The present study proposes two mixed integer linear programming model for two important aspects of integrated production-distribution scheduling: order acceptance and batch direct delivery. Moreover, as many companies are unable to provide sufficient transportation facilities to deliver the customer orders due to high costs of initial investment, transportation is outsourced to a third-party logistics provider in which the transportation cost is dependent on the batch. The aim of this paper is trading off among the revenue of accepted orders, costs of delivery, and penalties for tardiness incurred in an integrated production-distribution in a supply chain to maximize the total of benefit. In addition, since the problem in this study is strongly NP-hard, an adaptive genetic algorithm is used to solve large-scale instances in this regard that use the adaptive search approach. A representation procedure is introduced based on two optimal properties of the problem. For the initial population, four heuristics are developed. To explore and locate the algorithm in a better neighborhood, a local search is made use of. Taguchi experimental design was applied to set the appropriate parameters of the algorithms. Moreover, to verify the developed model and evaluate the performance of algorithm against the exact solution, a commercial solver is used. The obtained results on generated random instances reveal the appropriate performance of heuristics, the adaptive approach and local search on the genetic algorithm. Furthermore, the effect of different parameters and factors of the proposed model on the profit shows that the order acceptance and the more vehicles of the company improve the profit. (C) 2017 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.