) in order to minimize the process make-span. A nonlinear mathematical programming model is proposed to determine the sequences of the parts processed on the machines, which is solved by a two-stage heuristic algorithm. Because of the complexity of the CPS problem, it is divided into two sub-problems: the Intra-cell part scheduling problem (Intra-CPS) and the Inter-CPS. The two-stage heuristic algorithm consists of a local search combined genetic algorithm (LSC-GA) whose neighborhood is based on the disjunctive graph model and a heuristic algorithm for finding a lower make-span through roulette selection (LMW-HEU). When solving the Intra-CPS problem, the sequence of parts processed by each machine and the sequence of parts to be transferred by AGV within manufacturing cells are determined cell by cell by the LSC-GA. Then, the sequence of parts from different cells that need to be processed on the same machine is determined by LMW-HEU in the Inter-CPS problem. A series of experiments were conducted to test the two-stage algorithm. The results demonstrate the effectiveness of the proposed two-stage algorithm.

This paper deals with the numerical approximation problem of the optimal control problem governed by the Euler-Bernoulli beam equation with local Kelvin-Voigt damping, which is a nonlinear coefficient control problem with control constraints. The goal of this problem is to design a control input numerically, which is the damping and distributes locally on a subinterval of the region occupied by the beam, such that the total energy of the beam and the control on a given time period is minimal. We firstly use the finite element method (FEM) to obtain a finite-dimensional model based on the original PDE system. Then, using the control parameterization method, we approximate the finite-dimensional problem by a standard optimal parameter selection problem, which is a suboptimal problem and can be solved numerically by nonlinear mathematical programming algorithm. At last, some simulation studies will be presented by the proposed numerical approximation method in this paper, where the damping controls act on different locations of the Euler-Bernoulli beam.

This article is an attempt to presents a mathematical model to optimize oil production from wells which are set to produce oil in accordance with gas lift system. This process is carried out by determining the economic level of oil production of wells and also reduction of production costs by minimizing the rate of gas used for oil production at an optimum level. Therefore, the information on the characteristics of wells are collected and used as input data of the PIPESIM software application. The performance curve of each of the wells was prepared using this application. In the following section, the non-linear multi-objective programming model of oil production optimization has been developed. The validity of the optimum solution depends on the validity of the presented nonlinear mathematical programming model, therefore, the model components and the relationships between them were described. In order to test the validity of the wells’ performance charts in the gas-lift system, the obtained data were compared to the real data obtained from one of the wells through a T paired comparison test and their validity was confirmed at a significance level of 5%. The point which is of more considerable importance in the results of this study is if the wells under study undergo the production at maximum level, the maximum production would be 24,326 BPD which would require 34.702 MMScf/D of gas to be injected into the wells. Now if the level of consumed gas would reduce to 14/835 MMScf/D. Decreases in oil production only 5.7%, if the saved gas is for example used in the gas lift system for a number of wells comparable to the number of wells in this study, an increase of over 100% will be achieved in oil production. This would simultaneously reduce the rate of injected gas and increase the oil production.

PurposeThe purpose of this paper is to evaluate the rate of discrepancy between the group of expected project results and the group of corresponding results realized preliminarily at the design stage.Design/methodology/approachThe authors formulate and solve the problem to determine the values of two assemblies of independent variables guaranteeing the project with the best (X→*) and as well this one with the worst (X→**) tolerance field of the expected Zx realization. The problem is formulated as an optimization one in nonlinear mathematical programming and it is solved by applying the flexible tolerance method.FindingsBy the use of basic relations in statistical science an expression of standard deviation σZx of Zx is found and proposed. The limits in which are expected to be change in the deviations between the main project results and the corresponding ones of the implemented design, mathematically defined previous to its realization.Research limitations/implicationsThe accent is put on the cases when the device characteristics are presented as polynomials, obtained on the bases of the design of experiments (DOE) and the response surface methodology. An arbitrary technical characteristic Zx=Z(x→) is presented.Practical implicationsA researcher could confine numerically the tolerance field between project results and expected realized ones in the whole investigated region.Originality/valueThe paper is characterized by an original approach and a new expression of standard deviation is proposed which will be of interest to designers.

