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.

Mixed-Integer Programming Model for Fixture Layout Optimization

1999 ◽  
Vol 121 (4) ◽  
pp. 701-708 ◽  
Author(s):  
Q. A. Sayeed ◽  
E. C. De Meter
Keyword(s):  
Integer Programming ◽  
Mixed Integer Programming ◽  
Programming Model ◽  
Optimal Solution ◽  
Geometric Error ◽  
Mixed Integer ◽  
Integer Programming Model ◽  
Mixed Integer Programming Model ◽  
Fea Model ◽  
Candidate Regions

Workpiece deformation during machining is a significant source of machined feature geometric error. This paper presents a linear, mixed integer programming model for determining the optimal locations of locator buttons, supports, and their opposing clamps for minimizing the affect of static workpiece deformation on machined feature geometric error. This model operates on discretized candidate regions as opposed to continuous candidate regions. In addition it utilizes a condensed FEA model of the workpiece in order to minimize model size and computation expense. This model has two advantages over existing nonlinear programming (NLP) formulations. The first is its ability to solve problems in which fixture elements can be placed over multiple regions. The second is that a global optimal solution to this model can be obtained using commercially available software.

scholarly journals Solving the Quality of Service Multicast Tree Problem

2021 ◽  
Vol 33 (2) ◽  
pp. 163-172
Author(s):  
Claudio Enrique Risso-Montaldo ◽  
Franco Rafael Robledo-Amoza ◽  
Sergio Enrique Nesmachnow-Cánovas
Keyword(s):  
Quality Of Service ◽  
Integer Programming ◽  
Mixed Integer Programming ◽  
Multicast Tree ◽  
Mixed Integer ◽  
Programming Formulation ◽  
Integer Programming Formulation ◽  
Realistic Problem ◽  
Problem Instances

This article presents a flow-based mixed integer programming formulation for the Quality of Service Multicast Tree problem. This is a relevant problem related to nowadays telecommunication networksto distribute multimedia over cloud-based Internet systems. To the best of our knowledge, no previous mixed integer programming formulation was proposed for Quality of Service Multicast Tree Problem. Experimental evaluation is performed over a set of realistic problem instances from SteinLib, to prove that standard exact solvers can find solutions to real-world size instances. Exact method is applied for benchmarking the proposed formulations, finding optimal solutions and low feasible-to-optimal gaps in reasonable execution times.

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.

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