The purpose of the paper is the development of a mathematical model and a heuristic approach where the routes are constructed and the service period is determined for the design of an internal milk-run material supply system. The material supply by this system occurs on a just-in-time basis from a central warehouse to several stations of an assembly line. The objective of the proposed mathematical model is the minimization of the total material handling and inventory holding cost. Besides, the proposed heuristic approach intends to construct routes based on an initial service period value and attempts to improve the solution by considering different period values. The most suitable solution is decided on the basis of the least total material handling and WIP/inventory holding cost. The application of the proposed heuristic in a TV assembly plant demonstrates the utility of it to the real practice.