A lumber company has three sources of wood and five markets where wood is demanded. The annual quantity of wood available in the three sources of supply are 15, 20, and 15 million board feet respectively. The amount that can be sold at the five markets is 11, 12, 9, 10, and 8 million board feet, respectively. The company currently transports all of the wood by train. It wishes to evaluate its transportation schedule, possibly shifting some or all of its transportation to ships. The unit cost of shipment (in $10,000) along the various routes using both methods is described in the table below.Cost per unit of Rail Transport
Supply
Market 1
Market 2
Market 3
Market 4
Market 5
A
23
42
16
20
39
B
31
48
23
18
22
C
28
39
36
35
17
Cost per unit of Ship Transport
Supply
Market 1
Market 2
Market 3
Market 4
Market 5
A
20
45
28
None
38
B
38
52
26
25
33
C
None
43
44
38
30
The management needs to decide to what extent to continue to rely on rail transportation. Evaluate the following options by modeling the problems mathematically and make proper recommendations through solving developed mathematical models.
1.
How much does it cost use rail transport exclusively?
2.
How much does it cost to use ships exclusively?
3.
How much does it cost to use the cheapest available mode of transportation on each route?
4.
Suppose that there is an annual cost of $50,000 to operate any ships (but that this cost does not vary with the number of shipping lines kept open). What is the optimal transportation plan?
5.
How would your answer change if you learned that the supply at Center B and the demand at market 3 were both expected to increase by 10 million board feet?
Hint: You can use optimization software (GAMS, Lingo) or Excel to solve the required optimization models.