Optimal number of bypasses: Minimizing cost of calls to wireless phones under Calling Party Pays

In telecommunications, Calling Party Pays is a billing formula that prescribes that the person who makes the call pays its full cost. Under CPP land-line to wireless phone calls have a high cost for many organizations. They can reduce this cost at the expense of installing wireless bypasses to replace land-line to wireless traffic with wireless-to-wireless traffic, when the latter is cheaper than the former. Thus, for a given time-horizon, the cost of the project is a trade-off between traffic to-wireless and the number of bypasses. We present a method to determine the number of bypasses that minimizes the expected cost of the project. This method takes into account hourly varying traffic intensity. Our method takes advantage of parallels with inventory models for rental items. Examples illustrate the economic value of our approach.