An Overview of Hybrid Flow Shop Scheduling: Sustainability Perspective

This paper is survey of hybrid flow shop scheduling problems. An HFS scheduling problem is a classical flow-shop in which parallel machines are available to perform the same operation. Most real world scheduling problems are NP-hard in nature. The hybrid flow shop scheduling problems have received considerable research attention. The several optimization and heuristic solution procedures are available to solve a variety of hybrid flow shop scheduling problems. It discusses and reviews sustainability of several variants of the hybrid flow shop scheduling problem for economical analysis, each in turn considering different assumptions, constraints and objective functions. Sustainability is the long-term maintenance of responsibility, which analysis the economics and encompasses the concept of stewardship. The Hybrid flow shop problem has sustained for several decades with multi – objective constraints. The paper shows some fruitful directions for future research and opportunities in the area of hybrid flow shop. DOI: 10.4018/jgc.2012070106 International Journal of Green Computing, 3(2), 78-91, July-December 2012 79 Copyright © 2012, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. ◦ Each stage ‘k’ has M (k) ≥ 1 machines in parallel and in at least one of the stages M (k) > 1. • All jobs are processed following the same production sequence: stage 1, stage 2....... stage m. • Each job j requires a processing time on machines. 2. HYBRID FLOW SHOP CLASSIFICATION The HFS problems are classified according to their shop configuration, constraints, assumptions, and the objective function considered. The configuration defines the structure of the shop, including the number of stages and the number and characteristics of the machines per stage. The configuration compared four parameters α 1, α 2, α 3 and α 4. α 1 denotes the general configuration of the shop (i.e., Hybrid flow shop). α 2 is the number of stages in the shop. α 3 and α 4 describe the properties of machines per stage. The notation (α 3 α 4) k means that there are α 4 parallel machines of the type α 3 in stage k (Pinedo, 2002). The second element is list of constraints and assumptions. The most common constraints and assumptions are: 1. Job j cannot start processing before its release date rj. 2. The jobs are processed in every stage in the same order. 3. The precedence constraints between operations from different jobs. 4. The processing of job j is restricted to the set of machines at stage k. This is known as eligibility. 5. The preemptions are permitted. 6. The buffer capacities between stages are limited. The jobs must wait in the previous stage until sufficient space is released. 7. The machines are available at all times. 8. No-wait jobs are not allowed to wait between two successive stages. This implies that the shop operates under the First in First out (FIFO) discipline. The objective function is a third element. The HFS problems are NP-hard problems even with m = 2 according to Hoogeveen, Lenstra, and Veltman (1996). So the most of the authors are considered only single objective functions. The objective functions are described in Table 1 (see Table 1 in the Appendix). 3. LITERATURE REVIEW The hybrid flow shop scheduling problem has been widely discussed in the literature and has many industrial applications. Most of the studies related to HFS problems are concentrated on problems with identical processors. In this paper, we proposed within a reasonable scope of problems that according to the author’s discretion. HFS problems are both generic cases and special cases of standard problem with limited number of assumptions, sustainability Figure 1. Schematic view of hybrid flow shop 12 more pages are available in the full version of this document, which may be purchased using the "Add to Cart" button on the product's webpage: www.igi-global.com/article/overview-hybrid-flow-shopscheduling/70000?camid=4v1 This title is available in InfoSci-Journals, InfoSci-Journal Disciplines Engineering, Natural, and Physical Science. Recommend this product to your librarian: www.igi-global.com/e-resources/libraryrecommendation/?id=2