Contrary to previous methods in production management, today’s approaches mainly focus on the whole supply chain parties’ considerations. Considering production planning and distribution, as the two main functions in supply chain (SC) management, in an integrated manner in order to enhance the SC advantages is one of today’s main dilemma. Here, we have firstly proposed and investigated the integrated production and air transportation scheduling problem with time windows for the due date to minimize the total SC costs. Since the problem was NP-hard, two new coordinated and integrated solution procedures have been presented based on meta-heuristics. Four algorithms (i.e., simulated annealing (SA), genetic algorithm, particle swarm optimization/district PSO (PSO/DPSO), and hybrid variable neighborhood search–simulated annealing (H-VNS–SA)) have been developed in both procedures. For the first time in literature, we probe different encoding schemes in the proposed algorithms. In addition, by using Taguchi experimental design, the parameters of the algorithms have been tuned. Besides, to study the behavior of the algorithms, different problem sizes have been generated and the results of two procedures have been compared together and discussed. Finally, a comparison of the proposed algorithms with some state-of-art optimized algorithms has been presented to prove statistically better performance of the proposed algorithms in most cases.

与以前的生产管理方法相反，今天的方法主要集中于整个供应链各方的考虑。将生产计划和分配作为供应链（SC）管理的两个主要功能，以增强SC的优势的集成方式成为当今的主要难题之一。在这里，我们首先提出并研究了带有到期日的时间窗的生产和航空运输的综合调度问题，以最大程度地减少总成本。由于问题是NP难题，因此基于元启发法提出了两个新的协调和集成解决方案过程。四种算法（即模拟退火（SA），遗传算法，粒子群优化/区域PSO（PSO / DPSO），两种方法都已经开发了混合变量邻域搜索模拟退火算法（H-VNS-SA）。在文献中，我们首次在提出的算法中探讨了不同的编码方案。此外，通过使用Taguchi实验设计，对算法的参数进行了调整。此外，为了研究算法的行为，已经生成了不同的问题大小，并且比较了两个过程的结果并进行了讨论。最后，将提出的算法与一些最新的优化算法进行了比较，以在大多数情况下证明所提出算法的更好的统计性能。算法的参数已调整。此外，为了研究算法的行为，产生了不同的问题大小，并且将两个过程的结果进行了比较和讨论。最后，将提出的算法与一些最先进的优化算法进行了比较，以证明在大多数情况下所提出算法的统计上更好的性能。算法的参数已调整。此外，为了研究算法的行为，已经生成了不同的问题大小，并且比较了两个过程的结果并进行了讨论。最后，将提出的算法与一些最先进的优化算法进行了比较，以证明在大多数情况下所提出算法的统计上更好的性能。