The two-stage no-wait/blocking proportionate super shop scheduling problem

We analyze the 'no-wait' proportionate two-stage super shop scheduling problem with the objective of minimising the maximum job completion time (makespan). The existing simple sorting procedures for the open shop and the job shop do not work on the super shop. We show that the problem is still solvable in time using a procedure based on dynamic programming (DP). A unique feature of this procedure is that the state variable is defined based on the number of jobs; thus, reducing the complexity to polynomial. The same procedure solves the super shop problem with the blocking constraint. We also consider the case of machine dominance and show that the problem can be solved in linear time. Finally, we highlight the differences between the super shop with 'no-wait' and 'synchronous' processing modes via a numerical example.