BUS606: Operations and Supply Chain Management

The time-cost trade-off problem has been studied since the 1960s and is considered as a difficult combinatorial problem. The solving process of mathematical programming involves converting the relationship between activity time and crash cost in the network diagram into a mathematical model and then using linear programming, integer programming, or dynamic programming to solve the model. Kelley used parametric linear programming to determine an optimal schedule. Butcher assumed that activity time and direct cost were in irregular forms and used dynamic programming to obtain the shortest completion schedule when the direct cost was known. Perera constructed three constraint models of crashing workload, scheduled completion, and network diagram loop and utilized linear programming to solve the optimal crashing scheduling. Russel and Caselton applied dynamic programming to analyze the two-dimensional problem of resolving the start time of each activity in the unit and the buffer time for entering the next unit. They constructed a mathematical analysis model to obtain the shortest schedule. Reda constructed a minimum-cost linear programming model that can calculate a specific construction period for an engineering project on the basis of the relationship among activity constraints. Moselhi and EI-Rayes adopted the model of Russell and Caselton to construct a resource scheduling model that considers the direct and indirect costs of activities in accordance with the principle of minimum total project cost. Burns et al. combined linear and integer programming to solve the trade-off between construction schedule and cost. Feng et al. used a hybrid approach to minimize construction project time and cost simultaneously through a combination of simulation and mathematical algorithms. Sakellaropoulos and Chassiakos proposed the incorporation of parameters describing the actual project into the mathematical model, followed by an analysis of the time and cost of project scheduling. Moussourakis and Haksever presented a mixed integer programming model that minimizes the total cost subject to a project deadline or the project completion time subject to a budget constraint for various types of activity cost functions. Chassiakos et al. utilized an integer linear programming model to obtain an optimal project time-cost curve that considers all activity time-cost alternatives simultaneously. Liberatore and Bruce used a hybrid mathematical model to analyze the time and cost of a project. Mokhtari et al. developed a hybrid approach for the stochastic time-cost trade-off problem to improve project completion probability in a specified deadline from a risky value to a confident probability through simulation and a mathematical program. Gonen proposed a linear programming approach for budget allocation and demonstrated the budget constraint method, including sensitivity analysis. Sato and Hirao used a mathematical modeling approach to analyze the trade-off problem between budgets and critical risks. Ghaffari et al. employed a fuzzy linear programming model to assess project risks on the basis of project life cycles. Zeng et al. used a stochastic optimization model to establish the total expected travel time cost. Dupont et al. used a mixed integer linear programming model to show profit-and-loss targets. Atan and Eren established mixed integer linear methods for several leveling objectives by using a heuristic algorithm.

Although the time-cost trade-off issue appears to have no unique optimum solution, mathematical programming provides a correct calculated solution. Therefore, this study uses the results of risk sensitivity analysis from Monte Carlo simulation to analyze activities in critical paths and adopts IBM ILOG CPLEX optimizing software for mathematical programming to solve the issue wherein the crash cost and delay penalty are considered. A time-cost trade-off analysis is performed by calculating the relationship between optimal project completion time and crash cost in consideration of risks through the constructed mathematical programming model.