Scheduling of two parallel machines with linear decreasing time slot costs to minimize total weightedcompletion time

Key Points

• This approach minimizes the total weighted completion time and total machine time slot cost, enhancing efficiency.
• An exact pseudopolynomial dynamic programming algorithm efficiently handles arbitrary integer processing times.
• Modification leads to a polynomial algorithm when all jobs possess unit processing times, simplifying complexity.
• Implications suggest notable improvements in scheduling efficiency, potentially applicable to various operational settings.