|Frozen vegetables are commonly sold in mixes, anywhere from Peas
and Carrots to an Oriental Blend, which may have nine or ten ingredients.
Shifting from one blend to another may requires a 'wash-down' so that all old
product is expunged from the equipment before a new run is started. If one is
packing carrots and then blueberries, the presence of a carrot in the
blueberries might be disconcerting to the consumer.
However, if the first packing job is carrots (say into 'poly' bags) and
the second one is peas and carrots, then the new production can commence
immediately. If the subsequent run from that uses peas, carrots, and
pearl onions, then, again, no wash-down is needed. The objective of the
scheduling system is to sequence work to minimize wash-downs.
A Product consists of one to ten Ingredients, which differ in both
selection and ratio. The ratio of the components isn't important for
A Product 'telescopes' into a product with a larger number of Ingredients
if it's list of ingredients is a precise subset. If one if the ingredients
in the smaller blend is not in the larger blend, then the smaller product
is not considered a subset.
Since product mixes can range from 1 to 10 items, it is necessary to
render intermediate tables that have all of the possible subset combinations.
Therefore, a 10 item blend has 10 single items, 9 pairs starting with the
lowest numbered item, 8 pairs starting with the next lowest item, etc.
It then has 8 triplets starting with the lowest numbered item, 7 trips
starting with the next lowest item, etc. This way a query can be run
that shows the precise commonality of ingredients at 1 item, 2 items, 3
Products of the same list of ingredients form a class, a situation that
occurs if there are (say) 7 items but the ratios are different. Products
are grouped into classes, and then the classes are compared to see if
Many products don't have any 'successors', meaning that any repacking
operation will require a washdown afterwards. These are given a 'high
number' sort sequence so that they appear at the end of the recommended
Production runs that have two stages (say a 3 item blend telescoping into
a 4 item blend) are given the next lowest number, and a production run
that has the most successive products is given the lowest number. Therefore,
a production schedule might show the following:
1 item -> 2 item -> 4 item -> 7 item -> wash-down
2 item -> 3 item -> wash-down
7 item -> wash-down
1 item -> wash-down
The input to this system is a spreadsheet that itemizes the customer orders.
Once it is imported into the SQL-Server database the repacks are grouped
by product, the products are classed, the classes are telescoped, the
telescoped groups are prioritized, the repacks belonging to those groups
are ordered by their group membership, and the entire aggregation is
exported back into spreadsheet form. This process takes less than
five minutes on the system which we use, which is a dual 2 Ghz Xeon
server with 1GB of main memory.
While this particular system is targeted at food packaging, there
could be other industries that have similar requirements. This may be
true in metals alloying, specialty chemicals, personal care products,
or the fabrication of certain building materials like insulation.
There may also be some corresponding problems in service businesses.