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Solving a Production-Routing Problem with Price-Dependent Demand Using an Outer Approximation Method
Computers & Operations Research ( IF 4.6 ) Pub Date : 2020-11-01 , DOI: 10.1016/j.cor.2020.105019
Somayeh Torkaman , Mohammad Reza Akbari Jokar , Nevin Mutlu , Tom Van Woensel

Abstract A production-routing problem with price-dependent demand (PRP-PD) is studied in this paper. Demand follows a general convex, differentiable, continuous and strictly decreasing function in price. The problem is modeled as a mixed integer nonlinear program (MINLP). Two Outer Approximation (OA) based algorithms are developed to solve the PRP-PD. The efficiency of the proposed algorithms in comparison with commercial MINLP solvers is demonstrated. The computational results show that our basic OA algorithm outperforms the commercial solvers both in solution quality and in computational time aspects. On the other hand, our extended (two-phase) OA algorithm provides near-optimal solutions very efficiently, especially for large problem instances. These findings prevail both for linear and for nonlinear demand functions. Additional sensitivity analyses are conducted to investigate the impact of different problem parameters on the optimal solution. The results show that the manufacturer should give higher priority to the retailer who has lower price sensitivity and who is closer to the manufacturer. Another takeaway is that a larger market size and a lower price sensitivity lead to more profit.

中文翻译:

使用外逼近方法解决具有价格相关需求的生产路线问题

摘要 本文研究了具有价格依赖需求的生产路线问题(PRP-PD)。需求遵循价格的一般凸函数、可微分函数、连续函数和严格递减函数。该问题被建模为混合整数非线性程序 (MINLP)。开发了两种基于外逼近 (OA) 的算法来解决 PR​​P-PD。与商业 MINLP 求解器相比,所提出的算法的效率得到了证明。计算结果表明,我们的基本 OA 算法在解决方案质量和计算时间方面都优于商业求解器。另一方面,我们的扩展(两阶段)OA 算法非常有效地提供了接近最优的解决方案,尤其是对于大型问题实例。这些发现适用于线性和非线性需求函数。进行了额外的敏感性分析,以研究不同问题参数对最佳解决方案的影响。结果表明,制造商应优先考虑价格敏感度较低且距离制造商较近的零售商。另一个要点是,更大的市场规模和更低的价格敏感性会带来更多的利润。
更新日期:2020-11-01
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