Question

Case: Titan Electric Company

The Titan Electric Company (TEC) manufactures and distributes electronic transformers used to distribute electric power throughout the US. The company started with a small manufacturing plant in Reno and gradually built a customer base throughout the Southwest. A distribution center was established in Denver, and later, as business expanded, their second and third distribution centers were established in Tucson and Sacramento. To date, the company operates two plants, three distribution centers and nine warehouse locations. Manufacturing costs differ between the company’s production plants. The cost of each transformer produced at the Reno plant is $1200. The newer Las Vegas plant utilizes more efficient equipment; as a result, manufacturing costs $1050 per transformer.

The cost of shipping a transformer from each of the two plants to each of the three distribution centers is shown in Table 1, below. Note that due to lack of Interstate highways, no shipments are allowed from Reno plant to the Tucson distribution center. The annual production capacity is 30,000 transformers at the Reno plant and 20,000 at the Las Vegas plant.

Table 1. Shipping Costs to Distribution Centers
	Distribution Center
Plants	Sacramento	Denver	Tucson
Reno	23.50	38.20	--
Las Vegas	38.00	32.00	33.00

The company serves their nine warehouses from the three distribution centers. The forecast of the number of meters needed in each warehouse for the next quarter is shown in Table 2, below.

Table 2. Demand Forecast
Warehouse	Demand
Albuquerque	6300
Dallas	4900
Los Angeles	2100
Omaha	1200
Phoenix	6100
Salt Lake City	4800
San Francisco	2800
Seattle	8600
Wichita	4500

The cost per unit of shipping from each distribution center to each warehouse is given in Table 3, below. Note that some distribution centers cannot serve certain warehouses. These are indicated by a dash, “—”. Titan is interested in developing manufacturing plans for its plants, and shipping plans for its distribution centers that result in the lowest overall costs.

Table 3. Shipment Costs to Customer Zones
	Distribution Center
Customer Zone	Sacramento	Denver	Tucson
Albuquerque	--	27.00	27.50
Dallas	--	30.00	29.00
Los Angeles	24.50	32.00	27.00
Omaha	--	26.00	32.00
Phoenix	32.55	25.75	18.50
Salt Lake City	31.50	27.50	--
San Francisco	19.75	47.50	--
Seattle	28.00	38.80	--
Wichita	--	22.00	--

Assignment Questions

1. With the current supply chain design, how many transformers are produced at each plant and how many are shipped from each distribution center?
   
2. What is Titan’s total manufacturing costs for the year? What is Titan’s total distribution costs for the year?
   
3. How much could Titan save if they could produce more transformers at the Las Vegas plant? How many more transformers could they produce and ensure that the same set of binding constraints remain binding?
   
4. Which warehouse is the most expensive to stock one additional transformer?
   
5. Over the next five years, Titan is anticipating moderate growth in demand of 5000 transformers. Would you recommend that Titan consider plant expansion at this time? If so, at which plant and why?
   

6.Titan is considering a proposal to ship up to 2000 transformers directly from its Las Vegas plant to the Salt Lake City warehouse. The cost of shipping directly is estimated to be $50 per transformer, with no change in manufacturing costs. Under this new plan, what are the new manufacturing and shipping plans? How much would Titan save?

Answer 1

The formulation of LP and the constrains

The solution for all the mentioned are

Reno is full.