During 2001, many European markets for mobile phones reached saturation. Because of this, mobile phone operators started to shift their focus from growth and market share to cut-ting costs. One way to do this is to reduce spending on international calls. These calls are routed through network operating companies called carriers. The carriers charge per call-minute for each destination, and they often use a discount on total business volume to price their services. A mobile phone operator must decide how to allocate destinations to carriers.

V-Mobile, a mobile phone operator in Denmark, must make such a decision for a T-month planning horizon when it has C carriers to choose from, D destinations for its customers’ calls, and there are I price intervals for a typical carrier. (These intervals define a carrier’s discount structure.) The inputs include the following:

■ The price per call-minute for destination d from carrier c in price interval i in month t

■ The (forecasted) number of call-minutes for destination din month t

■ The lower and upper limits for carrier c in price interval i

■ The lower and upper limits on capacity (number of call-minutes) for carrier c in month t

■ The penalty per call-minute (to discourage poor-quality options) for carrier c to destination din month t

V-Mobile wants to find a least-cost way of routing its call-minutes through the various carriers. Of course, it hopes to take advantage of price discounts offered by the carriers.

The file c06_02.xlsxprovides inputs for one version of V-Mobile’s problem. This version has T = 2, C = 3, D = 5, and I = 3. The decision variables should include the following:

■ The number of call-minutes routed through carrier c to destination din price interval i in month t

■ A binary variable for each carrier c and price interval i combination that equals 1 if the total call-minutes for this carrier (over all destinations and months) falls in price interval i, and equals 0 otherwise.

Develop an optimization model that helps V-Mobile allocate its international calls in a cost-efficient manner. Then write a brief memo stating (1) how V-Mobile should implement your results for this particular version of the problem and (2) how the model would need to be modified for other potential problem parameters.