This paper concerns the production model that the Automatic Guided Vehicles(AGVs) is used as transporters in assembly line. The model suggests that assembly parts may inter the beginning of the line in multiple units instead entering one unit at a time. Costs are occured in proportion to the number of vehicle on the line and job flow time. Here, the objective of this model is to determine the number of vehicle to minimize the total cost for M products production. Theoretical results are proved which lead to the development of algorithm for solution search. The solution search procedure is illustrated by a numerical example.