A Combinatorial 2-Approximation Algorithm for the Parallel-Machine Scheduling with Release Times and Submodular Penalties

In this paper, we consider parallel-machine scheduling with release times and submodular penalties (P|rj,reject|Cmax+π(R)), in which each job can be accepted and processed on one of m identical parallel machines or rejected, but a penalty must paid if a job is rejected. Each job has a release time and a processing time, and the job can not be processed before its release time. The objective of P|rj,reject|Cmax+π(R) is to minimize the makespan of the accepted jobs plus the penalty of the rejected jobs, where the penalty is determined by a submodular function. This problem generalizes a multiprocessor scheduling problem with rejection, the parallel-machine scheduling with submodular penalties, and the single machine scheduling problem with release dates and submodular rejection penalties. In this paper, inspired by the primal-dual method, we present a combinatorial 2-approximation algorithm to P|rj,reject|Cmax+π(R). This ratio coincides with the best known ratio for the parallel-machine scheduling with submodular penalties and the single machine scheduling problem with release dates and submodular rejection penalties.

Research on green single machine scheduling based on improved ant colony algorithm

This paper studies the green single-machine scheduling problem that considers the delay cost and the energy consumption of manufacturing equipment and builds its integrated optimization model. The improved ant colony scheduling algorithm based on the Pareto solution set is used to solve this problem. By setting the heuristic information, state transition rules, and other core parameters reasonably, the performance of the algorithm is improved effectively. Finally, the model and the improved algorithm are verified by the simulation experiment of 10 benchmark cases.

Single Machine Scheduling Problems With Sequence-dependent Setup Times and Precedence Delays

Sequence-dependent setup times (SDSTs) and delayed precedence (DP) occur commonly in various manufacturing settings. This study investigated the single machine scheduling problem with SDSTs and DP constraints arising in an amplifier assembly company. A mixed-integer linear programming model and a lean iterated greedy (LIG) algorithm is proposed to search for the best job sequence with minimum makespan. Based on the characteristic of delayed precedence constraints of the problem, the proposed LIG algorithm implements a straightforward but effective lean construction mechanism, which can keep the search process within the feasible solution space and quickly converge toward the (near-) global optimum. Computational results reveal that LIG significantly outperforms the state-of-the-art algorithm in terms of solution quality and computational efficiency. This study mainly contributes to providing a simple, effective, and efficient algorithm that can facilitate industrial applications and act as a new benchmark approach for future research.

The Due Date Assignment Scheduling Problem with Delivery Times and Truncated Sum-of-Processing-Times-Based Learning Effect

This paper considers a single-machine scheduling problem with past-sequence-dependent delivery times and the truncated sum-of-processing-times-based learning effect. The goal is to minimize the total costs that comprise the number of early jobs, the number of tardy jobs and due date. The due date is a decision variable. There will be corresponding penalties for jobs that are not completed on time. Under the common due date, slack due date and different due date, we prove that these problems are polynomial time solvable. Three polynomial time algorithms are proposed to obtain the optimal sequence.