There have two ways for scheduling and planning in ERP: MRP and Kanban. MRP is to push while Kanban is to pull. So Kanban and MRP are not compatible. You should NOT use them together in your ERP system.
But somebody think there are two kind of kanban:kanban with MRP and kanban without MRP.
they mean we can do scheduling using kanban and MRP concurrently. Of course, right now there has derived kanban, which may compatible with MRP.
For MRP, the scheduling and planning are top-to-down; this is push system. The kind of planning and scheduling is oriented stock, generally speaking. Of course, you can use MRP for make-to-order environment. However, from scheduling and planning perspective, MRP is push system.
For kanban, the scheduling and planning are down-to-top, the purpose is to keep zero inventory. This is pull system. You know pull system and push system carry out planning and scheduling from different, even totalling reverse directions.
In ERP/MRPII, there have two manufacturing types, make-to-stock and make-to-order. Make-to-stock is based on forecast, while make-to-order is based on real order.
The difference between kanban and MRP is the point from which the planning and scheduling begin. So Kanban and MRP can be for forecast or real order. Acturally, in SAP/Oracle/BaaN, forecast will be transferred to production order, or say, internal order. Together with real order, or call external order, we call order.
Both MRP and kanban are based on order, regardless internal or external order.
In MRP, when we face the order, we will calculate the material requirement and then allocate to the corresponsing business units, say plant,work center, etc. So this is called push system.
In kanban, the business unit will ask the materials to be supplied according to the order, so this is called pull system.