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In practice, we can observe periodically the proportion of demand which would accept backloggingand the corresponding waiting time for the next replenishment. Then the statistical techniques, suchas the nonlinear regression method, can be used to estimate the backlogging rate. The analytical formulationsof the problem on the general framework described have been given. The condition which guaranteesthe unique solution is obtained and the complete proof of corresponding second-order sufficientconditions for optimum is also provided.
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