Aggregate production planning (APP) is concerned with determining the optimum production and workforce levels for each period over the medium term planning horizon. It aims to set overall production levels for each product family to meet fluctuating demand in the near future. APP is one of the most critical areas of production planning systems. After the state-of-the-art summaries in 1992 by Nam and Logendran [ Nam, S. J., & Logendran, R. (1992). Aggregate production planning-a survey of models and methodologies. European Journal of Operational Research, 61(3), 255-272. ], which specifically summarized the various existing techniques from 1950 to 1990 into a framework depending on their abilities to either produce an exact optimal or near-optimal solution, there has not been any systematic survey in the literature. This paper reviews the literature on APP models to meet two main purposes. First, a systematic structure for classifying APP models is proposed. Second, the existing gaps in the literature are demonstrated in order to extract future directions of this research area. This paper covers a variety of APP models' characteristics including modeling structures, important issues, and solving approaches, in contrast to other literature reviews in this field which focused on methodologies in APP models. Finally some directions for future research in this research area are suggested.

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Abstract. In traditional scheduling problems and many real-world applications, the production operations are scheduled regardless of distribution decisions. Indeed, the completion time of a job in such problems is de ned traditionally as the time when the production sequences of a job are nished. However, in many practical environments, completed orders are delivered to customers immediately after production stages without any further inventory storage. Therefore, in this paper, we investigate an integrated scheduling model of production and distribution problems simultaneously. It is assumed that products proceed through a permutation ow shop scheduling manufacturing system and are delivered to customers via available vehicles. The objective of our integrated model is to minimize the Maximum Returning Time (MRT), which is the time it takes for the last vehicle to deliver the last order to a relevant customer and return to production center. The problem is formulated mathematically, and then an Improved Imperialist Competitive Algorithm (I-ICA) is proposed for solving it. Furthermore, a su cient number of test problems are generated for computational study. Various parameters of the algorithm are analyzed to calibrate the algorithm by means of the Taguchi method. At the end, the e ectiveness of the proposed model and suggested algorithm is evaluated through a computational study where the obtained results show the appropriate performance of the integrated model and solving approach in comparison to those of the other algorithms.

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