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A robust model for a leader-follower competitive facility location problem in a discrete space

机译：离散空间中领导者跟随者竞争性设施位置问题的鲁棒模型

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摘要

This paper aims at determining the optimal locations for the leader's new facilities under the condition that the number of the follower's new facilities is unknown for the leader. The leader and the follower have some facilities in advance. The first competitor, the leader, opens p new facilities in order to increase her own market share. On the other hand, she knows that her competitor, the follower, will react to her action and locate his new facilities as well. The number of the follower's new facilities is unknown for the leader but it is assumed that the leader knows the probability of opening different numbers of the follower's new facilities. The leader aims at maximizing her own market share after the follower's new facilities entry. The follower's objective is also to maximize his own market share. Since the number of the follower's new facilities is unknown for leader, "Robust Optimization" is used for maximizing the leader's market share and making the obtained results "robust" in various scenarios in terms of different numbers of the follower's new facilities. The optimal locations for new facilities of both the leader and the follower are chosen among pre-determined potential locations. It is assumed that the demand is inelastic. The customers probabilistically meet their demands from all different facilities and the demand level which is met by each facility is computed by Huff rule. The computational experiments have been applied to evaluate the efficiency of the proposed model.
机译：本文旨在确定领导者的新设施的最佳位置，前提是领导者不知道跟随者的新设施的数量。领导者和跟随者事先有一些设施。第一个竞争对手（领导者）开设了新设施，以增加自己的市场份额。另一方面，她知道竞争对手（追随者）将对她的行动做出反应，并找到他的新设施。领导者不知道跟随者的新设施的数量，但是假定领导者知道打开不同数量的跟随者的新设施的可能性。领导者的目标是在追随者进入新设施后，最大化自己的市场份额。追随者的目标也是最大化自己的市场份额。由于领导者不知道跟随者的新设施的数量，因此“鲁棒优化”用于最大化领导者的市场份额，并根据跟随者的新设施的数量，在各种情况下使获得的结果“稳健”。在预定的潜在位置中选择领导者和跟随者的新设施的最佳位置。假设需求是无弹性的。客户很可能满足所有不同设施的需求，每个设施所满足的需求水平由霍夫规则计算。计算实验已应用于评估所提出模型的效率。

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