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.

Distributionally Robust Optimization Under a Decision-Dependent Ambiguity Set with Applications to Machine Scheduling and Humanitarian Logistics

We introduce a new class of distributionally robust optimization problems under decision-dependent ambiguity sets. In particular, as our ambiguity sets, we consider balls centered on a decision-dependent probability distribution. The balls are based on a class of earth mover’s distances that includes both the total variation distance and the Wasserstein metrics. We discuss the main computational challenges in solving the problems of interest and provide an overview of various settings leading to tractable formulations. Some of the arising side results, such as the mathematical programming expressions for robustified risk measures in a discrete space, are also of independent interest. Finally, we rely on state-of-the-art modeling techniques from machine scheduling and humanitarian logistics to arrive at potentially practical applications, and present a numerical study for a novel risk-averse scheduling problem with controllable processing times. Summary of Contribution: In this study, we introduce a new class of optimization problems that simultaneously address distributional and decision-dependent uncertainty. We present a unified modeling framework along with a discussion on possible ways to specify the key model components, and discuss the main computational challenges in solving the complex problems of interest. Special care has been devoted to identifying the settings and problem classes where these challenges can be mitigated. In particular, we provide model reformulation results, including mathematical programming expressions for robustified risk measures, and describe how these results can be utilized to obtain tractable formulations for specific applied problems from the fields of humanitarian logistics and machine scheduling. Toward demonstrating the value of the modeling approach and investigating the performance of the proposed mixed-integer linear programming formulations, we conduct a computational study on a novel risk-averse machine scheduling problem with controllable processing times. We derive insights regarding the decision-making impact of our modeling approach and key parameter choices.

Matheuristic Algorithm for Job-Shop Scheduling Problem Using a Disjunctive Mathematical Model

This paper focuses on the investigation of a new efficient method for solving machine scheduling and sequencing problems. The complexity of production systems significantly affects companies, especially small- and medium-sized enterprises (SMEs), which need to reduce costs and, at the same time, become more competitive and increase their productivity by optimizing their production processes to make manufacturing processes more efficient. From a mathematical point of view, most real-world machine scheduling and sequencing problems are classified as NP-hard problems. Different algorithms have been developed to solve scheduling and sequencing problems in the last few decades. Thus, heuristic and metaheuristic techniques are widely used, as are commercial solvers. In this paper, we propose a matheuristic algorithm to optimize the job-shop problem which combines a genetic algorithm with a disjunctive mathematical model, and the Coin-OR Branch & Cut open-source solver is employed. The matheuristic algorithm allows efficient solutions to be found, and cuts computational times by using an open-source solver combined with a genetic algorithm. This provides companies with an easy-to-use tool and does not incur costs associated with expensive commercial software licenses.

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.