Due-date assignment scheduling with only mean and support of processing times

Abstract

We consider a single-machine scheduling problem with due-date assignment and stochastic processing times, where only the mean and support (i.e. an interval bounded with lower and upper values) of processing times are known to the decision maker. The objective is to jointly determine a scheduling policy and a set of due dates for all jobs, so as to minimise the total expected individually weighted costs of earliness, tardiness and due-date assignment. By identifying an upper bound with the robust optimisation approach and a lower bound, and using a linear function of them to approximate the studied objective function, we establish an approximated problem. Then, a branch-and-bound algorithm is proposed to find an optimal solution for the approximated problem. Finally, a series of computational experiments are conducted to examine the performance of problem approximation and two developed heuristic algorithms. HIGHLIGHTS Study due-date assignment scheduling problem with stochastic processing times. Apply the mean and support (interval data) to model stochastic processing times. Use a linear function of identified lower and upper bounds to make an approximation. Derive optimal due-date assignment and develop branch-and-bound algorithms. Evaluate the efficiency of branch-and-bound algorithm and heuristic algorithms.