An EPTAS for machine scheduling with bag-constraints

Machine scheduling is a fundamental optimization problem in computer science. The task of scheduling a set of jobs on a given number of machines and minimizing the makespan is well studied and among other results, we know that EPTAS's for machine scheduling on identical machines exist. Das and Wiese initiated the research on a generalization of makespan minimization, that includes so called bag-constraints. In this variation of machine scheduling the given set of jobs is partitioned into subsets, so called bags. Given this partition a schedule is only considered feasible when on any machine there is at most one job from each bag. Das and Wiese showed that this variant of machine scheduling admits a PTAS. We will improve on this result by giving the first EPTAS for the machine scheduling problem with bag-constraints. We achieve this result by using new insights on this problem and restrictions given by the bag-constraints. We show that, to gain an approximate solution, we can relax the bag-constraints and ignore some of the restrictions. Our EPTAS uses a new instance transformation that will allow us to schedule large and small jobs independently of each other for a majority of bags. We also show that it is sufficient to respect the bag-constraint only among a constant number of bags, when scheduling large jobs. With these observations our algorithm will allow for some conflicts when computing a schedule and we show how to repair the schedule in polynomial-time by swapping certain jobs around

Multitasking Scheduling with Shared Processing

Recently, the problem of multitasking scheduling has attracted a lot of attention in the service industries where workers frequently perform multiple tasks by switching from one task to another. Hall, Leung and Li (Discrete Applied Mathematics 2016) proposed a shared processing multitasking scheduling model which allows a team to continue to work on the primary tasks while processing the routinely scheduled activities as they occur. The processing sharing is achieved by allocating a fraction of the processing capacity to routine jobs and the remaining fraction, which we denote as sharing ratio, to the primary jobs. In this paper, we generalize this model to parallel machines and allow the fraction of the processing capacity assigned to routine jobs to vary from one to another. The objectives are minimizing makespan and minimizing the total completion time. We show that for both objectives, there is no polynomial time approximation algorithm unless P = NP if the sharing ratios are arbitrary for all machines. Then we consider the problems where the sharing ratios on some machines have a constant lower bound. For each objective, we analyze the performance of the classical scheduling algorithms and their variations and then develop a polynomial time approximation scheme when the number of machines is a constant

Multitasking Scheduling with Shared Processing

Recently, the problem of multitasking scheduling has attracted a lot of attention in the service industries where workers frequently perform multiple tasks by switching from one task to another. Hall, Leung and Li (Discrete Applied Mathematics 2016) proposed a shared processing multitasking scheduling model which allows a team to continue to work on the primary tasks while processing the routinely scheduled activities as they occur. The processing sharing is achieved by allocating a fraction of the processing capacity to routine jobs and the remaining fraction, which we denote as sharing ratio, to the primary jobs. In this paper, we generalize this model to parallel machines and allow the fraction of the processing capacity assigned to routine jobs to vary from one to another. The objectives are minimizing makespan and minimizing the total completion time. We show that for both objectives, there is no polynomial time approximation algorithm unless P=NP if the sharing ratios are arbitrary for all machines. Then we consider the problems where the sharing ratios on some machines have a constant lower bound. For each objective, we analyze the performance of the classical scheduling algorithms and their variations and then develop a polynomial time approximation scheme when the number of machines is a constant

Unrelated Machines Scheduling With Machine Eligibility Restrictions

In this paper we present a new heuristic algorithm to minimize the makespan for scheduling jobs on unrelated parallel machines with machine eligibility restrictions ( R^ I M .1 C^^). To the best of our knowledge, the problem has not been addressed previously in the literature. The multi-phase heuristic algorithm incorporates new concepts from the multi-depot vehicle routing in the constructive heuristic. A computational study includes problems with two or four machines, up to 105 jobs, and three levels of a machine selection parameter. The heuristic algorithm solution values are compared to optimal solution values. The results show that the heuristic algorithm can yield solutions within a few percent of the optimal solutions with performance improving as the number of jobs to be scheduled increases

A Proactive Approach for Coping with Uncertain Resource Availabilities on Desktop Grids

International audienceUncertainties stemming from multiple sources affect distributed systems and jeopardize their efficient utilization. Desktop grids are especially concerned by this issue as volunteers lending their resources may have irregular and unpredictable behaviors. Efficiently exploiting the power of such systems raises theoretical issues that received little attention in the literature. In this paper, we assume that there exist predictions on the intervals during which machines are available. When these predictions have a limited error, it is possible to schedule a set of jobs such that the effective total execution time will not be higher than the predicted one. We formally prove it is the case when scheduling jobs only in large intervals and when provisioning sufficient slacks to absorb uncertainties. We present multiple heuristics with various efficiencies and costs that are empirically assessed through simulations

AN EFFICIENT HEURISTIC TO BALANCE TRADE-OFFS BETWEEN UTILIZATION AND PATIENT FLOWTIME IN OPERATING ROOM MANAGEMENT

Balancing trade-offs between production cost and holding cost is critical for production and operations management. Utilization of an operating room affects production cost, which relates to makespan, and patient flowtime affects holding cost. There are trade-offs between two objectives, to minimize makespan and to minimize flowtime. However, most existing constructive heuristics focus only on single-objective optimization. In the current literature, NEH is the best constructive heuristic to minimize makespan, and LR heuristic is the best to minimize flowtime. In this thesis, we propose a current and future deviation (CFD) heuristic to balance trade-offs between makespan and flowtime minimizations. Based on 5400 randomly generated instances and 120 instances in Taillard’s benchmarks, our CFD heuristic outperforms NEH and LR heuristics on trade-off balancing, and achieves the most stable performances from the perspective of statistical process control