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We  deal with the relationship termination problem in the context of individual-level customer relationship management (CRM) and use a Markov decision process to determine the most appropriate occasion for termination of the relationship with a seemingly unprofitable customer. As a particular case, the beta-geometric/beta-binomial model is considered as the basis to define customer behavior and it is explained how to compute customer lifetime value when one needs to take account of the firm’s choice as to whether to continue or terminate relationship with unprofitable customers. By numerical examples provided by simulation, it is shown how a stochastic dynamic programming approach can be adopted in order to obtain a more precise estimation of the customer lifetime value as a key criterion for resource allocation in CRM.     

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In traditional data envelopment analysis (DEA) the uncertainty of inputs and outputs is not considered when evaluating the performance of a unit. In other words, effects of uncertainty on optimality and feasibility of models are ignored. This paper introduces a new model for measuring the efficiency of decision making units (DMUs) having interval inputs and outputs. The proposed model is based on interval DEA (IDEA) in which the inputs and outputs are limited to be within uncertainty bounds. In this model, the inputs and outputs take fixed values for each DMU such that the sum of efficiencies is maximized. The DMUs are evaluated by the same production possibility set (PPS). The efficiency is measured based on the proposed conservatism level for each input and output. Indeed, the inputs and outputs are defined by the presented conservatism level. The proposed model is integrated measuring all the DMUs efficiencies simultaneously. These efficiency scores lie between the optimistic and pessimistic cases introduced by Despotis and Similar (2002) [11].