# Thread: mathmatical solution to stocking

1. hi.

working for a retailer and the back stock sucks. everything is numerically ordered like the alphabet.

well my q for any a is:

Is there a way to calculate an effective way organize the back stock so that certain products are not at the bottom shelves (mostly heavy ones) and it effectively stretches from one side of the shelves to the other (since we use both sides)?

2.

3. If you want a mathematical/algorithmic answer, I think you're going to have to make the question a lot clearer and more precise. Off the top of my head, it sounds like some kind of packing problem, but there really aren't enough details.

4. Originally Posted by chero
working for a retailer and the back stock sucks. everything is numerically ordered like the alphabet.
Yes, I provided something similar several years ago.

You need to explain what "sucks" means. Seriously, because I need to know what to minimize.

By "numerically ordered", you mean by UPC code or some other item or stock number?

And what do you mean by "it effectively stretches from one side of the shelves to the other"? Specifically, what is "it"?

Lastly, you will need to give me a general layout of the shelving, especially in relationship to the Receiving & Shipping area(s).

5. Back stock does not have "receiving & shipping" but only a set of shelves for holding extra inventory and another set for ordered items (that should be going out to customers). No problem for the latter as it is alphabetic order and limited in amount of products it must hold.

"It" refers to the order of items. On a normal shelf, there is no back. so if a shelf is in the middle of the room, and you can walk around it, items can be placed so there are two sides. an invisible line to separate product.

everything is listed by product number, but done so that resembles alphabet. in which item 1235 is followed by item 136749674 which is followed by 2583.

there are thousands of products but only a few will remain in back stock. so item 136749674 may be in the back only temporarily until it is shipped back to the hub because the customer it was ordered for refused to pay but no one else has ever asked for it. where as item 1235 is not continuously bought in the front, but a few customers may want it from time to time.

how might an algorithm/mathematical equation look like or be made?

"sucks" refers to the manner in which the back stock was put together. it was done with half-effort, so some is out of order and there is no room to put extra items if need be. some items can't fit so they go ontop or left on the ground. many items are crazy heavy and found their way at the very bottom.

I don't want to go into great detail because I wouldn't want to burden anyone with providing an actual solution or example. an explaination as to how it may be done would be sufficient, if anyone would want to supply an answer.

6. Okay, this is a good start. Back stock is stock waiting for space to open in the store's customer shelves. I have a few ideas, and you can mix and match them to your own delight (or dismay). For now, you know more about what suits your situation. Yes, I talk about algorithms last for some strange reason.

If you simply don't have enough back stock space for everything, then the misery of overflow, etc will always haunt you no matter how you try to juggle the back stock. So, ...

Question #1: Is there *almost always* enough shelving space available in back stock? That is, if you could simply throw *all* the items on shelves *anywhere*, would they all fit? If not, then it's a good idea to develop sufficient shelf space needed on most days, plus some extra space (10 to 25%?) for business expansion (or to help with this back stock problem) .

Fixed indexing is not a problem if enough shelf space is allocated for each index, but this doesn't seem to be the case. Also, if required shelf space varies greatly from week to week or season to season, then flexible indexing might be helpful. So, ...

Question #2: Is the indexing of shelves (or shelving units) currently fixed? (For example, shelving units 1 and 2 for stock #'s beginning with a "1", shelving units 3 and 4 for stock #'s beginning with a "2", etc.) If fixed, then consider making the indexing flexible, like the indexing of shoe sizes on the shelves in shoe stores using mobile signs. This would also involve shifting stock across shelves or from shelf to shelf, or among units when you re-index the shelves. You would probably want to re-index the shelves when a new shipment arrives.

Just for general thinking, *roughly* (please) ...

Question #3, etc: On a typical day, ...
How many different stock numbers are in back stock?
How many individual items?
How many items put out for sale?
How many items returned to hub?
What is the general nature of the items (dry goods, liquids, foods, perishable, etc)?
About how many feet of shelving are in back stock?
About how large is the back stock area (feet by feet)?
Where does your stock come from if not S&H?
Does the business use a computer to track inventory?

Just for general thinking purposes, shelving units have a few basic dimensions: a – individual units (as you have shown), b – partitions of units (eg, left, middle, right, etc), c – shelf level (along the vertical y axis for each unit), and d – shelf spot (along the horizontal x axis for each unit).

