Discrete Time/Cost Trade-off Project Scheduling Problem with Tardiness Bounds

We consider a discrete time/cost trade-off problem with due dates and an upper bound on the total tardiness. Our motivation stems from information technology projects held in the Ministry of Health in Turkey. Our primary objective is to minimise the total cost while obeying the total tardiness bound. We formulate the problem as a mixed integer linear program and propose a heuristic approach that leverages the optimal solutions from the linear programming relaxation of the model. To assess the performances, we conduct tests on instances from relevant literature and the Ministry of Health projects, and report favourable results. We employ the optimal solutions to the constrained optimisation problem to generate the exact non-dominated objective vectors' set with respect to total tardiness and total cost. Additionally, we present an evolutionary algorithm to find an approximate set. The algorithms are demonstrated using the projects of the Ministry of Health in Turkey. [Received: 5 February 2023; Accepted: 10 September 2023]