Warehouse simulation

Today I'll share with you a warehouse simulation I had to do a month ago.

Let's consider a warehouse of a specific product whose sale price is 2€ per unit. Customer visits are distributed like a Poisson process (0.5 customers per hour) and the amount of products that each customer wants follows this distribution:

Request	1 unit	2 units	3 units	4 units
Probability	0.3	0.4	0.2	0.1

In order to satisfy the demand, the owner of the warehouse keeps a stock of products. When the inventory is low, he asks the distributor for more units. The orders policy is periodic. When the inventory is fewer than 30 and there aren't any pending orders, the owner asks for more units in a way that the inventory would end up having 100 units.

In each order there's a base price of 10€ (it doesn't matter the amount of units the owner asked). Additionally the cost per unit included in the order will depend on the amount of units asked. If the amount of units requested is less than 50, the price will be 1€/unit. However if the owner asks 50 or more units, the price would be 75 cents per unit.

The delivery time follows a normal distribution (with a mean of 48 hours and a standard deviation of 0.8 hours). The delivery will be paid as soon as it arrives. An agreement with the provider entitles us with a discount of 0.01% for every three hours of delay in the delivery. On the other hand, it will be 0.01% more expensive for every three hours it arrives sooner.

The owner of the warehouse spends 0.1€ per product each hour (due to physical storage, refrigeration, …).

If the customer asks for a greater amount than what is available, the warehouse sells all it has.

a) Simulate the behaviour of the warehouse during 5 months. Estimate the expected profits, the proportion of completely satisfied customers and the percentage of time the inventory remains zero. Let's assume the initial inventory is 70 units of product.

b) Represent graphically the evolution of the inventory level during the mentioned 5 months.

c) Try to identify what changes you could implement to improve the behaviour of the inventory model (get more profits and more satisfied customers).

For the first question, I've programmed a Python script. In order to run it, you need to have installed the NumPy library. I'll show you the output of a few simulations:

 

This is the graph that represents the evolution of the inventory. For this question, I commented the final part of the code (when the results of the simulation are printed) and put at the end of each iteration a line of code that printed in one line the stock available. Then, I used LibreOffice to plot the graphic. Maybe I should use better tools and techniques the next time.

For the last question. There's an obvious way to reduce the losses: sell all the stock and forget about new orders. That way, we don't have order expenses and we keep maintenance to a minimum. Of course, we'll have a lot of potential losses (a lot of unsatisfied clients), but it's the best way to solve this problem that I've found so far (maintenance is too expensive!). Nevertheless, I challenge the reader to get better results. Mine are these:

Don't change the product sale price, that's cheating.