Automatic Generation of Mixed Integer Programming for Scheduling Problems Based on Colored Timed Petri Nets

2018 ◽  
Vol E101.A (2) ◽  
pp. 367-372 ◽  
Author(s):  
Andrea Veronica PORCO ◽  
Ryosuke USHIJIMA ◽  
Morikazu NAKAMURA
Keyword(s):  
Integer Programming ◽  
Petri Nets ◽  
Mixed Integer Programming ◽  
Automatic Generation ◽  
Mixed Integer ◽  
Scheduling Problems ◽  
Timed Petri Nets

Application of Mixed-Integer Programming and Dispatching Rules on Parallel Machine Scheduling with Inserted Idle Time

2013 ◽  
Vol 437 ◽  
pp. 748-751
Author(s):  
Chi Yang Tsai ◽  
Yi Chen Wang
Keyword(s):  
Integer Programming ◽  
Mixed Integer Programming ◽  
Parallel Machines ◽  
Optimal Solution ◽  
Parallel Machine Scheduling ◽  
Idle Time ◽  
Dispatching Rules ◽  
Mixed Integer ◽  
Scheduling Problems

This research considers the problem of scheduling jobs on unrelated parallel machines with inserted idle times to minimize the earliness and tardiness. The aims at investigating how particular objective value can be improved by allowing machine idle time and how quality solutions can be more effectively obtained. Two mixed-integer programming formulations combining with three dispatching rules are developed to solve such scheduling problems. They can easy provide the optimal solution to problem involving about nine jobs and four machines. From the results of experiments, it is found that: (1) the inserted idle times decreases objective values more effectively; (2) three dispatching rules are very competitive in terms of efficiency and quality of solutions.

Presolve Reductions in Mixed Integer Programming

2020 ◽  
Vol 32 (2) ◽  
pp. 473-506 ◽  
Author(s):  
Tobias Achterberg ◽  
Robert E. Bixby ◽  
Zonghao Gu ◽  
Edward Rothberg ◽  
Dieter Weninger
Keyword(s):  
Integer Programming ◽  
Mixed Integer Programming ◽  
Mixed Integer ◽  
Scheduling Problems ◽  
Planning And Scheduling ◽  
Integer Programs ◽  
Mixed Integer Programs ◽  
Key Factor ◽  
The Difference ◽  
Feasible Solutions

Mixed integer programming has become a very powerful tool for modeling and solving real-world planning and scheduling problems, with the breadth of applications appearing to be almost unlimited. A critical component in the solution of these mixed integer programs is a set of routines commonly referred to as presolve. Presolve can be viewed as a collection of preprocessing techniques that reduce the size of and, more importantly, improve the “strength” of the given model formulation, that is, the degree to which the constraints of the formulation accurately describe the underlying polyhedron of integer-feasible solutions. As our computational results will show, presolve is a key factor in the speed with which we can solve mixed integer programs and is often the difference between a model being intractable and solvable, in some cases easily solvable. In this paper we describe the presolve functionality in the Gurobi commercial mixed integer programming code. This includes an overview, or taxonomy of the different methods that are employed, as well as more-detailed descriptions of several of the techniques, with some of them appearing, to our knowledge, for the first time in the literature.

scholarly journals Mixed Integer Programming-Based Liveness Test for FMS with Full Routing Flexibility

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Lida Dong ◽  
Tianyang Chi ◽  
Chengcheng Zhu ◽  
Jun Yin
Keyword(s):  
Integer Programming ◽  
Petri Nets ◽  
Mixed Integer Programming ◽  
Flexible Manufacturing ◽  
Flexible Manufacturing Systems ◽  
Manufacturing Systems ◽  
Mixed Integer ◽  
Routing Flexibility ◽  
Liveness Property

Mixed integer programming (MIP) is an important technique to verify the liveness property of sequential flexible manufacturing systems (FMS) modeled by Petri nets. When there are some fully flexible routings in FMS, the existing MIP-based methods are not suitable for testing their liveness. This paper defines a subclass of S*PR nets firstly, namely, OSC-S*PR nets, and concludes that an OSC-S*PR net is live if there exist no non-max′-controlled siphons. Accordingly, determining whether or not an OSC-S*PR net is live can also be realized by using standardized mixed integer programming (MIP) tools. Furthermore, the liveness property of S*PR nets can be tested in two steps: first, for a given S*PR net, constructing an OSC-S*PR net to ensure that if the latter is live then the former must be live; second, testing liveness of the constructed OSC-S*PR net by the aforementioned MIP-based algorithm. In the end, the performance of the method is demonstrated by an application of FMS.

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