Batch Size Algorithm
Original Publication Date: 1990-Jul-01
Included in the Prior Art Database: 2005-Mar-16
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.
Batch Size Algorithm
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.
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
3) With increasing number of items to be batched, batch size
variation will converge to the range from PREF to MAX.
x = 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:
where MOD(x, y) is
the modulus function and returns
the remainder of (x/y).
Number of MAX sized batches:
NMAX = (f(x) + ABS(f(x));
Number of PREF sized batches:
NPREF = (g(x) + ABS(g(x)) + (h(x) - ABS(h(x));
Number of pieces in the odd lot:
NODD = x - MAX * (NMAX) - PREF * (NPREF)
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