An integrated scheduling problem of PCB components on sequential pick-

and-place machines: Mathematical models and heuristic solutions

Authors:

William Ho and Ping Ji

Published Date:

April 2009

Presented by:

Mark Sydenham

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Function of Paper Process planning issues

Setup optimization○ Line assignment○ Machine grouping○ PCB grouping○ PCB sequencing

Process optimization○ Component allocation○ Feeder arrangement○ Component sequencing

The purpose of this paper is to integrate the feeder arrangement and component sequencing for sequential pick-and-place (PAP) machines. In other words, optimize these problems simultaneously. By using two methods Mathematical modeling A hybrid genetic algorithm

Why is optimizing these problems simultaneously important?

If, for example, the arrangement of components in the feeders is not made carefully and the sequencing is optimized, the over-all system performance can be very poor.

So to maximize performance by minimizing production time, these two problems must be solved simultaneously.

Is this paper related to the technical area in the course?

Yes, it is related. In class we have discussed electronics assembly and pick and place machines. And this paper is attempting to optimize this pick and place process.

Design of Pick and Place Machines The machine The process

Design principle or purpose Minimize the distance the placing head

travels, which in turn, reduces the take needed to place all the components

Definition of parameters for the mathematical models

The different mathematical models formulatedM3 (non-linear – contain both binary and integer values)

M4 (linear version of M3)

M5 (simplified version of M3)

M6 (M5 made linear)

Experimental equipment for the mathematical models These equations were optimized by

two software packagesCPLEX

○ A integer linear programming solver○ Used to solve M4

BARON ○ A computational system for solving non-

convex optimization problems○ Used to solve M5

Results of mathematical models Mathematical models are too complex

and require too much time to solve.

The hybrid genetic algorithm method (HGA) The basic idea of

this method is to maintain a population of possible solutions that evolve as the process proceeds

Method

Method continued

Results of the HGA method Solved in 9 seconds versus 11 hours or

15 days

Results Summary

Mathematic MethodVery accurate but takes to long to perform

HGA MethodReaches a good, but not perfect,

optimization very quickly.

Technical advancement?

Authors boast that their results constitute a reduction of about 2.2 seconds in cycle time per PCB.

Is this advancement practical for industrial use? There is the potential for this study to

benefit industry but the explanation on how to perform the proposed HGA method is difficult to understand

Which industries would benefit from this study? Manufacturers of PCB Manufacturers of machines that are

used to produce PCB