This paper considers a coordination scheduling of production and delivery on a single machine. A customer places some jobs to a manufacturer at the planning horizon. Processed jobs are delivered in batches to their customer. Each batch can dispatch to its customer at some fixed delivery dates, and different delivery dates corresponding to different delivery cost. The objective is to find a coordinated production-and-delivery schedule to minimize the weighted sum of the scheduling cost and delivery cost. We consider four main objective functions in scheduling theory, construct the models in single machine environment, analyze the problem complexity and give optimal algorithms to solve the problems under the constraint that the delivery cost are non-increasing with respect to time.