Does anybody know about an mathematical optimization model which combines vendor managed inventory with fixed lot-sizes for production? That is, a model that performs a simultaneous production and delivery (transportation) planning with respect to production and transportation lot sizes.

So the keyfigures should be fixed lot-sizes for production, transportation assets, capacities and costs from vendor to VMI-stock, known demand on customer (retailer) side and inventory restrictions for the VMI-stock.

It will be also helpful if you just know about any paper or similiar which has recognized this problem.

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