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 $10.50.
The San Bernardino plant utilizes newer and more efficient equipment; as a result,
manufacturing costs are $0.50 per meter less than at the El Paso plant.
Due to the company’s rapid growth, not much attention had been paid to the efficiency of its
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 $)
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.
Table B: Quarterly Demand Forecast
The cost per unit of shipping from each distribution center to each customer zone is given in
Table C; note that some distribution centers cannot serve certain customer zones. These are
indicated by a dash, “—”.
Table C: Shipping Cost from the Distribution Centers to the Customer Zones
In its current supply chain, demand at the Dallas, San Antonio, Wichita, and Kansas City customer
zones is satisfied by shipments from the Fort Worth distribution center. In a similar manner, the
Denver, Salt Lake City, and Phoenix customer zones are served by the Santa Fe distribution
center, and the Los Angeles and San Diego customer zones are served by the Las Vegas
distribution center. To determine how many units to ship from each plant, the quarterly
customer demand forecasts are aggregated at the distribution centers, and a transportation
model is used to minimize the cost of shipping from the production plants to the distribution
centers.
Managerial Report (Please prepare a report with a Word file)
You are hired to make recommendations for improving Darby LLC’s supply chain. Your report
should address, but not be limited to, the following issues:

1. Please try your best to draw the Supply Chain diagram to show the network of plants, DCs
   and Customer zones. In the diagram, please label the shipping cost per unit, production
   capacity and demand size of each customer zone.
2. If the company does not change its current supply chain, what will its lowest distribution
   costs be for the following quarter? Please draw a diagram to show the optimal solution and
   label your solution on the diagram.
3. Suppose that the company is willing to consider dropping the distribution center
   limitations; that is, customers could be served by any of the distribution centers for which
   costs are available. Currently, the shipping from Ft. Worth to Salt Lake City, Phoenix, Los
   Angeles and San Diego can be outsourced to UPS at a flat rate of $3.5 per unit, regardless
   of destination. In addition, the shipping from Las Vegas to Dallas, San Antonio, Wichita, and
   Kansas City can be outsourced to Fedex at a flat rate of $4.0 per unit. Can costs be
   reduced? If so, by how much?
4. The company wants to explore the possibility of satisfying some of the customer demand
   directly from the production plants. In particular, the shipping cost is $0.30 per unit from
   San Bernardino to Los Angeles and $0.70 from San Bernardino to San Diego. The cost for
   direct shipments from El Paso to San Antonio is $3.50 per unit. Can distribution costs be
   further reduced by considering these direct plant-to-customer shipments?

Sample Solution