We model and solve the production routing problem (PRP) with time windows, product deterioration and split delivery. A bi-objective PRP model for a single perishable product, which is subject to deterioration, is presented. The two objectives represent the economic and social aspects of sustainability, whereas the environmental impact is enforced by incorporating ad-hoc constraints. The economic dimension of sustainability consists of minimizing the costs related to the production, setup, holding, transportation and lateness penalty. The social responsibilities are modelled through maximizing the total freshness of the delivered products at all nodes over the planning horizon. The outcomes of our formulation are represented by the lot sizes, and the amounts of product to be delivered, as well as the routing at each planning period. To solve the resulting problem, we develop an interval robust possibilistic approach, and we carry out an experimental study and a sensitivity analysis. Finally, we further validate our optimization model and solution method using a real-life case of a food factory producing a product that is subject to perishability and deterioration.

中文翻译：

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建模和解决具有时间窗和社会可持续性的双目标生产-运输问题

我们通过时间窗口、产品劣化和拆分交付来建模和解决生产路线问题 (PRP)。提出了一种易腐烂产品的双目标 PRP 模型，该产品易变质。这两个目标代表了可持续性的经济和社会方面，而环境影响是通过结合临时约束来实施的。可持续性的经济维度包括最大限度地减少与生产、设置、持有、运输和延迟罚款相关的成本。社会责任是通过在规划范围内最大化所有节点交付产品的总新鲜度来建模的。我们制定的结果由批量大小、要交付的产品数量以及每个计划期间的路线来表示。为了解决由此产生的问题，我们开发了一种区间稳健的可能性方法，并进行了实验研究和敏感性分析。最后，我们使用食品厂生产易腐烂和变质产品的真实案例进一步验证了我们的优化模型和求解方法。