What is the optimal shipment pattern and system cost

Question

Assignment:

Q: Both TelecomOne and HighOptic are manufacturers of the latest generation of telecommunication equip­ment. TelecomOne has focused on the eastern half of the United States. It has manu­facturing plants located in Baltimore, Memphis, and Wichita, and serves markets in Atlanta, Boston, and Chicago. HighOptic has targeted the western half of the United States and serves markets in Denver, Omaha, and Portland. HighOptic has plant located in Cheyenne and Salt Lake City. Plant capacities, market demand, variable production and transportation cost per thousand units shipped, and fixed costs per month at each plant are shown in Table 1

Inputs - Costs, Capacities, Demands (Table 1 for TelecomOne and HighOptic)
	Demand City Production and Transportation Cost per 1000 Units						Fixed	Capa-
Supply City	Atlanta	Boston	Chicago	Denver	Omaha	Portland	Cost ($)	city
Baltimore	1,675	400	685	1,630	1,160	2,800	7,650	18
Cheyenne	1,460	1,940	970	100	495	1,200	3,500	24
Salt Lake	1,925	2,400	1,425	500	950	800	5,000	27
Memphis	380	1,355	543	1,045	665	2,321	4,100	22
Wichita	922	1,646	700	508	311	1,797	2,200	31
Demand	10	8	14	6	7	11

The constraints ensure that all market demand is satisfied and also ensure that no factory produces more than its capacity.

The optimal demand allocation is presented here in Table 2. Observe that it is optimal for TelecomOne not to produce anything in the Wichita facility even though the facility is operational. With the demand allocation as shown in Table 2, TelecomOn incurs a monthly variable cost of $14,886,000 and a monthly fixed cost of, $13,950, for a total monthly cost of $28,836,000. HighOptic incurs a monthly variable-cost of 12,865,000 and a monthly fixed cost of $8,500,000 for a total monthly cost of $21,365,000.

Table 2	Optimal Demand Allocation for TelecomOne and HighOptic
			Atlanta	Boston	Chicago	Denver	Omaha	Portland
TelecomOne		Baltimore	0	8	2
		Memphis	10	0	12
		Wichita	0	0	0
HighOptic		Salt Lake				0	0	11
		Cheyenne				6	7	0

Management at both TelecomOne and HighOptic has decided to merge the two companies into a single entity to be called TelecomOptic. Management feels that signifi­cant benefits will result if the two networks are merged appropriately. TelecomOptic will have five factories from which to serve six markets. Management is debating whether all five factories are needed. They have assigned a supply chain team to study the network for the combined company and identify the plants that should be shut down.

Questions:

1) Given the text TelecomOptic example, answer the following questions assuming that these two firms are merged. Each question should be answered independent of the other questions. You do not necessarily need "Solver" - you can use a model with some logic and get close enough.

A. If all 5 plants are kept open, what is the optimal shipment pattern and system cost?

B. A fire has prompted the decision to shut down the Baltimore plant. Assuming that the other 4 plants must be kept open, what is the optimal network without Baltimore and the monthly cost of this new network configuration? What is the value to the supply chain network, of having the Baltimore Plant available (when compared to the situation in a)?

C. If all 5 plants are kept open, but Cheyenne cannot supply Portland, how should the network be configured, what are the shipment patterns, and what is the resulting monthly cost?