ABC Corporation is a large computer manufacturer. ABC currently operates three service centers for their East Asia customers, in Tokyo, Soul, and Shanghai. Customers throughout Asia that have service contracts with ABC call their local office to request service when they encounter a problem with their mainframe computer. An engineer is then dispatched to the customer site from the service center. Often the engineer needs to order new parts that are then shipped from the service center to the customer site. Alex Wong, vice president of operations at ABC, has received complaints from several major customers about the timeliness of the service operation at ABC, with many customers having to wait more than two days for parts to reach the customer from the service center. At the same time, the shipping costs as well as the costs of maintaining the service centers have increased substantially.

Alex is considering relocating some of the service centers, and possibly decreasing their number from three to two in order to decrease operating costs. In addition to Tokyo, Soul, and Shanghai, Alex is considering Guangzhou and Hongkong as possible locations for service centers. Alex Wong’s staff has assembled the cost information shown in Table 1, which contains the staff’s best estimates of the annual operating costs for each of the five possible service center locations.

The major customers of ABC are located in five countries or areas: Japan, South Korea, Mainland China, Taiwan and Malaysia. Table 2 shows the percentage of major customers in each of these five countries or areas. Table 3 shows the average shipping time (in days) from each of the potential service center locations to each of the five customer country locations.

Alex would like to minimize the total operating costs while maintaining some pre-specified service requirement. In particular, Alex has decided to require that the average shipping time to each of five countries or areas from the customer service centers should not exceed 1.5 days. Moreover, Alex would like to ensure that the average shipping time across all five countries should be at most 1.1 days.

Table 1 Annual operating costs of five possible service center locations in $ million

	Service Center Location
	Tokyo	Soul	Shanghai	Guangzhou	Hongkong
Operating Cost ($ million)	20	15	22	21	16

Table 2 The percentage of ABC’s major customers in each of five countries or areas

Country	Percentage of customers
Japan	25%
Mainland China	30%
Taiwan	15%
Malaysia	10%
South Korea	20%

Table 3 Average shipping time, in days, from each of the possible service center locations to each of these five countries or areas.

	Service Center Location
Country/Area	Tokyo	Soul	Shanghai	Guangzhou	Hongkong
Japan	0.5	2.5	1.5	2.0	3.0
Mainland China	2.0	3.0	1.0	0.5	2.0
Taiwan	3.0	2.0	2.0	1.5	1.0
Malaysia	3.0	1.0	2.0	2.0	0.5
South Korea	1.5	2.0	0.5	1.0	2.0

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