Machine Scheduling Modelling

Several machine structures are considered in the theory of scheduling including the following  

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. 

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In the past four decades, a significant amount of theoretical research has been done in scheduling as well as in dispatching. Along the way, a notation has evolved that succinctly captures the structure of most machine scheduling models studied in the Uterature. A short description of this framework and notation is presented here (see Lawler et al. 1989 Pinedo 1995). 

Wagner HM (1995) An integer programming model for machine scheduling. Nav Res... 

A MILP model is formulated for the addressed unrelated parallel machine scheduling problem with sequence-dependent setup times in manufacturing (/ S,> Cmax) which is based on an adapted standard form of the unrelated parallel machine scheduling problem. We first need notation which is defined as follows. 

Cappadonna PA, Costa A, Fichera S (2013) Makespan minimization of unrelated parallel machines with limited human resources. Procedia CIRP 12 450 55 Edis EB, Oguz C, Ozkarahan I (2013) Parallel machine scheduling with additional resources notation, classification, models and solution methods. Eur J Oper Res 230(3) 449—463 Kaplan S, Rabadi G (2012) Exact and heuristic algorithms for the aerial refueling parallel machine scheduling problem with due date-to-deadline window and ready times. Comput Ind Eng 62 (l) 276-285... 

Balakiishnan N, Kanet JJ, Sridhaian V (1999) Eaily/tardy scheduling with sequence dependent setups on uniform parallel machines. Comput Oper Res 26(2) 127-141 Coleman B (1992) Technical note a simple model for optimization the single machine early/tardy problem with problem with sequence-dependent setups. Prod Oper Manage l(2) 225-228 Davis JS, Kanet JJ (1993) Single-machine scheduling with early and tardy completion costs. Naval Res Logistics (NRL) 40(1) 85-101... 

Using a model framework, such as resource allocation, to model problems ranging from seminar room allocation to scheduling machine time for production lots in a factory. 

The Daresbury Laboratory CRAY-1 computer is accessed by means of an IBM 370/165 which is linked to computers at the S.E.R.C s Rutherford Laboratory, C.E.R.N. and workstations in many Universities. The S.E.R.C. network in fact incorporates links to 10 mainframe and 76 minicomputers and to 44 different sites. The CRAY-1 was installed at Daresbury for an initial period of two years, extendable for a third year. The S.E.R.C. buys an average of eight hours per day from CRAY Research Inc. Ltd., and the possibility exists that the machine will be upgraded to a CRAY-1 Model S/500. Proposals are also under consideration for the installation of supercomputers at the two largest University regional computer centres - London and Manchester - and at the S.E.R.C s Rutherford Laboratory where the existing twin IBM 360/195 machines are scheduled for replacement in 1982/3. Again these machines would be accessible via workstations in a number of University departments around the U.K. 

Comparing alternative scheduling and work-allocation rules Queueing models can be used to compare different scheduling rules. They can also be used to explore the way in which performance is changed as more information about jobs or customers is acquired and that information used to modify the routing and allocation of jobs or customers to machines or... 

The models usually do not consider preferences. In a model, a job either can or cannot be processed on a given machine. In reahty, it often occurs that a job can be scheduled on a given machine but that there is a preference (for one reason or another) not to schedule it on the machine in question scheduling it on the machine in question would only be done in case of an emergency. 

In the later stages of design, discrete event simulation offers a more accurate method for modeling an FMS by taking into considerations aspects such as layout configuration, number of machines, tools and fixtures, size of buffers, part routing heuristics, and production scheduling rules. 

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