As for back stock overflow, consider using one or more standalone units. So, for simplicity sake, if you have shelving units 1 through 10 for stock #'s beginning with 0 through 9, then shelving units 11 and 12 could be for overflow. I just realized that this amounts treating back stock overflow as the back stock of the back stock. Crazy.

BIG/HEAVY items

For very heavy items, people think of putting them on the very bottom so shelving doesn't get top heavy, but you know the pain/danger of bending so low, even if you do "use your knees". Maybe the heaviest items can go on the next shelf up from the bottom. Or use a two-wheeler.

This leaves the bottom shelf open, perhaps for overflow from the shelves above. Maybe you have concerns about liquid items, These could go on bottom shelves, so if they break, they only run onto the floor instead onto other items.

You can spread out big/heavy items if their stock numbers fall together. For example, items 123405, 123406, 123407, 123408, etc are all big items. One solution is to index ALL items by stock number BUT read *backwards* beginning with the last digit, so 123405 goes on shelving unit #5, 123406 on unit #6, etc.

You can *play* with the stock numbers, so the big 12340X items goes on their appropriate shelves, overflow units would go on shelves for items numbered 2340X, overflow from there to shelves for items numbered 340X, etc.

Businesses use a word "benchmark" (ie, a standard or point of reference in measuring or judging quality, value, etc.). In business, it refers to another business that you can use as a model for a section of your business operation, such as back stock. This other business doesn't need to be in your particular niche of the retail market. For example, if you work in a grocery store, you don't necessarily need to use Walmart, Kroger, Safeway, etc for a benchmark. You might use a shoe store, a prescription pharmacy, etc as a benchmark.

No, not grams and liters. The word "metric" simply means "measurement". If what "sucks" is heavy items, then weight is a metric. If it's customers stealing expensive items, then price is a metric. Metric is how you would measure things to determine their importance. It's how you compare the proposed back stock system to the current back stock system. When you sit down and go through the math (which, yes, is not perfect and often includes — and typically must use — estimates), and you find that "what sucks" in the proposed system is much less than the current system, then it's worth changing, and you "have the numbers" to prove it. The metrics and math is what makes it scientific, compared to, say, a "seat of the pants" approach (ie, "it just seems right") or maybe the owner's nephew wants it done a particular way even though he's an idiot or maybe it's done a certain way because "we've always done it that way" (ugh! that means no one knows why).

Algorithm

So, as for an algorithm, you would use various metrics depending on what "sucks", which is a perfectly good scientific term (jk). For example, you might show that every day, 24 items weighing 50 lbs each must be carried 80 feet from the back stock into the store. 24 x 50 x 80 = 96,000. Do this for all items, and sum them for a grand total. However, this is why I asked about Shipping & Receiving, because if you place the heavy items closer to the customer shelves, then you first must bring them in from the loading dock. So, you either lug them a long distance from the loading dock to the back stock and then a short distance to the customer shelves, or a short distance from the dock to the back stock and then a long distance to the shelves. Same thing really, unless the boss has big burly guys receiving them, and cute little clerkettes shelving them.

7. If the only problem is finding something on the shelf which may be out of numerical order by stock number, then all you would have to do is make a database that shows the location of each item, and log its location any time you put something on the shelf. Then you could put stuff anywhere it fits.

8. Originally Posted by Harold14370
If the only problem is finding something on the shelf which may be out of numerical order by stock number, then all you would have to do is make a database that shows the location of each item, and log its location any time you put something on the shelf. Then you could put stuff anywhere it fits.
That would also prevent the need for "shifting stock across shelves or from shelf to shelf, or among units when you re-index the shelves".
And a spreadsheet might be enough - or even index cards for "old school" people.

You could also assign areas to different products types - heavy items on middle shelves; electrical goods on the right side of the warehouse; furniture on the left; etc.
This can help for when the process goes wrong and you need to find something "manually".

9. Sounds similar to a problem I worked on for a large beverage supplier during my university days. Just some comments:

1. The first place that fits packing strategy is far from optimal (as any game of tetris will show)
2. Your constraints are very important here - a small change in those can cause a large change in optimal strategy
3. I think we used GA eventually to try solve the problem, but your mileage may vary.

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