The production decision-making of a Make-to-Order enterprise in which the demand is uncertainty is studied. Such enterprises frequently face a scenario that the customer’s product order demands varies unpredictably over time，while the set-up cost for producing a single batch of products is high，but enterprises can delay the delivery by paying some delay penalty. An appropriate production strategy to reduce the cost loss，i. e. ，the decision-making of when to produce which product under uncertain future order demand to optimize the total set-up production cost and delay penalty cost should be of crucial importance. Previous studies have generally assumed that demand information，including order arrival time and order size，fluctuates randomly. However，in reality，such information is often unpredictable and cannot be characterized by probability distribution. Therefore，this paper considers the optimal production decision-making in the case of unknown future order demand from the perspective of online theory. A corresponding mathematical model is constructed，and a competition strategy is designed. It is proved that there is a superior constant competition ratio. Numerical analysis further validates the effectiveness of the strategy.