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The production planning and distribution are among the most important decisions in the supply chain. Classically, in this problem, it is assumed that all orders have to produced and separately delivered; while, in practice, an order may be rejected if the cost that it brings to the supply chain exceeds its revenue. Moreover, orders can be delivered in a batch to reduce the related costs. This paper considers the production planning and distribution problem with order acceptance and package delivery to maximize the profit. At first, a new mathematical model based on mixed integer linear programming is developed. Using commercial optimization software, the model can optimally solve small or even medium sized instances. For large instances, a solution method, based on imperialist competitive algorithms, is also proposed. Using numerical experiments, the proposed model and algorithm are evaluated

The production-distribution problem with order acceptance and package delivery: models and algorithm