A single machine batch scheduling problem is addressed. A batch is a set of jobs processed contiguously and completed together when the processing of all jobs in the batch is finished. Processing of a batch requires a machine setup time common for all batches. Two external resources can be used to linearly compress setup and job processing times. The setup times are jointly compressible by one resource and the job processing times are jointly compressible by another resource, i.e., the amount of resource consumption for setup time compression is the same for all setups and the amount of resource consumption for job processing time compression is the same for all jobs. Polynomial time algorithms are presented to find an optimal batch sequence and optimal amounts of resource consumption such that either total job completion time is minimized, subject to an upper bound on total weighted resource consumption, or total weighted resource consumption is minimized, subject to an upper bound on total job completion time. The algorithms are based on results from linear programming and from batch scheduling with fixed setup and processing times.
[Show abstract][Hide abstract] ABSTRACT: In classical deterministic scheduling problems, the job processing times are assumed to be constant parameters. In many practical cases, however, processing times are controllable by allocating a resource (that may be continuous or discrete) to the job operations. In such cases, each processing time is a decision variable to be determined by the scheduler, who can take advantage of this flexibility to improve system performance. Since scheduling problems with controllable processing times are very interesting both from the practical and theoretical point of view, they have received a lot of attention from researchers over the last 25 years. This paper aims to give a unified framework for scheduling with controllable processing times by providing an up-to-date survey of the results in the field.
"The items must first be batched and then sequenced before the processing begins. Ng et al. (2004) address a single-machine batch-scheduling problem where a batch comprises a set of jobs processed contiguously and completed together when the processing of all jobs in the batch is completed. Potts and Kovalyov (2000) review the literature on scheduling with batching, giving details of the basic algorithms, and refer to other significant results where two cases are considered: jobs may be batched if they share the same setup time on a machine and several jobs can be simultaneously processed on a machine. "
[Show abstract][Hide abstract] ABSTRACT: Seamless steel tube is one of the major products in iron and steel industries. Production of seamless steel tube is characterized as follows: (1) rolling batch is considered as a job to be scheduled; (2) the production process consists of multiple stages; (3) different setup times are required for different rolling batches to be processed; and (4) product variety is frequently changed on the same equipment. This paper takes the Tianjin Seamless Steel Tube Company (China) as the research background. The seamless Steel Tube Scheduling (SSTS) problem can be viewed as a flowshop scheduling problem with sequence-dependent setup times. The objective is to minimize the makespan considering rolling batches to be scheduled. For a small-scale problem, an optimal solution to the problem is found using a branch-and-bound method in which the lower bound is determined according to the mth (the last) machine in the flowshop scheduling. For a large-scale problem, a near-optimal solution to the problem is found by two-stage heuristic algorithms based on a neighborhood search method. Finally, the proposed optimal and approximate algorithms are implemented on a computer using Microsoft VC++6.0. A computational experiment with a large amount of randomly generated problem instances is designed to compare the performance of the algorithms. The following results can be drawn from the computer simulation experiments. For a small-scale problem, the proposed branch-and-bound can yield an optimal solution. The best heuristics can yield a near-optimal solution with an average 0.8% deviation from the optimal solution within a reasonable time.
International Journal of Production Economics 02/2007; 105(2-105):357-371. DOI:10.1016/j.ijpe.2004.04.011 · 2.75 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: This paper presents a Greedy Randomized Adaptive Search Procedure (GRASP) to minimize the makespan of a capacitated batch-processing machine. Given a set of jobs and their processing times and sizes, the objective is to group these jobs into batches and schedule the batches on a single batch-processing machine such that the time taken to complete the last batch of jobs (or makespan) is minimized. The batch-processing machine can process a batch of jobs simultaneously as long as the total size of all the jobs in that batch does not exceed the machine capacity. The batch-processing time is equal to the longest processing time for a job in the batch. It has been shown that the problem under study is non-deterministic polynomial-time hard. Consequently, a GRASP approach was developed. The solution quality of GRASP was compared to other solution approaches such as simulated annealing, genetic algorithm, and a commercial solver through an experimental study. The study helps to conclude that GRASP outperforms other solution approaches, especially on larger problem instances.
International Journal of Advanced Manufacturing Technology 09/2013; 68(1-4). DOI:10.1007/s00170-013-4737-z · 1.46 Impact Factor
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