A Hong Kong-based textile company that distributes textiles worldwide is owned of the Yang family. Current plans are to remain in Hong Kong until the transition in the governments. The company hopes to use its current base to expand operations to the mainland. The company has factories in the Bahamas, Hong Kong, Korea, Nigeria and Venezuela, each weaving fabrics of two or more raw fibers: cotton, polyester and/or silk. The mills serve eight company distribution centers (DCs) located near geographic centers of activity of customers Because transportation costs have historically been less than 10% of total expenses, the administration has paid little attention to the logistics of shipments. Ching Yang returns from Mexico, where he just finished his degree in marketing. He believes that every year he can save the company hundreds of thousands of dollars, maybe millions, just by improving logistics (distribution) of the fabrics from the factories to the CDs. An evidently poor example is that of Current allocation of fabric production from Mexico to the CD of the city of Nigeria instead of Venezuela, less than a third of the distance. Similarly, the Manila CD receives the most of its textiles from Nigeria and Venezuela, although the Hong Kong plants themselves are much closer. Of course, the cost of sending a roll of fabric does not depend only on the distance. Table 1 Provides the actual costs by the company. The demands of the distribution center are seasonal, so a new shipping plan must be made every month. Table 2 provides fabric requirements. for the month of March. Textile factories have different capacities to produce various types of cloth. Table 3 provides the amounts that apply during March.

	Los Angeles	Chicago	London	Mexico City	Manila	Rome	Tokyo	N.Y.
Bahamas	2	2	3	3	7	4	7	1	Cost
Hong Kong	6	7	8	10	2	9	4	8
Korea	5	6	8	11	4	9	1	7
Nigeria	14	12	6	9	11	7	5	10
Venezuaela	4	3	5	1	9	6	11	4

	Los Angeles	Chicago	London	Mexico City	Manila	Rome	Tokyo	N.Y.	Demand
Cotton	500	800	900	900	800	100	200	700
Polyester	1000	2000	3000	1500	400	700	900	2500
Silk	100	100	200	50	400	200	700	200

Capacity

Mill	Cotton	Polyester	Silk
Bahamas	1000	3000	0
Hong Kong	2000	2500	1000
Korea	1000	3500	500
Nigeria	2000	0	0
Venezuela	1000	2000	0

Problem 3

Yang learns that changes may need to be made to the March plans. Whether gets a new client, the demand for cotton in Manila and Mexico City will increase by 10% at each location. Meanwhile, a large client in New York might cut, which would reduce demand for polyester by 10% in both New York and Chicago. Find the optimal schedule and total costs (a) for cotton and (b) for polyester.