Uroš Klanšek

MINLP optimization model for the nonlinear discrete time-cost trade-off problem

This paper presents the mixed-integer nonlinear programming (MINLP) optimization model for the nonlinear discrete time-cost trade-off problem (NDTCTP). The nonlinear total project cost objective function of the proposed MINLP optimization model is subjected to a rigorous system of generalized precedence relationship constraints between project activities, project duration constraints, logical constraints, and a budget constraint. By means of the proposed MINLP optimization model, one can obtain the minimum total project cost, the project schedule with the optimal discrete start times and the optimal discrete durations of the activities, as well as the optimal time-cost curves of the project. The proposed model yields the exact optimum solution of the NDTCTP. Solving the NDTCTP, using the proposed MINLP model, avoids the need for (piece-wise) linear approximation of the nonlinear expressions. The MINLP model handles the discrete variables explicitly and requires no rounding of the continuous solution into an integer solution. The applicability of the proposed optimization model is not limited to weakly NDTCTPs. A numerical example from the literature and an example of the project time-cost trade-off analysis are presented at the end of the paper in order to show the advantages of the proposed model.

Solving the nonlinear discrete transportation problem by MINLP optimization

The Nonlinear Discrete Transportation Problem (NDTP) belongs to the class of the optimization problems that are generally difficult to solve. The selection of a suitable optimization method by which a specific NDTP can be appropriately solved is frequently a critical issue in obtaining valuable results. The aim of this paper is to present the suitability of five different Mixed-Integer Nonlinear Programming (MINLP) methods, specifically for the exact optimum solution of the NDTP. The evaluated MINLP methods include the extended cutting plane method, the branch and reduce method, the augmented penalty/outer-approximation/equality-relaxation method, the branch and cut method, and the simple branch and bound method. The MINLP methods were tested on a set of NDTPs from the literature. The gained solutions were compared and a correlative evaluation of the considered MINLP methods is shown to demonstrate their suitability for solving the NDTPs.

COST OPTIMIZATION OF TIME SCHEDULES FOR PROJECT MANAGEMENT

Abstract The paper presents the cost optimization of the time schedules for project management. The nonlinear programming (NLP) model for the cost optimization of the time schedules under the generalized precedence relations between the project activities was developed and applied. The existing NLP optimization models have focused on the cost optimal solution of the project scheduling problems which include simplifying assumptions regarding the precedence relationships among the project activities. In this way, this research work aims to propose the NLP optimization model for making optimal time-cost decisions applicable to actual projects in project management. The generalized reduced-gradient method was used for the NLP optimization. The obtained results include the minimum total cost project schedules and the optimal project time-cost curves. The proposed optimization approach enables the insight into the interdependence between the project duration and the total project cost. The decision-maker can more effectively estimate the effect of the project deadline on a total project cost before the submission of a tender. An application example and an example of the time-cost trade-off analysis are presented in the paper to demonstrate the advantages of the proposed approach.

A comparison between MILP and MINLP approaches to optimal solution of Nonlinear Discrete Transportation Problem

Finding an exact optimal solution of the Nonlinear Discrete Transportation Problem (NDTP) represents a challenging task in transportation science. Development of an adequate model formulation and selection of an appropriate optimization method are thus significant for attaining valuable solution of the NDTP. When nonlinearities appear within the criterion of optimization, the NDTP can be formulated directly as a Mixed-Integer Nonlinear Programming (MINLP) task or it can be linearized and converted into a Mixed-Integer Linear Programming (MILP) problem. This paper presents a comparison between MILP and MINLP approaches to exact optimal solution of the NDTP. The comparison is based on obtained results of experiments executed on a set of reference test problems. The paper discusses advantages and limitations of both optimization approaches.

Cost Optimal Project Scheduling

Cost Optimal Project Scheduling This paper presents the cost optimal project scheduling. The optimization was performed by the nonlinear programming approach, NLP. The nonlinear total project cost objective function is subjected to the rigorous system of the activity precedence relationship constraints, the activity duration constraints and the project duration constraints. The set of activity precedence relationship constraints was defined to comprise Finish-to-Start, Start-to-Start, Start-to-Finish and Finish-to-Finish precedence relationships between activities. The activity duration constraints determine relationships between minimum, maximum and possible duration of the project activities. The project duration constraints define the maximum feasible project duration. A numerical example is presented at the end of the paper in order to present the applicability of the proposed approach.

