We examine the problem of scheduling a given set of jobs on a single machine to minimize total early and tardy costs. Two dispatch priority rules are proposed and tested for this NP-complete problem. These were found to perform far better than known heuristics that ignored early costs. For situations where the potential cost savings are sufficiently high to justify more sophisticated techniques, we propose a variation of the Beam Search method developed by researchers in artificial intelligence. This variant, called Filtered Beam Search, is able to use priority functions to search a number of solution paths in parallel. A computational study showed that this search method was not only efficient but also consistent in providing near-optimal solutions with a relatively small search tree. The study also includes an investigation of the impacts of Beam Search parameters on three variations of Beam Search for this problem.production/scheduling, deterministic job shop, single stage
The proportionate flowshop is a special class of flowshops in which the operation times of jobs are proportionate, e.g., because of differences in the speeds of machines. In this paper, we make use of a special property of proportionate flowshops, namely that the bottleneck in the shop is almost always the one where job operations are proportionately longer than for any other operations (the slowest machine) to demonstrate a scheduling procedure that makes scheduling decisions by focusing on the information and consequences at the bottleneck resource. This is called the Focused Approach. The scheduling objective is to minimize the total tardiness cost of jobs, where each job may have a different tardiness cost. The decision rule used in this approach is the Idle Time Rule whose development is described in this paper. The approach was tested using approximately proportionate flowshops of different sizes. The results obtained for small 3-machine problems were compared against the optimal permutation schedules obtained using Branch-and-Bound and was found to be near-optimal. For larger problems using 4- and 8-machine flowshops, the results were compared to five other scheduling methods. The focused approach performed far better than those other scheduling methods not only in minimizing tardiness cost, but also minimizing the percentage of tardy jobs and the percentage of processing time to work-in-process time. Finally, the two-product shop where the bottleneck was dynamic was studied and, using a simple strategy to track bottlenecks, the focused approach was again found to perform well compared with other heuristic methods.production/scheduling: flow shop, queues: deterministic, heuristics
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