Cost  assignment is Allocation of consumed resources to the consumer activities or cost objects.

Cost assignment (or cost attribution) The procedures by which direct or indirect costs are charged to or made the responsibility of particular cost centers, and ultimately charged to the products manufactured or services provided by the organization. Procedures used to achieve cost attribution include absorption costing, activity-based costing, and marginal costing. All these are part of Cost assignment

Cost centre on the other hand is The area of an organization for which costs are collected for the purposes of cost ascertainment, planning, decision making, and control. Cost centres are determined by individual organizations; they may be based on a function, department, section, individual, or any group of these. Cost centres are of two main types: production cost centres in an organization are those concerned with making a product, while service cost centres provide a service (such as stores, boiler house, or canteen) to other parts of the organization.

Cost assignment (cost allocation )  is identification of costs with cost objectives, also called cost apportionment, cost assignment, cost distribution, and cost reapportionment. There are basically three aspects of cost allocation: (1) choosing the object of costing. Examples are products, processes, jobs, or departments; (2) choosing and accumulating the costs that relate to the object of costing. Examples are manufacturing expenses, selling and administrative expenses, joint costs, common costs, service department costs, and fixed costs; and (3) choosing a method of identifying (2) with (1). For example, a cost allocation ( or Cost assignment) base for allocating manufacturing costs would typically be labor-hours, machine-hours, or production units.