Stochastic Capacitated P-Median Problem with Normal Distribution

In this paper, by developing the capacitated p-median problem (cpmp) mathematical planning model, we try to model the problem in such a way that the service to customers according to the service level is effective in the optimum solution, and to some extent, brings the cpmp closer to actual circumstances. adding the service level will convert the cpmp from a deterministic state to a stochastic model in which demands can have any distribution function. if the customer demand follows the normal distribution function, this stochastic model can be converted to a mixed integer nonlinear programming. this obtained model is used in a real case study to develop tanks of an oil refinery so that the costs are minimized and the customer demand is met at an acceptable level. in addition, comparing the new model with the traditional cpmp model, by solving a real case study, shows the efficiency of the proposed model.