Practical Project

Supply Chain Design with Linear Programming

The Darby LLC manufactures and distributes meters used to measure electric power consumption. The company started with a small production plant in El Paso and gradually built a customer base throughout Texas. A distribution center was established in Fort Worth, Texas, and later, as business expanded, a second distribution center was established in Santa Fe$,$ New Mexico.

The El Paso plant was expanded when the company began marketing its meters in Arizona, California, Nevada, and Utah. With the growth of the West Coast business, the Darby Company opened a third distribution center in Las Vegas and just two years ago opened a second production plant in San Bernardino, California. Manufacturing costs differ between the company's production plants. The cost of each meter produced at the El Paso plant is $\backslash (\backslash$$ $10\mathrm{.}50\backslash ).$ The San Bernardino plant utilizes newer and more efficient equipment; as a result, manufacturing costs are $\backslash (\backslash$$ $0\mathrm{.}50\backslash )$ per meter less than at the El Paso plant.

Due to the company's rapid growth, not much attention had been paid to the efficlency of lts supply chain, but Darby's management decided that it is time to address this issue. The cost of shipping a meter from each of the two plants to each of the three distribution centers is shown in Table A$.$

Table A: Shipping Cost per Unit from Production Plants to Distribution Centers $($In $\backslash$$$)$

The quarterly production capacity is $30,000$ meters at the older El Paso plant and $20,000$ meters at the San Bernardino plant. Note that no shipments are allowed from the San Bernardino plant to the Fort Worth distribution center. The company serves nine customer zones from the three distribution centers. The forecast of the number of meters needed in each customer zone for the next quarter is shown in Table B$.$