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In this paper, integrated production and batch delivery scheduling problem for make to order production system and one customer in supply chain has been addressed. One manufacture received n orders from one customer. Orders must be processed by single machine and sent in batches to customer. Sending several jobs as a batch leads to less transportation cost but may increase the cost of tardiness jobs. The objective is determining the production and delivery scheduling so that the related costs is minimized. The problem is strongly NP-hard. In this paper, one new math programming model including Mixed Integer Programming (MIP) model, Ant Colony System (ACS) and Elastic Ant System (EAS) are presented for solving it. In order to evaluate the efficiency of these two methods computational tests based on full factorial experimental design has been conducted. Computational test is performed for evaluation of these methods. The obtained results show that the heuristic algorithm is efficient which has been verified by using. Analysis of variance (ANOVA) technique. The results showed that the ACS is the most efficient method. [ABSTRACT FROM AUTHOR]