Transitive Reduction Approach to Large-Scale Parallel Machine Rescheduling Problem With Controllable Processing Times, Precedence Constraints and Random Machine Breakdown

Abstract

This paper studied a novel parallel machine rescheduling problem with controllable processing times under machine breakdown and precedence constraints. This problem is strongly <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {NP}$ </tex-math></inline-formula> -hard, and we modeled it as a mixed-integer problem (MIP). The primal problem is decomposed into the discrete subproblem and the continuous one. We treat the discrete with the dispatching rule and analyze the continuous in the terms of mathematical programming. Pros and cons from the analysis lead us to implement the commercial solver. The proposed method is capable of efficiency and nonzero initial state. We introduce transitive reduction to cull the redundant constraints out of its directed acyclic graph (DAG) representation. Transitive reduction extends the efficiency from the dispatching rule to the solver. The proposed method can do the predictive scheduling and pick up the partial solution left by the machine breakdown in the reactive session. As a result, the complete method solves the rescheduling problem with efficiency, and allows for large cases. At last, the computational results showed that this technique significantly brought down the time and RAM consumption in using the solver. This technique allows the scheduler to solve big instances with computational economy and efficiency.