MINLP OPTIMIZATION OF STEEL FRAMES

In this paper we deal with the topology and standard optimization of unbraced steel frames with rigid beam-to-column connections. The optimization has been performed by the Mixed-Integer Non-linear Programming (MINLP) approach. The MINLP performs a discrete topology and standard dimension optimization, while continuous parameters are simultaneously calculated inside the continuous space. As the discrete/continuous optimization problem of steel frames is non-convex and highly non-linear, the Modified Outer-Approximation/EqualityRelaxation (OA/ER) algorithm has been used for the optimization. Two practical examples with the results of the optimization are shown at the end of the paper.

2.5 – The MINLP Approach to Cost Optimization of Structures

The paper presents the Mixed-Integer Non-Linear Programming (MINLP) approach to cost optimization of structures. The MINLP is a combined discrete/continuous optimization technique, where the discrete binary 0-1 variables are defined for the optimization of the discrete topology, material and standard sizes alternatives and the continuous variables for the optimization of continuous parameters. An economic objective function of the manufacturing material and labour costs is subjected to structural analysis and dimensioning constraints. The Modified Outer-Approximation/Equality-Relaxation (OA/ER) algorithm is used for the optimization. The accompanied Linked Multilevel Hierarchical Strategy (LMHS) accelerates the convergence of the algorithm. Three examples of the cost optimization of steel structures are presented at the end of the paper.

An integration of spreadsheet and project management software for cost optimal time scheduling in construction

Abstract Successful performance and completion of construction projects highly depend on an adequate time scheduling of the project activities. On implementation of time scheduling, the execution modes of activities are most often required to be set in a manner that enables in achieving the minimum total project cost. This paper presents an approach to cost optimal time scheduling, which integrates a spreadsheet application and data transfer to project management software (PMS). At this point, the optimization problem of project time scheduling is modelled employing Microsoft Excel and solved to optimality using Solver while organization of data is dealt by macros. Thereupon, Microsoft Project software is utilized for further managing and presentation of optimized time scheduling solution. In this way, the data flow between programs is automated and possibilities of error occurrence during scheduling process are reduced to a minimum. Moreover, integration of spreadsheet and PMS for cost optimal time scheduling in construction is performed within well-known program environment that increases the possibilities of its wider use in practice. An application example is shown in this paper to demonstrate the advantages of proposed approach.

Survey Of Accomplishments in BIM Implementation in Croatia, The Czech Republic, Germany and Slovenia

Building information modelling (BIM) may currently be considered the fastest developing concept in the field of construction management, aiming to become a global standard. Although the roots of the concept date back to the mid-1970s, some original expectations are still missing from its implementation. There has been a time gap between its theoretical and practical implementations. While the simultaneous development of information technologies is one reason for the implementation delay, other reasons remain unclear. This paper analyzes the gaps between theoretical and practical BIM application, as well as the legislation regarding BIM implementation in four countries (in alphabetical order: Croatia, the Czech Republic, Germany, and Slovenia). The paper additionally presents a survey of current practical BIM applications as well as general and theoretical feedback from construction projects that implemented BIM.

Application of “Einstein's riddle” in solving construction machine allocation problems

“Einstein’s riddle” is a popular example of constraints satisfaction problem. Since its introduction, different forms and variations of the riddle have been presented. Regardless of the variant of the riddle, its solution is considered a tough challenge for humans. Researchers have developed and are still developing mathematical models, as well as computational simulation models for solving it. In this article, the authors have modified a previously published mathematical model and developed a computational spreadsheet model for solving the riddle, which provides a unique solution for the riddle. The model was also tested in a small and medium-scaled form for solving constraint satisfaction problems regarding the allocation of construction machines. The authors have also highlighted the model’s limitations for solving such problems and made suggestions regarding necessary modifications in the model to solve more complex problems in the same domain.