A model proposal for the optimization of hybrid project scheduling problems with flexible precedence constraints: An application in the museum design industry

The evolving expectations of museum visitors, the integration of technological advancements into exhibition techniques, and innovations in presentation approaches have significantly increased the need for interdisciplinary expertise in the museum design. Within this context, the necessity of employing scientific methods has become evident. This study addresses a resource-constrained hybrid project scheduling problem with flexible precedence constraints faced by a company operating in the museum design industry. The primary objective is to minimize the total project completion time through the development and solution of a mathematical model. The model incorporates 19 distinct activities, each characterized by specific durations, assigned expert teams, flexible and strict precedence relations, and dynamic constraints. The problem is formulated as a Mixed-Integer Linear Programming (MILP) model and solved using the CPLEX solver within the Python programming environment. The optimal solution was obtained after 104,768 iterations. The resulting model consists of 7,668 variables and 23,774 constraints, of which 7,629 are binary variables highlighting the computational complexity of the problem. Based on real-world data provided by stakeholders in the museum design industry, the initially planned 260-day project duration was reduced to 171 days in the optimal solution. To benchmark the performance of the proposed model, the Critical Path Method (CPM) was also applied, although not fully suitable due to the dynamic nature of some constraints. The CPM approach yielded a total project duration of 197 days. The optimization model outperformed the target duration by 34.23% and the CPM result by 13.19%. Moreover, a 15,16% improvement was observed in resource workload efficiency when compared to the CPM outcome. The study characterizes the problem as a hybrid project scheduling problem with flexible precedence constraints, shaped by the unique structure of the constraints and the data. Both mathematical and CPM-based solutions are visualized using activity network diagrams and Gantt charts. For the mathematical model, And/Or Precedence Constraints were particularly illustrated using appropriate diagrammatic techniques. The dynamic and complex nature of the constraints distinguishes this research from others in the existing literature and demonstrates its contribution to the field.