Mixed-integer nonlinear programming based optimal time scheduling of construction projects under nonconvex costs

Abstract

Original scientific paper 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. Keywords: construction management; discrete optimization; mixed-integer nonlinear programming; nonconvex costs; time schedulingOptimalno terminsko planiranje građevinskih projekata s nekonveksnim troškovima pomoću mješovitog cjelobrojnog nelinearnog programiranja Izvorni znanstveni članakOptimalno terminsko planiranje projekata s nekonveksnim troškovima predstavlja zahtjevan problem u organizaciji građenja. Nekonveksni odnosi između vremena i troškova mogu nastupiti u građevinskom projektu kada su na raspolaganju različite varijante za trajanje njegovih aktivnosti zbog mogućnosti izbora različitih tehnoloških procesa za izvođenje radova ili široke pristupačnosti proizvodnih resursa. Izvor nekonveksnosti problema troškovne optimizacije terminskog plana je moguće naći i u dogovorenom odnosu između trajanja projekta te penala ili premije iz ugovora o građenju. Cilj ovoga rada je predstaviti optimalno terminsko planiranje projekata s nekonveksnim troškovima pomoću mješovitog cjelobrojnog nelinearnog programiranja. U tu svrhu je razvijen i primijenjen optimizacijski model. Za prikaz prednosti optimizacije s mješovitim cjelobrojnim nelinearnim programiranjem su u radu predstavljeni uporaba razvijenog modela na primjeru iz literature i primjer analize ovisnosti ukupnih troškova građevinskog projekta o dužini njegovoga trajanja uzimajući u...