A Minimax Mathematical Programming Framework For Robust Production Scheduling In Smart Manufacturing Systems

Abstract

Smart manufacturing systems should have production schedules that are still efficient despite variations in processing times and machine availability from their nominal values. In this paper, propose a minimax mathematical programming framework for robust production scheduling in smart manufacturing systems to explicitly minimize the maximum possible production loss on account of bounded uncertainties. The framework includes job assignment, machine sequencing, start time assignment, tardiness, makespan, and machine capacity constraints within an integrated mixed-integer minimax model. Uncertainties in processing times and machine availability are described by budgeted polyhedral uncertainty sets so that the conservativeness of the robust schedule can be regulated by uncertainty budget parameters. Unlike approaches that consider the uncertainty effect on the objective as an abstract perturbation, this approach explicitly accounts for the propagation of processing time deviations on completion times, tardiness, makespan, and machine capacity requirements. A dual reformulation for the joint uncertain capacity constraints is derived. To solve this problem, a column-and-constraint generation algorithm is devised where a mixed integer master scheduling problem is repeatedly solved with respect to a continuous linear adversarial subproblem. Studies prove theoretical properties, including feasibility, monotonicity of the robust objective, asymptotic recovery to the deterministic limit, and finite convergence of the decomposition algorithm. The numerical experiments include production problems with configurations of 12×4 to 100×20 jobs-machines and compare the proposed approach with deterministic, stochastic, traditional robust, and dynamic MPC approaches. These results illustrate the superiority of the proposed minimax framework for uncertainty-aware smart manufacturing scheduling.