For the third box of t-shirts, it's becoming clear that the Dirichlet prior isn't really adequate to come up with the best orders. From a state like this:
| |
MXS |
MS |
MM |
ML |
MXL |
M2XL |
M3XL |
WS |
WM |
WL |
WXL |
W2XL |
totals |
| Lifetime received |
1 |
4 |
19 |
13 |
4 |
3 |
1 |
3 |
9 |
4 |
6 |
3 |
70 |
| Lifetime queued |
0 |
1 |
19 |
12 |
2 |
0 |
0 |
3 |
8 |
1 |
2 |
1 |
49 |
| Lifetime shipped |
0 |
1 |
18 |
11 |
2 |
0 |
0 |
3 |
8 |
1 |
2 |
1 |
47 |
| |
|
|
|
|
|
|
|
|
|
|
|
|
|
| Actual inventory (received - shipped) |
1 |
3 |
1 |
2 |
2 |
3 |
1 |
0 |
1 |
3 |
4 |
2 |
23 |
| Inventory once caught up (received - queued) |
1 |
3 |
0 |
1 |
2 |
3 |
1 |
0 |
1 |
3 |
4 |
2 |
21 |
We're getting an order like this:
Optimal order:
MXS : 0
MS : 0
MM : 13
ML : 8
MXL : 2
M2XL: 0
M3XL: 0
WS : 3
WM : 6
WL : 1
WXL : 1
W2XL: 1
Note how the Dirichlet prior is resulting in requests to buy more L, XL, and 2XL women's shirts even though in all cases I already have >=2x as many of each size as has ever been requested. This seems clearly to be waste: the problem is that the model can't use the knowledge that women are generally under-represented to reduce the expected number of orders for any given women's size.
Instead, we want to estimate a hierarchical structure, pooling knowledge of the gender ratio of orders to improve the posterior frequencies of a given gendered size. This would require upgrading from trivial closed-form Dirichlet math to (likely PyMC3) MCMC methods for the hierarchical likelihood.
For the third box of t-shirts, it's becoming clear that the Dirichlet prior isn't really adequate to come up with the best orders. From a state like this:
We're getting an order like this:
Note how the Dirichlet prior is resulting in requests to buy more L, XL, and 2XL women's shirts even though in all cases I already have >=2x as many of each size as has ever been requested. This seems clearly to be waste: the problem is that the model can't use the knowledge that women are generally under-represented to reduce the expected number of orders for any given women's size.
Instead, we want to estimate a hierarchical structure, pooling knowledge of the gender ratio of orders to improve the posterior frequencies of a given gendered size. This would require upgrading from trivial closed-form Dirichlet math to (likely PyMC3) MCMC methods for the hierarchical likelihood.