This paper aims to determine the strength properties of jointed rock masses by means of the homogenization method. To reflect the microstructure of jointed rock masses, a representative element volume (REV) is selected. Assuming being rigid and perfectly plastic and utilizing the Mohr-Coulomb yield criterion for rock and joints, an upper bound limit analysis method is proposed based on the homogenization theory. By using the finite element method and Goodman joint element, a nonlinear mathematical programming with equality constraints is formulated, which can be solved by a direct iterative algorithm. Numerical results show the strength of jointed rock masses behaves anisotropy with different joint directions. This method presents an effective tool for the strength analysis of jointed rock masses.

New mathematical programming models are proposed, developed and evaluated in this study for estimating missing precipitation data. These models use nonlinear and mixed integer nonlinear mathematical programming (MINLP) formulations with binary variables. They overcome the limitations associated with spatial interpolation methods relevant to the arbitrary selection of weighting parameters, the number of control points within a neighbourhood, and the size of the neighbourhood itself. The formulations are solved using genetic algorithms. Daily precipitation data obtained from 15 rain gauging stations in a temperate climatic region are used to test and derive conclusions about the efficacy of these methods. The developed methods are compared with some naive approaches, multiple linear regression, nonlinear least-square optimization, kriging, and global and local trend surface and thin-plate spline models. The results suggest that the proposed new mathematical programming formulations are superior to ...

In this paper a direct method for solving variational problems using nonclassical parameterization is presented. A nonclassical parameterization based on nonclassical orthogonal polynomials is first introduced to reduce a variational problem to a nonlinear mathematical programming problem. Then, using the Lagrange multiplier technique the problem is converted to that of solving a system of algebraic equations. Illustrative examples are given to demonstrate the validity and applicability of the technique.

We consider a scheduling problem where the processing time of any job is dependent on the usage of a discrete renewable resource, e.g. personnel. An amount of $k$ units of that resource can be allocated to the jobs at any time, and the more of that resource is allocated to a job, the smaller its processing time. The objective is to find a resource allocation and a schedule that minimizes the makespan. We explicitly allow for succinctly encodable time-resource tradeoff functions, which calls for mathematical programming techniques other than those that have been used before. Utilizing a (nonlinear) integer mathematical program, we obtain the first polynomial time approximation algorithm for the scheduling problem, with performance bound $(3 + \varepsilon)$ for any $\varepsilon > 0$. Our approach relies on a fully polynomial time approximation scheme to solve the nonlinear mathematical programming relaxation. We also derive lower bounds for the approximation.

Berth scheduling is the process of determining the time and position at which each arriving ship will berth. This paper attempts to minimize the serving time to ships, after introducing a proposed mathematical model, considers the berth allocation problem in form of mixed integer nonlinear programming. Then, to credit the proposed model, the results of Imai et al.'s model have been used. The results indicate that because the number of nonlinear variables in the proposed model is less than prior model, so by using the proposed model, we can obtain the results of model in less time rather than prior model.

In this paper, new classes of generalized invex functions called B-(p, r)-pseudo-invex and B-(p, r)-quasi-invex (with respect to η and b) are introduced. These classes of functions are defined by relaxing the definitions of the classes of quasi-invex and pseudo-invex functions earlier defined by Hanson (J. Math. Anal. Appl. 1981, 80:545–550), and also the concept of B-(p, r)-invexity (with respect to η and b) earlier introduced by Antczak (J. Math. Anal. Appl. 2003, 286:187–206). Further, mathematical programming problems involving generalized B-(p, r)-invex functions with respect to η and b are considered. The sufficient optimality conditions and various duality results are established for such optimization problems.

This paper addresses the problem of parts scheduling in a cellular manufacturing system (CMS) by considering exceptional parts processed on machines located in multiple cells. To optimize the scheduling of parts as well as to minimize material handling between cells, the practice has to develop processing sequences for the parts in cells. A commonly chosen objective is to find part sequences within cells which results in a minimum tardiness. This paper proposes a nonlinear mathematical programming model of the problem by minimizing the total weighted tardiness in a CMS. To solve the mathematical model, a scatter search approach is developed, in which the common components of scatter search are redefined and redesigned so as to better fit the problem. This scatter search approach considers two different methods to generate diverse initial solutions and two improvement methods, and adopts the roulette wheel selection in the combination method to further expand the conceptual framework and implementation of the scatter search. The proposed approach is compared with the commercial solver CPLEX on a set of test problems, some of which are large dimensions. Computational results have demonstrated the effectiveness of this scatter search approach.

