We consider a geographical region with spatially separated customers, whose demand is currently served by some pre-existing facilities owned by different firms. An entering firm wants to compete for this market locating some new facilities. Trying to guarantee a future satisfactory captured demand for each new facility, the firm imposes a constraint over its possible locations (a finite set of candidates): a new facility will be opened only if a minimal market share is captured in the short-term. To check that, it is necessary to know the exact captured demand by each new facility. It is supposed that customers follow the partially binary choice rule to satisfy its demand. If there are several new facilities with maximal attraction for a customer, we consider that the proportion of demand captured by the entering firm will be equally distributed among such facilities (equity-based rule). This ties breaking rule involves that we will deal with a nonlinear constrained discrete competitive facility location problem. Moreover, minimal attraction conditions for customers and distances approximated by intervals have been incorporated to deal with a more realistic model. To solve this nonlinear model, we first linearize the model, which allows to solve small size problems because of its complexity, and then, for bigger size problems, a heuristic algorithm is proposed, which could also be used to solve other constrained problems. PDF  XML

中文翻译：

---

具有最小市场份额约束和基于权益的平局打破规则的离散竞争性设施选址模型

我们考虑一个地理区域，其客户在空间上是分开的，目前其需求由不同公司拥有的一些现有设施满足。一家新进公司希望通过定位一些新设施来竞争这个市场。为了保证未来对每个新设施的满意需求，该公司对其可能的地点（一组有限的候选人）施加了限制：只有在短期内获得最小市场份额的情况下，才会开设新设施。为了进行检查，有必要知道每个新设施准确捕获的需求。假定客户遵循部分二进制选择规则来满足其需求。如果有几个对客户具有最大吸引力的新设施，我们认为进入公司所捕获的需求比例将在这些设施之间平均分配（基于权益的规则）。这种联系破裂的规则涉及我们将处理非线性约束的离散竞争性设施选址问题。此外，已纳入对客户的最小吸引力条件和按间隔近似的距离以处理更现实的模型。为了解决这个非线性模型，我们首先将模型线性化，由于其复杂性，它可以解决小尺寸问题，然后，对于大尺寸问题，提出了一种启发式算法，该算法还可用于解决其他约束问题。PDF XML