Using Optimisation, the improvement over guessing seem small at first glance, so what the hell. But a £3,364 improvement a week, just from better packing might covers his wages...

Summary: Using Optimisation, the improvement over guessing seem small at first glance, so what the hell. **But a £3,364 improvement a week**, just from better packing might covers his wages or drawings for the week or make the factory profitable rather than unprofitable. **It is also, over a year £174,928 in additional profit. Not turnover, but profit. All from NOT guessing.**

Optimisation of profits is what we do. We show you how to make more profit from what you have got. If it is good enough for the entire FTSE, why don’t you use it? It was a mystery to us until we looked. You don’t have access to the people, the techniques or the maths.

Here, we take a simple example, a man with a van going to market. We will help him to maximise his profits when he gets there and sells his stock.

**The products**

He has only two products to sell. They are called **X and Y** and come in different sized boxes with different weights. The boxes can be split into individual loose wrapped products of 100 per box.

You do not often come across companies which make only two products, but there are many processes in **FTSE, small and medium companies** where optimisation for two products can be applied. (iSimutron Ltd, www.iSimutron.com optimse as many things as you make or sell)

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**The Van**

He can sell whatever he can get into the van at the market and the customers appear to want a bit more than he can make or ship, of each product. He must not overload the van or carry things on the roof.

The van has an inside size of 3 meters by 3 meters by 5 meters, which gives it a total usable volume of **45 cubic meters.**

It has a load limit of only **1 metric ton or 1000 Kg.**

**His products**

There are two products he can get into the van without busting it!

The first is in a box which is a cube with has a volume of **0.7 cubic meters. This is product X**. It can be opened and split into 100 wrapped products, if this is needed to optimise packing the van.

The other product is a box which is a cube which has a **volume of 0.3 cubic meters. This is product Y**. This can also be opened into 100 wrapped products to optimise packing.

Product X, the big one weighs only **5Kg**

Product Y, the smaller one, weighs **30Kg**

The Profit on a box of X is **£100** on a sale

The Profit on a box of Y is **£500** on a sale

**He can sell everything he takes to market**

**His Van's Limits**

**Load capacit**y of the van which is **1000 Kg**

**Volume capacity** of the van which is **45 cubic meters**.

**His Profit Maximisation problem**

The question is, what is the best mix of boxes to put into his van to make the greatest profit at market where he can sell everything? Remember: The customers really want some of both products.

**The total profit is going to be £100 times the number of product X in the van plus £500 times the number of product Y in the van**. Simples, surely?

The natural way to do this is by guessing. Product X is appealing because it is light and will not bust the suspension. He can fill his van with this, easily keeping to the weight limit. The van will take 45 cubic meters. **That is 64 boxes of product X tightly packed in. No room for Product Y though.**

**Or a profit of £6,400 at market.**

However, this leaves out the smaller, heavier and more profitable product Y and will disappoint customers who require it and who will ultimately go elsewhere.

He can work out that product Y is smaller and has a higher profit of **£500 per box.**

So how about filling the van with that and forgetting bulky product X. Trying to put 100 boxes of Y into the van (It won’t even fill it) to make £50,000 at market sounds good, but that weighs 3000 Kg. Its 2000kg more than the 1000Kg load limit!

The maximum number of product Y he can put onto the van, splitting a box is **33.33 Boxes. **That is **999 Kg**, so there is no load capacity left even for a single box of product X.

This is going to make a profit for him of **£16,500**, which is a lot more than **£6,400** for a van full of Product X. The downside is that customers who want product Y will be disappointed and will go elsewhere for both products.

So how about half and half? That makes sense, surely. Half the weight limit with the heavy product Y and half the volume or even all of the rest of the volume, if the suspension will take it, with light but large product X.

Let’s see. **500kg of Y is 500/30 or 16.66 boxes**, so rather than split a box, **let’s say 17 boxes.** That is **510Kg**, 17 boxes of Product Y occupy 5.1 cubic meters which is next to nothing! It leaves nearly 40 cubic meters of load space. That is **£8,500 in profits** at £500 a box.

That now leaves 490 Kg for product X before the van is fully loaded to the weight limit. That is 98 boxes. But we can’t get 98 boxes into the van even when it is empty! Accounting for the volume of 17 boxes of Product Y, that leaves **57 Boxes of X with a profit of £5,700**

The total profit of this mix is **£14,200** which is not bad. It is less than **£16,500 **for a van filled to the weight limit with Y, but at least the customers will be happy

**He has a niggling feeling that he can do better**. He can mess around with different ratios and do lots of calculations but there are millions of combinations which work. Which is the best? Are any better than the van filled with Y alone and lose customers? Can he do better than £14,200

We can do the entire job in one go, through what is called Linear Programming (LP) and the Simplex Optimisation Algorithm.

The answer. Using LP and the Simplex, the optimal profit is, all in one go once we have worked out where to put the figures into the maths and spend a day or so getting the information out of you and cleaning it up (It took me 6 days to write this and correct all the maths, get the pictures right and not write nonsense)

**Optimal Solution: p (For profit) = £17564.1; **Wow!! More than **£16,500 for** Y alone, now that is a surprise, given out guestimate of packing of **£14,200**.

**Or you can pack 53.8 boxes of X and 24.3 Boxes of Y**

So, using our maths, we get a solution, **£17564.1**, which is greater than the best of the guesses, **£14,200** and both of the one-product solutions, hated by the customers! He might think, "The improvements seem small, so what the hell, but a **£3,364** improvement a week might covers his wages or drawings for the week or make the factory profitable rather than unprofitable. It is also, over a year **£174,928 in additional profit. Not turnover, but profit.**

**So maybe our fee of a few thousand and a retainer to do this and keep on top of it as things change or if he adds new products, is worth it after all.**

**You can, if you wish, ignore this next bit. It is best explained at a meeting.**

If you are into graphs and maths, have a look at this, done with the same software.

You can see the numbers of boxes involved in the two single product attempts on the x and y axis. For the figures and the profits see the table below.

The blue dot is the optimal of 53.8 for x and 24.3 for y.

You cannot see the guess because it is somewhere in the white area – a desert in which he could have wandered for days

And the for the mathematically inclined, the figure behind the graph are below:

If you look, the same answers are there for a van filled with X and a van filled with Y. Our man’s guess is not visible, because our Man was wandering around somewhere in that vast white area.

**Why then do you need iSimutron?**

Now that you know how to do it, why do you need me and the team at iSimutron?

Well, firstly it is hard to get the figures, hard to get the figures into the maths and then hard to do the maths itself.

**Dr Who Land!**

More importantly, **what happens if our Van Owner has three products to sell?** To solve it graphically, you will have to draw a graph in one of these:

Got any 3-D graph paper?

Well we can do it with maths without it.

**How about a van with 4 or 5 or 30 products?**

Try drawing a graph in one of these!

If you do not want to use our services and the maths that the **FTSE** uses, then I suggest that you **call for Dr Who!! Or ask someone from the FTSE why they use it and you don’t.**