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# Batch Size Algorithm

IP.com Disclosure Number: IPCOM000036126D
Original Publication Date: 1989-Sep-01
Included in the Prior Art Database: 2005-Jan-28
Document File: 3 page(s) / 33K

IBM

## Related People

Schantz, HG: AUTHOR

## Abstract

This article describes an algorithm for batching items into job lots in a manufacturing line. First, the Batch Size Algorithm will be presented, then a specific application will be described, and finally, the application of the algorithm to other areas will be discussed.

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Batch Size Algorithm

This article describes an algorithm for batching items into job lots in a manufacturing line. First, the Batch Size Algorithm will be presented, then a specific application will be described, and finally, the application of the algorithm to other areas will be discussed.

The Batch Size Algorithm assumes some absolute maximum batch size (MAX), and a lower preferred batch size (PREF). The algorithm's three formulas provide the number of MAX sized batches, the number of PREF sized batches, and the number of pieces in the odd lot, if any. The results will satisfy the following three conditions:
1) In no case are more lots released than the minimum

number possible given the absolute maximum batch size.
2) Given condition (1) above, the number of PREF sized

lots will be maximized.
3) With increasing number of items to be batched, batch

size variation will converge to the range from PREF to

MAX.

Letx = the number of items to be batched; MAX = the absolute maximum number of items allowed in

a batch;

PREF = the preferred number of items in a batch; where 2 < (PREF + 1) < MAX.

Define three functions: f(x) = INT (_x_) - INT ( MAX-1-MOD x + INT ( x-1 ) , MAX + 1 ); MAX

MAX

( MAX - PREF ) g(x) = INT ( MAX - MOD x + INT ( x-1 ) , MAX + 1 ); MAX ( MAX - PREF ) h(x) = INT(_x_)+INT(_x_)-INT( x-1)-INT(MAX-1-MOD x-1+INT( x-1),MAX 1) MAX PREF PREF

MAX

( MAX -

PREF ) where MOD x, y is the modulus function and returns the remainder of (x/y).

Then: Number of MAX sized batches: NMAX = (f(x) + ABS(f(x));

2

Number of PREF sized batches: NPREF = (g(x) + ABS(g(x)) + (h(x) - ABS(h(x));

2 2

Number of pieces in the odd lot: NODD = x - MAX * (NMAX) - PREF * (NPREF)

1

Page 2 of 3

The Batch Size Algorithm was created for use with a pinch point tool. Under current release procedures, 50 items/batch is the maximum batch size. These 50 item batches create delays in an area of the line where one set of extended process time tools has a maximum capacity of 40 pieces. For instance, if 102 items were to be released currently, they would be batched 50-50-2. The two 50- piece jobs would have to be split, either under utilizing two tools at the same time, or doubling the lot cycle time through the area by under utilizing the same tool twice sequentially. Use of the algorithm allows the number of these batches in excess of 40 items to be minimized, without increasing the total number of jobs. Such an increase in the total number of jobs would adversely impact the rest of the line with additional set up requirements. Using the...