Competitive two-agent scheduling with deteriorating jobs on a single parallel-batching machine

We consider a scheduling problem in which the jobs are generated by two agents and have time-dependent proportional-linear deteriorating processing times. The two agents compete for a common single batching machine to process their jobs, and each agent has its own criterion to optimize. The jobs may have identical or different release dates. The batching machine can process several jobs simultaneously as a batch and the processing time of a batch is equal to the longest of the job processing times in the batch. The problem is to determine a schedule for processing the jobs such that the objective of one agent is minimized, while the objective of the other agent is maintained under a fixed value. For the unbounded model, we consider various combinations of regular objectives on the basis of the compatibility of the two agents. For the bounded model, we consider two different objectives for incompatible and compatible agents: minimizing the makespan of one agent subject to an upper bound on the makespan of the other agent and minimizing the number of tardy jobs of one agent subject to an upper bound on the number of tardy jobs of the other agent. We analyze the computational complexity of various problems by either demonstrating that the problem is intractable or providing an efficient exact algorithm for the problem. Moreover, for certain problems that are shown to be intractable, we provide efficient algorithms for certain special cases

Theoretical and Computational Research in Various Scheduling Models

Nine manuscripts were published in this Special Issue on “Theoretical and Computational Research in Various Scheduling Models, 2021” of the MDPI Mathematics journal, covering a wide range of topics connected to the theory and applications of various scheduling models and their extensions/generalizations. These topics include a road network maintenance project, cost reduction of the subcontracted resources, a variant of the relocation problem, a network of activities with generally distributed durations through a Markov chain, idea on how to improve the return loading rate problem by integrating the sub-tour reversal approach with the method of the theory of constraints, an extended solution method for optimizing the bi-objective no-idle permutation flowshop scheduling problem, the burn-in (B/I) procedure, the Pareto-scheduling problem with two competing agents, and three preemptive Pareto-scheduling problems with two competing agents, among others. We hope that the book will be of interest to those working in the area of various scheduling problems and provide a bridge to facilitate the interaction between researchers and practitioners in scheduling questions. Although discrete mathematics is a common method to solve scheduling problems, the further development of this method is limited due to the lack of general principles, which poses a major challenge in this research field