Tabu search for a parallel-machine scheduling problem with periodic maintenance, job rejection and weighted sum of completion times

We consider in this work a bicriteria scheduling problem on two different parallel machines with a periodic preventive maintenance policy. The two objectives considered involve minimization of job rejection costs and weighted sum of completion times. They are handled through a lexicographic approach, due to a natural hierarchy among the two objectives in the applications considered. The main contributions of this paper are first to present a new problem relevant to practice, second, to develop a mixed-integer-linear-program model for the problem, and third, to introduce two generalizable tabu-search metaheuristics relying on different neighborhood structures and solution spaces. Computational results for 120 instances (generated from a real case) are reported to empirically demonstrate the effectiveness of the proposed metaheuristics.

An Efficient Batch Scheduling Model for Hospital Sterilization Services Using Genetic Algorithm

A major challenge faced by hospitals is to provide efficient medical services. The problem studied in this article is motivated by the hospital sterilization services where the washing step generally constitutes a bottleneck in the sterilization services. Therefore, an efficient scheduling of the washing operations to reduce flow time and work-in-process inventories is of great concern to management. In the washing step, different sets of reusable medical devices may be washed together as long as the washer capacity is not exceeded. Thus, the washing step is modeled as a batch scheduling problem where washers have nonidentical capacities and reusable medical device sets have different sizes and different ready times. The objective is to minimize the sum of completion times for washing operations. The problem is first formulated as a nonlinear integer programming model. Given that this problem is NP-hard, a genetic algorithm is then proposed to heuristically solve the problem. Computational experiments show that the proposed algorithm is capable of consistently obtaining high-quality solutions in short computation times.

Explorable Uncertainty in Scheduling with Non-uniform Testing Times

The problem of scheduling with testing in the framework of explorable uncertainty models environments where some preliminary action can influence the duration of a task. In the model, each job has an unknown processing time that can be revealed by running a test. Alternatively, jobs may be run untested for the duration of a given upper limit. Recently, Dürr et al. [4] have studied the setting where all testing times are of unit size and have given lower and upper bounds for the objectives of minimizing the sum of completion times and the makespan on a single machine. In this paper, we extend the problem to non-uniform testing times and present the first competitive algorithms. The general setting is motivated for example by online user surveys for market prediction or querying centralized databases in distributed computing. Introducing general testing times gives the problem a new flavor and requires updated methods with new techniques in the analysis. We present constant competitive ratios for the objective of minimizing the sum of completion times in the deterministic case, both in the non-preemptive and preemptive setting. For the preemptive setting, we additionally give a first lower bound. We also present a randomized algorithm with improved competitive ratio. Furthermore, we give tight competitive ratios for the objective of minimizing the makespan, both in the deterministic and the randomized setting.

Scheduling a proportionate flow shop of batching machines

In this paper we study a proportionate flow shop of batching machines with release dates and a fixed number $$m \ge 2$$ m ≥ 2 of machines. The scheduling problem has so far barely received any attention in the literature, but recently its importance has increased significantly, due to applications in the industrial scaling of modern bio-medicine production processes. We show that for any fixed number of machines, the makespan and the sum of completion times can be minimized in polynomial time. Furthermore, we show that the obtained algorithm can also be used to minimize the weighted total completion time, maximum lateness, total tardiness and (weighted) number of late jobs in polynomial time if all release dates are 0. Previously, polynomial time algorithms have only been known for two machines.

An Efficient Batch Scheduling Model for Hospital Sterilization Services Using Genetic Algorithm

A major challenge faced by hospitals is to provide efficient medical services. The problem studied in this article is motivated by the hospital sterilization services where the washing step generally constitutes a bottleneck in the sterilization services. Therefore, an efficient scheduling of the washing operations to reduce flow time and work-in-process inventories is of great concern to management. In the washing step, different sets of reusable medical devices may be washed together as long as the washer capacity is not exceeded. Thus, the washing step is modeled as a batch scheduling problem where washers have nonidentical capacities and reusable medical device sets have different sizes and different ready times. The objective is to minimize the sum of completion times for washing operations. The problem is first formulated as a nonlinear integer programming model. Given that this problem is NP-hard, a genetic algorithm is then proposed to heuristically solve the problem. Computational experiments show that the proposed algorithm is capable of consistently obtaining high-quality solutions in short computation times.

A Note on Flow Shop Scheduling with the Effects of Learning and Deterioration

In this note, we consider the machine scheduling problems with the effects of learning and deterioration. In this model, job processing times are defined by functions dependent on their starting times and positions in the sequence. The scheduling objectives are makespan, sum of completion times. It is shown that even with the introduction of learning effect and deterioration jobs to job processing times, several flow shop problems remain polynomially solvable.