A New Mathematical Programming Model and Arena Simulation Model to Investigate a Parallel Machine Scheduling Problem With Deterioration Effect and Skilled Human Resources

The just-in-time policy is a production strategy aimed at enhancing efficiency by reducing inventories and delays. Minimizing tardiness and earliness in scheduling problems allows production systems to align more closely with this policy. The present study focuses on a parallel machine scheduling problem with the objective to minimize both tardiness and earlyness, considering the existing availability of qualified human resources. For this problem, an original MixedInteger Linear Programming (MILP) model is formulated to identify optimal solutions. The complexity of the problem necessitates the proposal of a polynomial-time algorithm to enhance its efficiency. This algorithm is rigorously simulated using Arena software to validate its performance and effectiveness in real-world scenarios, demonstrating its capability to significantly reduce scheduling discrepancies and enhance overall production efficiency.