Flow shop

Baker, K.R., A comparative study of flow-shop algorithms. Oper. Res. 23(1) (1975). 

Lagweg, BJ., Lenstra, J.K., and Rinnooy Kan, A.H.G., A general bounding scheme for the permutation flow-shop problem. Oper. Res. 26(1) (1978). 

Single Parallel Multiproduct Multipurpose (flow-shop) (job-shop)... 

Mendez, C.A., Henning, G.P. and Cerd , J. (2001) An MILP continuoustime approach to short-term scheduling of resource-constrained multistage flow-shop batch facilities. Comput. Chem. 

In order to illustrate the approach, a case study is considered. The case study is a multi-stage multiproduct chemical batch plant demonstrator with a plant topology similar to flexible flow shops. Two recipes to produce the end-products are given. The end-products blue (B) and green (G) are produced from three raw materials, yellow (Y), red (R) and white (W). Each batch of the product results from two batches of the raw materials. The production process considered is two batches of material Y and W reacts to produce one batch of B similarly two batches of R and... 

A number of factors affecting production sequence should be taken into account for static scheduling, such as the part process property, FMS structure, and optimization index. The part process property determines what kind of production method should be used. Flow-shop, flexible-flow-line, and job-shop are three major strategies for producing ptuts. Different methods can be used to generate static scheduling for the different production strategies. 

Fm = a flow shop of m machines that is, m machines in series. A job after completion at one machine joins the queue at the next machine. AU queues operate under the first-in-first-out cUscipUne, that is, a job caimot pass another while waiting in a queue. 

Fm p,y = Pj J,WjCj denotes a so-called proportionate flow shop with m machines, i.e., m machines in series, with the processing times of job j on all m machines identical and equal to Pj (which is the reason this flow shop is called proportionate) the objective is to find the order in which the n jobs go through the system so that the sum of the weighted completion times is minimized. 

Figure 2 Hybrids of Flow Shops ruid Parallel Machines.

The earliest due date nde, which schedides the jobs in increasing order of their due dates, minimizes the maximum lateness on a single machine (see Jackson 1955), that is, l f , , as well as in a proportionate flow shop, that is, Fm py = pj L. However, it does not provide an optimal solution for other due date-related problems, such as l 27j. Instances of l 27j with... 

Dynamic programming is an optimization technique that is particularly well suited for scheduling problems with makespans that are schedule independent, such as, single-machine problems without setups, proportionate flow shops, and problems with till processing times being identical. It can also be applied on scheduling problems with makespans that do depend on the sequence. 

Ignall, E., and Schrage, L. E. (1965), Application of the Branch and Bound Technique to Some Flow-Shop Problems, Operations Research, Vol. 13, pp. 400-412. 

Daouas, T., Ghedira, K., and Muller, J. (1995), Distributed Flow Shop Scheduling Problem versus Local Optimization, in Proceedings of the First International Conference on Multi-Agent Systems, MIT Press, Cambridge, MA. 

Tsujimura, Y, Park, S., Chang, S., and Gen, M. (1993), An Effective Method for Solving Flow Shop Scheduling Problems with Fuzzy Processing Times, Computers and Industrial Engineering, Vol. 25, pp. 239-242. 

Flow shop companies producing products in high volume use estimates as temporary work standards. It is to be hoped that these temporary standards wiU be replaced as soon as possible with accurate time studies, work sampling, or predetermined time standards. 

The flowshop problem is the simplest structure that resembles a simple supply chain structure. The problem is extensively studied in the literature with various models of different types and efficiencies developed and examined for different objective functions and constraints. Integer programming was one of the first models developed for optimizing flow shops. 

Flow shop production structure is composed of n stages of processing units, Mi, M2,. .., Mn, in which different jobs pass through in the same sequence (Fig. 3.2). A job j in each stage i is processed for a certain time py. The requirement is to determine the order of processing the n jobs starting at time zero with no interruption in a minimum time span (makespan). 

This problem is one of the basic flow shop production structures and one of the early mathematically modeled scheduling problems. A Mixed Integer Programming (MIP) model was developed by Wagner [11]. The model (adopted from French [3]) is as follows. 

The number of variables in this model is + 2 m — l)(n — 1) and the number of constraints is nm + n — m + 1. Flow shop problems with two or three stages can be solved using simple algorithms such as Johnson s method. Other methods such as branch and bound and dynamic programming are also available for solving larger size problems. 

The job shop has a more general structure than the flow shop in which each job go through multiple processing stages (or machines) in an order that might be different than other jobs. The basic job shop scheduling problem holds the same assumptions that were made for the basic flow shop problem. In addition it is assumed that each job may be processed by a machine at most once, i.e., without recirculation. 

Roeva, O. Real-World Application of Genetic Algorithms. In Tech, Rijeka (2012) Syam, W.P., Al-Harkan, I.M. Comparison of three meta heuristics to optimize hybrid flow shop scheduling problem with parallel machines. In WASET, vol. 62, pp. 271-278 (2010)... 

Scholz-Reiter B, Rekersbrink H, Gorges M (2010b) Dynamic flexible flow shop problems - scheduling heuristics versus autonomous control. CIRP Aim Manufact Technol 59(1) 465 68 SFB (2012) http //www.sfb637.uni-bremen.de/uploads/ pics/folie 3.jpg... 

Pheromone based emergent shop floor control system for flexible flow shops. Artif Intell Eng 15(4) 343-352... 

The most common used notation for theoretical scheduling is the so-called three-field notation introduced by Graham et al. (1979). The notation foresees three fields called a p y. The first field defines the scheduling environment a equal to F stands for flow shop, / for job shop, P for parallel machines, and O for open shop. A number can be inserted to indicate the number of machines. The second field specifies job characteristics indicating, for example, the preemption, ready times, and additional resources. The third field specifies the performance index (objective). Some examples can be the following l Sjk C,nax denotes a single-machine problem with sequence-dependent setup times and minimization of maximum completion time makespan)-, JmWCmax denotes a job-shop problem with m machines an[Pg.1094]

Zadeh N.N. and Porter B., 1998. Evolution strategies in flow-shop sequencing. Proceedings of the World Automation Co/igr 55, Anchorage, Alaska, USA, pp. 673-678. 

Process choice is product layout or a flow shop/assembly line... 

Flow shop—A form of manufacturing organization in which machines and operators handle a standard usually uninterrupted, material flow. The operators generally perform the same operations for each production run. A flow shop is often referred to as a mass production shop or is said to have a continuous manufacturing layout. 

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