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CASE 6.2 SELECTING TELECOMMUNICATION CARRIERS TO OBTAIN VOLUME DISCOUNTS 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 spend- ing on international calls. These calls are routed through network operating companies called car- riers. 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 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 d in 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 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.xlsx provides inputs for one version of V-Mobile's problem. This version has T = 2, C = 3, D = 5, and I = 3. The decision vari- ables 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 O 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. Carrier selection for telecommunication company with volume discounts Inputs Price intervals Carrier 1 Lower limit Upper limit 0 2000 2000 4000 4000 50000 Carrier 2 0 2500 5000 2500 5000 50000 Carrier 3 0 2000 2000 3500 50000 3500 Unit prices Month 1 Dest 1 Dest 2 Dest 3 Dest 4 Dest 3 Dest 5 Month 2 Dest 5 Dest 1 15 9 13 8 Dest 2 12 Carrier 1 9 12 15 10 15 Dest 4 10 8 15 8 10 13 8 10 13 13 7 10 5 10 7 10 5 10 8 13 Carrier 2 10 17 11 10 8 13 11 17 11 16 9 11 15 9 9 15 9 COCO B 8 9 13 16 14 12 14 12 5 9 13 Carrier 3 14 17 12 14 17 8 7 5 12 10 14 12 14 12 9 12 13 10 7 12 13 9 6 10 9 8 9 6 10 8 Dest 2 Dest 3 Desta Dest 4 Month 2 Dest 5 Dest 1 2 Dest 2 Dest 3 Penalties per call-minute Month 1 Dest 1 Carrier 1 2 Carrier 2 Carrier 3 Dest 4 Dest 5 Lower and upper bounds on capacity Month 1 Month 2 Lower bound Upper bound Lower bound Upper bound Carrier 1 0 2000 0 2000 Carrier 2 500 2000 500 2000 Carrier 3 0 2500 0 2500 2 2 3 3 Forecasted volumes 500 1000 800 1200 900 700 1000 600 1500 700