Inventory Management - Reduced Cost Minimizing cost of transportation and storage of items

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Lopez
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Inventory Management - Reduced Cost

I am looking for an optimization algorithm to minimize the cost of transportation and storage cost in warehouse.

Let's assume the following table gives us the weekly forecast of Demand.

+--------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
|              | Week 1  | Week 2  | Week 3  | Week 4  | Week 5  | Week 6  | Week 7  | Week 8  | Week 9  | Week 10 | Week 11 | Week 12 |
+--------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
| Demand       |  2,300  |  1,800  |  1,100  |  2,300  |  2,000  |  1,600  |  2,200  |  2,000  |  2,900  |  1,900  |  2,000  |   1,000 |
| Buffer       |    600  |    500  |    300  |    600  |    500  |    400  |    600  |    500  |    800  |    500  |    500  |     300 |
| Total Demand |  2,900  |  2,300  |  1,400  |  2,900  |  2,500  |  2,000  |  2,800  |  2,500  |  3,700  |  2,400  |  2,500  |   1,300 |
+--------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+

The transportation cost follows the below mentioned price buckets given the ordered amount of units.

+---------------+----------------------+
|     Units     | Delivery Cost / Unit |
+---------------+----------------------+
| Less than 500 |                   50 |
| 500 - 1000    |                   40 |
| 1000 - 1500   |                   35 |
| 1500 - 2000   |                   30 |
| 2000 - 2500   |                   25 |
| 2500 - 3000   |                   20 |
| 3000 above    |                   15 |
+---------------+----------------------+

There is fixed 30$ storage cost to maintain inventory in warehouse. Time for delivery of stock from order point is 5 days. So we need to order 5 days prior if a certain quantity is required today.

I am looking for an algorithm that would help minimize the total cost while meeting the demand for each week. Also the order point should be provided.

Primarily, I am looking for readings or tutorial that would help understand how to solve such a problem. It would be great if someone can help with this particular example.