In the p-center problem, it is assumed that the facility located at a node responds to demands originating from the node. This assumption is suitable for emergency and health care services. However, it is not valid for large-scale emergencies where most of facilities in a whole city may become functionless. Consequently, residents in some areas cannot rely on their nearest facilities. These observations lead to the development of a variation of the p-center problem with an additional assumption that the facility at a node fails to respond to demands from the node. We use dynamic programming approach for the location on a path network and further develop an efficient algorithm for optimal locations on a general network.

In this article, we analyze a location model where facilities may be subject to disruptions. Customers do not have advance information about whether a given facility is operational or not, and thus may have to visit several facilities before finding an operational one. The objective is to locate a set of facilities to minimize the total expected cost of customer travel. We decompose the total cost into travel, reliability, and information components. This decomposition allows us to put a value on the advance information about the states of facilities and compare it to the reliability and travel cost components, which allows a decision maker to evaluate which part of the system would benefit the most from improvements. The structure of optimal solutions is analyzed, with two interesting effects identified: facility centralization and co-location; both effects appear to be stronger than in the complete information case, where the status of each facility is known in advance.

In this article we propose the use of an information-content based measure as a proxy for supply chain complexity. The focus of our research is the problem of structural complexity in the supply chain, i.e. the complexity emanating from the proliferation of products, channels and markets. Notwithstanding it is widely agreed among practitioners that this proliferation damages supply chains, rendering them less efficient, there is still need for a mechanism for measuring structural complexity and evaluating its impact on the firm's performance. In an attempt to filling this void, we propose a definition that originates from the firm's business strategy and, based on it, suggest the direct use of entropy as a more austere measure for structural complexity than other available alternatives, which rely heavily in the use of typically hard to acquire data. We show that the suggested measure has some interesting mathematical properties (to which we refer to as internal consistency) together with the capability of reproducing certain empirical regularities observed in supply chain management (external consistency). Moreover, the proposed measure has attributes that are not present in other measures: it requires a limited and easily accessible amount of data, it allows direct comparison between firms or business units, and it is a useful tool for assessing the impact on structural complexity of alternative managerial decisions (the look-ahead property). Numerical examples are provided.

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