Abstract
Optimal project scheduling under nonconvex time-cost relations represents a challenging problem in construction management. The nonconvex time-cost relations may appear in a construction project when several different duration options are available for its activities due to alternative technological processes enabled for their realization or wide accessibility of production resources. The source of nonconvexity of the project scheduling optimization problem can also be the project penalty- or bonus-duration relations arranged within the construction contract. The aim of this paper is to present the mixed-integer nonlinear programming (MINLP) based optimal time scheduling of construction projects under nonconvex costs. For this purpose, the MINLP model was developed and applied. A numerical example from literature and an example of construction project time-cost trade-off analysis under practical nonconvex penalty function are given in the paper to demonstrate advantages of MINLP optimization. The example from literature first presented the capability of the MINLP approach to obtain the optimal solution for difficult, highly combinatorial nonconvex discrete project scheduling problem. Thereupon, the following example revealed that the optimal project time-cost curve may take very nonuniform shape on account of discrete nature of activity direct cost options and nonconvex relation between project duration and total cost. In this way, the presented study intends to provide practitioners with new information from the field of optimization techniques for project scheduling as well as an alternative view on performance of total cost when project duration is changed.
Highlights
The problem of cost optimal project time scheduling, i.e. the time-cost trade-off problem (TCTP), was originally initiated by Kelley and Walker in 1959 [1]
The aim of this paper is to present the MINLP based optimal solution of the nonconvex discrete TCTP
For a better presentation of the advantages of MINLP optimization, this paper introduces an example of the construction project time-cost trade-off analysis executed under practical nonconvex penalty function
Summary
The problem of cost optimal project time scheduling, i.e. the time-cost trade-off problem (TCTP), was originally initiated by Kelley and Walker in 1959 [1]. A numerical example from literature and an example of project time-cost trade-off analysis under practical nonconvex penalty function are given in the paper to demonstrate advantages of MINLP optimization. Since the MILP can only handle linear dependences between variables, the nonlinear time-cost relations were usually set with discrete or piece-wise linear terms, see Figs. The differences between the values of parameters for actual time-cost dependences, gained from the project analysis, and the approximated ones, included into the TCTP model, may lead the search algorithm to attain the sub-optimal solution. Meyer and Shaffer [40] presented one of the first mixed-integer linear programming (MILP) models for Figure 4 Unconstrained and constrained linear penalties It is common situation in construction business that constrained linear penalties are set in the contract. The project penalty- or bonus-duration relations can be the source of nonconvexity of the TCTP
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