Inventory Vs. Speed

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Hello;

I am working at the Strategy and Business Development Department of a textile factory, which produces fabrics. Nowadays, we are trying to plan and to execute a project that is basically about minimizing the lead time of specific types of our products. After some discussions with our managers, it turned out that we need to have more inventories of some of the raw materials or semi-produced products for the selected types, which a fabric producer would not like. Also, I am afraid; the types can exceed its numbers, since there are many types of even a basic product.

So now, I am trying to come up with something that minimizes both the inventory and the lead time. I have used the Contradiction Matrix for the problem and come up with some ideas, but I believe there are more to learn. I am open to any advises including any readings, patents, books etc.

Thank you very much for your attention