Static Single Machine Scheduling Problem Research Articles

Bi-objective single machine scheduling problem with stochastic processing times

In this study, a static single machine scheduling problem is investigated, where processing times are stochastic, due dates are deterministic and inserted idle time is allowed. Two objective functions are simultaneously taken into account, minimization of mean completion time and minimization of earliness and tardiness costs. A robust model is presented to tackle the problem, based on goal programming and a stochastic programming model named E-model. The proposed model not only obtains optimal operating systems, but also considers the variance of the objective functions and the correlation between them. Moreover, chance-constrained programming model is used to take into account the randomness in the constraints of the model. The model is presented with general distribution of processing times and the normal case is explored in experiments. Two sets of computational experiments are presented to test the efficiency of the proposed model. In the first set, the performance obtained by the bi-objective formulation is measured, where in the second set the performance obtained by incorporating robustness is measured. Results confirm the effectiveness of the proposed model, in both directions.

Multi-agent based approach for single machine scheduling with sequence-dependent setup times and machine maintenance

Scheduling of single machine in manufacturing systems is especially complex when the order arrivals are dynamic. The complexity of the problem increases by considering the sequence-dependent setup times and machine maintenance in dynamic manufacturing environment. Computational experiments in literature showed that even solving the static single machine scheduling problem without considering regular maintenance activities is NP-hard. Multi-agent systems, a branch of artificial intelligence provide a new alternative way for solving dynamic and complex problems. In this paper a collaborative multi-agent based optimization method is proposed for single machine scheduling problem with sequence-dependent setup times and maintenance constraints. The problem is solved under the condition of both regular and irregular maintenance activities. The solutions of multi-agent based approach are compared with some static single machine scheduling problem sets which are available in the literature. The method is also tested under real-time manufacturing environment where computational time plays a critical role during decision making process.

Solving a stochastic single machine problem with initial idle time and quadratic objective

We study a static single machine scheduling problem in which processing times are stochastic, due-dates and penalties for not completing jobs on time are deterministic, and an initial fixed idle time is allowed to be inserted before the processing of the first job begins on the machine. The objective is to determine the optimal sequence and the optimal initial idle time that jointly minimize the expected value of the sum of a quadratic cost function of idle time and the weighted sum of a quadratic function of job lateness. The problem is NP-hard to solve; however, we develop an exact algorithm based on a precedence relation structure among adjacent jobs. Our extensive computational results show that the algorithm can solve large problem instances quickly. We also demonstrate that the proposed problem is general in the sense that its special cases reduce to new stochastic models while its limiting cases simplify to some deterministic models.

Minimising a weighted quadratic function of job lateness in the stochastic single machine scheduling problem

We study a static single machine scheduling problem in which processing times, due-dates, and penalties for not completing jobs on time are distinct arbitrary random variables. The objective is to identify an optimal sequence, which minimises the expected weighted sum of a quadratic function of job lateness. The problem is NP-hard to solve; however, based on a precedence relation structure among adjacent jobs, we develop an exact algorithm. Our computational results demonstrate that the algorithm solves large problem instances quickly. Furthermore, the proposed problem is general in the sense that its special cases reduce to some classical deterministic or new stochastic single machine models.

Single facility scheduling with dual criteria: minimizing maximum tardiness subject to minimum number of tardy jobs

Abstract This paper considers the static single machine scheduling problem with the objective of minimizing the maximum tardiness of any job subject to the constraint that the total number of lardy jobs is minimum. Based on simple dominance conditions an o(n2) heuristic algorithm is proposed to find an approximate solution to this problem. The effectiveness of the proposed heuristic algorithm is empirically evaluated by solving a large number of problems and comparing them to the optimal solutions obtained through the branch and bound algorithm.

The stochastic single machine scheduling problem with earliness and tardiness costs

This paper studies the static single machine scheduling problem with earliness and tardiness costs where job processing times are random variables and due dates are distinct and deterministic. The objective is to identify an optimal sequence which minimizes the total expeted earliness plus tardiness cost. A case where processing times are normally distributed is fully explored. We demonstrate that variations in processing times increase cost and affect sequencing decisions. Three heuristics for finding an optimal sequence are proposed. The illustrative example and computational results indicate that optimal sequences and their expected costs are significantly different from those provided by the classical deterministic single machine models. Furthermore, our computational experiments show that two of the proposed heuristics perform well in identifying optimal sequences.