Optimal solution of printing press-flexible job-shop scheduling problem (PP-FJSSP) with exact and heuristic algorithms

In production related industries, optimizing scare resources and machine operations is one of the main goals toward improving operational efficiency and productivity while reducing cost. The Job shop scheduling problem (JSSP) model where one job can be process on one type of machine at a particular time is key to achieving this. However, Flexible job shop scheduling problem (FJSSP) extends JSSP by allowing machine operation to be processed by any qualified alternative machines. On this premise, this work seeks to optimize the operation of printing press system with j-jobs, k-tasks and m-machines using two optimization models viz: Integer Linear Programing (ILP) and Alldifferent Constraints Programing (ACP) models with a view to identifying the best model for this class of problem in terms of minimum makespan, optimality gap and computational time criteria as performance indicators. The ACP model yielded a comparative better result with makepan value of 233 minutes and optimal solution time of 0.21 seconds as against the ILP model with makespan value of 233 minutes and optimal solution time of 1.87 seconds. Hence, the ACP model is recommended for optimal operation in the printing company.