ProJeans
ProJeans manufactures fashion jeans and commercializes them in the USA. To offer more competitive prices, the company orders some of its fashion clothes from third parties manufacturers located in Bangladesh, Egypt, and Mexico.
Each manufacturer practices a different price and all manufacturers offer significantly discounted rates depending on the order size.
For example, suppose that ProJeans decides to order jeans pants from the factory in Bangladesh.
If they order 2,500 units, then they pay 5.08 USD/unit;
If they order 4,800 units, then they pay 5.08 USD/unit for the first 3,000 units and 4.22 USD/unit for the remaining 1,800 units;
If they order 6,000 units, then they pay 5.08 USD/unit for the first 3,000 units, 4.22 USD/unit for the next 2,000 units, and 3.37 for the remaining 1,000 units.
Also, the maximum number of jean pants that the factory in Bangladesh can produce and ship for the next season is 7,000 units.
The price tiers for multiple SKU-factory pairs are provided in the table below, where MOQ is the minimum order quantity.
| SKU ID | Supplier ID | SKU Name | Supplier | MOQ | Tier 1 | Price Tier 1 | Tier 2 | Price Tier 2 | Tier 3 | Price Tier 3 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | B | Jeans Pants | Bangladesh | 1,000 | 3,000 | 5.08 | 5,000 | 4.22 | 7,000 | 3.37 |
| 1 | E | Jeans Pants | Egypt | 1,500 | 3,500 | 5.83 | 5,000 | 5.33 | 8,000 | 4.43 |
| 1 | M | Jeans Pants | Mexico | 1,000 | 3,000 | 6.08 | 6,000 | 5.87 | 8,500 | 5.45 |
| 2 | B | Jeans Jacket | Bangladesh | 1,500 | 2,500 | 5.40 | 4,000 | 4.82 | 5,500 | 4.30 |
| 2 | E | Jeans Jacket | Egypt | 1,000 | 2,000 | 6.50 | 3,500 | 5.83 | 5,000 | 5.07 |
| 2 | M | Jeans Jacket | Mexico | 500 | 1,500 | 6.92 | 3,000 | 5.77 | 4,500 | 5.37 |
In addition to procurement costs, ProJeans must take transportation costs into account when planning for its sourcing strategy. The challenge with transportation cost is that it's based on the number of containers, not on the number of items shipped. We can assume that different SKUs can go in the same container and that up to 2400 items fit into one container.
For example, if ProJeans decides to order 10,000 items from the same country, it will require 5 containers, one of which will be less than 20% full.
Hence, in this case, it may be a good idea to order only 9600 (4X2400) or 12000 (5*2400) items from that country to maximize utilization.
The transportation cost from each country is provided in the table below.
| Origin | Destination | Cost ($/container) |
|---|---|---|
| Bangladesh | United States | 4,650 |
| Egypt | United States | 7,950 |
| Mexico | United States | 3,350 |
The expected demand for each SKU for the upcoming season is provided in the table below.
| SKU ID | SKU Name | Demand |
|---|---|---|
| 1 | Jeans Pants | 12,000 |
| 2 | Jeans Jacket | 6,000 |
How can ProJeans procure all the units it needs for the next season at minimum cost?
Diving Deeper
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It isn't easy to decide how many units to order from each supplier because we must juggle procurement and shipping costs simultaneously.
Furthermore, neither the acquisition nor the shipping cost is linear.
In fact, there are discounts as the order size increases, which makes it difficult even to implement analytical solutions.
And the fact that a partially full and a full container cost the same makes it crucial to consolidate orders as much as possible.
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As stated above, the ProJeans sourcing problem might not be so realistic but here is a short list of complexities that may arise for different companies:
1) We may have to deal with many more than just two SKUs and three suppliers, maybe hundreds or even thousands;
2) To calculate the cost to ship a container across borders, we may have to account for taxes and lead time, for instance;
3) There may also be multiple options for container size;
4) We assumed that it takes 2,400 units to fill a container, but we may have to account for the volume and weight of each type of SKU;
5) The cost per container may also depend on the total weight loaded into it;
6) We assumed that the two types of SKUs can go together in the same container, but this is not always the case;
7) Minimizing total cost may not be the only goal. For example, we may want to consider supplier reliability or preserve the business relationship with certain suppliers;
8) The goods may have multiple destinations inside the destination country;
9) There may be various routes that containers can take, for example, ocean via LA or NY;
10) There may also be other options for transportation mode, such as ocean, air, rail, or road;
11) A total budget might also create an additional constraint. For example, we may want to order as much as possible from the most reliable supplier without exceeding the total budget;
12) We may have incremental order quantity in addition to minimum order quantity;
13) The procurement cost function may have a different number of price tiers for each SKU-supplier combination;
14) A policy may require that a given percentage of each SKU sold by the company must be produced in the destination country.
Mip Wise can address any of these requirements and many more. For instance, it took us just a few hours to implement complexities 3, 4, and 12 listed above.
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We have solved this problem using a spreadsheet (see the Solving a Sourcing Problem with Spreadsheet blog post for details, including the link to the spreadsheet) and using mathematical optimization.
The mathematical optimization solution is much more robust and already addresses complexities 1 and 13 listed above. In particular, it solves instances with 10 SKUs and 8 suppliers in 16 seconds with an open-source solver (PuLP-CBC). By “solves” we mean that it finds a proven optimal solution, which is hard to obtain with the spreadsheet approach even for tiny instances as discussed in the Solving a Sourcing Problem with Spreadsheet blog post.