An Extension of Ramsey‐Boiteaux Pricing to Services Offering Limited Deferability Subject to Reliability Constraints and Fuzzy Demand Functions Available to Purchase

Ramsey‐Boiteaux pricing to services offering limited deferability subject to reliability constraints with a specific application to postal services has been investigated by the first of the above authors in. The general results derived in his paper involve welfare‐optimal pricing for a monopolist faced with stochastic demands which impact both demand and cost. These stochastic demands are modeled by probability distributions with fixed parameters. In this paper we extend this approach to the case where the model parameters are not known with certainty. This uncertainty is dealt with by representing the distribution parameters as fuzzy sets in which the membership of a particular value in the fuzzy set represents the degree of belief associated with this parameter value. This approach requires the solution of a system of nonlinear equations for each possible combination of parameter values, and the result is a fuzzy solution vector. This solution vector is then defuzzified to obtain a specific solution to the problem. As in, we illustrate our approach with an application of welfare‐optimal pricing in the context of postal services. Section I reviews relevant literature and discusses the nature of postal services. The problem statement together with general results are presented in Section II, and applied to a postal service problem in Section III. These results are further illustrated via numerical example in section IV. Conclusions are presented in Section V.