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首页> 外文期刊>International Journal of Production Research >A rectilinear distance location-relocation problem with a probabilistic restriction: mathematical modelling and solution approaches
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A rectilinear distance location-relocation problem with a probabilistic restriction: mathematical modelling and solution approaches

机译：具有概率限制的直线距离位置-位置迁移问题：数学建模和求解方法

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摘要

In this study, we have considered a multi-period centre facility location-relocation problem in the presence of a probabilistic polyhedral barrier uniformly distributed on a horizontal barrier route in rectilinear plane. The objective function of this location-relocation problem is the minimisation of the cost of maximum expected rectilinear barrier distance from demand points to the new facility plus the relocation cost (i.e. a changeover cost at the beginning of each period) in the form of a mixed integer quadratic-constrained mathematical programming. The computational results show that the non-linear solver of commercial software LINGO is only effective in solving small-sized problems. A linear approximation for the system constraints is proposed so that a new mixed integer linear programming model is generated which is solvable via CPLEX optimisation software. Moreover, we proposed a problem decomposition procedure that reduces the multi-period problem into a number of single-period problems with some modifications. To show the efficiency of the model and solution methodologies, a broad range of numerical examples are performed. Results indicate that the developed problem decomposition procedure obtains the near-optimal solution comparatively with the results obtained from the non-linear solver of LINGO, and that the lower bound problem can be useful for large-sized problems in a reasonable time. Moreover, a practical case example to show the model validity in real world is solved and to reality check from practice, results are compared with the problem without barrier.
机译：在这项研究中，我们考虑了在直线平面的水平障碍物路径上均匀分布的概率多面体障碍物的存在下的多周期中心设施的位置-迁移问题。该位置迁移问题的目标函数是将从需求点到新设施的最大预期直线障碍距离的成本和混合形式的迁移成本（即，每个周期开始时的转换成本）最小化整数二次约束数学规划。计算结果表明，商用软件LINGO的非线性求解器仅对解决小型问题有效。提出了针对系统约束的线性近似，从而生成了可通过CPLEX优化软件求解的新的混合整数线性规划模型。此外，我们提出了一个问题分解程序，该程序将多周期问题简化为许多单周期问题。为了显示模型和求解方法的效率，执行了许多数值示例。结果表明，与从LINGO的非线性求解器获得的结果相比，所开发的问题分解程序获得了近乎最优的解决方案，并且下界问题可以在合理的时间内用于大型问题。此外，解决了一个实际案例，证明了模型在现实世界中的有效性，并通过实践对现实进行了检验，将结果与无障碍的问题进行了比较。

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