Aggregate production planning (APP) is a method to make several decisions simultaneously on production, inventory, and workforce levels over a finite time horizon, aiming to maximize the profit or minimize the cost while meeting fluctuating demands. Building mathematical models that reflect real-world problems is often difficult, as the constraints are usually intricate and may interact with each other. Decomposing the interconnected system into a number of independent phases could simplify the problem; however, it may not guarantee the optimality of the best solutions due to the missed constraints between stages. In this study, two mixed integer programming models for the manufacturing of reusable plastic containers are presented. One is based on the flow of the material and the other is based on the level of the workforce at each period. The proposed models are able to (i) deal with varying demand, (ii) reflect various regulations and restrictions of public and private warehouses for storing materials, and (iii) identify the importance of subcontracting when demand increases dramatically. Both mathematical models are implemented in the case of packaging manufacturing. A comprehensive sensitivity analysis has been conducted on different parameters of the problem to test the effect of parameter changes. To sum up, the general framework of the mathematical models not only can be used for reusable container manufacturing but also the manufacturing of any type of product with a similar supply chain network.
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