In this paper, we present a penalty function with objective parameters for inequality constrained optimization problems. We prove that this type of penalty functions has good properties for helping to solve inequality constrained optimization problems. Moreover, based on the penalty function, we develop an algorithm to solve the inequality constrained optimization problems and prove its convergence under some conditions. Numerical experiments show that we can obtain a satisfactorily approximate solution for some constrained optimization problems as the same as the exact penalty function.

In the field of Deterministic Design Optimization (DDO), the designer reduces the structural cost without taking into account uncertainties concerning materials, geometry and loading. This way the resulting optimum solution may represent a lower level of reliability and thus a higher risk of failure. But in the Reliability-Based Design Optimization (RBDO) model, the mean values of uncertain system variables are usually used as design variables, and the cost is optimized subject to prescribed probabilistic constraints as defined by a nonlinear mathematical programming problem. Therefore, a RBDO solution that reduces the structural weight in uncritical regions does not only provide an improved design but also a higher level of confidence in the design. In this paper, we present the advantage of the DDO and RBDO models and next some recent methodologies in order to show that the RBDO model is a practical tool for structural engineers.

This paper proposes a new method for designing lightweight automotive body assemblies using multi-material construction with low cost penalty. Current constructions of automotive structures are based on single types of materials, e.g., steel or aluminium. The principle of the multi-material construction concept is that proper materials are selected for their intended functions. The design problem is formulated as a multi-objective nonlinear mathematical programming problem involving both discrete and continuous variables. The discrete variables are the material types and continuous variables are the thicknesses of the panels. This problem is then solved using a multi-objective genetic algorithm. An artificial neural network is employed to approximate the constraint functions and reduce the number of finite element runs. The proposed method is illustrated through a case study of lightweight design of an automotive door assembly.

© Springer International Publishing Switzerland 2016. Many organisations need periodic retraining of staff. Due to certain requirements on the composition of study groups, the planning of training sessions is an NP-hard problem. The paper presents linear and nonlinear mathematical programming formulations of this problem together with three column generation based heuristic optimisation procedures. The procedures are compared by means of computational experiments that use data originating from a large Australian electricity distributor with several thousand employees.

This paper presents a model for solving probabilistic travel distribution problems that involves fuzzy uncertainty. Using entropy measures for interval-valued problems, we extend those results to a fuzzy environment via extension principle and nonlinear mathematical programming methods. An application example is solved using the proposed fuzzy entropy method in order to analyze their results.

A technique is developed for optimal control of dynamic processes in boiler aggregate based on the nonlinear mathematical programming and its program implementation is conducted. A comparison is presented for the regulation of dynamic process of the loading variation of the TP-81 boiler on the basis of the given technique and while using the conventional proportional-integral-differential regulators.

This study attempts to optimize a delivery service strategy for Internet shopping by considering time-dependent consumer demand, demand–supply interaction and consumer socioeconomic characteristics. A nonlinear mathematical programming model is formulated for solving the optimal number and duration of service cycles for discriminating strategy by maximizing profit subject to demand–supply interaction. An example is employed to demonstrate the application of the model. Results suggest that discriminating service strategy is a better strategy in response to time-dependent consumer demand than uniform strategy. Finally, the proposed model is demonstrated to yield more profit than models that do not consider variations in consumer demand or demand–supply interaction.

This study deals with the optimization problem of material distributions for maximizing the applied internal pressure of thick-walled functionally graded material (FGM) circular pipes subjected to thermomechanical loading. For the FGM circular pipes without cracks, the ultimate internal pressure is determined using the tensile strength criterion. For the FGM circular pipes with cracks, radial edge cracks emanating from the inner surface of pipe are supposed and the ultimate internal pressure is determined using the fracture toughness criterion. The optimum material distribution for maximizing the applied internal pressure is obtained using a nonlinear mathematical programming method. Numerical results for a thick-walled TiC/Al2O3 FGM circular pipe reveal that the load carrying capacity can be improved markedly by choosing an optimum material distribution profile.