Developing the monthly shipping schedule using transshipment model
Kim Corporation is a large Korean manufacturer of heavy numerically controlled machines. The company has two plants, one in Seoul and the other in Pusan. Machines are shipped once a month to two distribution centers, one in Chicago and one in London. From there the machines are shipped to four sales centers, A, B, C, and D. A machine stays in a distribution center for about one month on the average. Shipping costs per machine are shown in Table below.
Table: Shipping costs
|
From/To
|
Shipping cost/machine
|
|
Seoul to Pusan
|
$150
|
|
Pusan to Seoul
|
$150
|
|
Seoul to Chicago
|
$1100
|
|
Seoul to London
|
$1250
|
|
Pusan to Chicago
|
$1180
|
|
Pusan to London
|
$1450
|
|
Chicago to London
|
$880
|
|
Chicago to A
|
$350
|
|
Chicago to B
|
$620
|
|
A to B
|
$538
|
|
B to A
|
$538
|
|
London to C
|
$465
|
|
London to D
|
$465
|
|
C to London
|
$590
|
|
C to D
|
$810
|
The company does not ship on routes that are not listed above (e.g., from Chicago to Seoul). The company can ship 550 units from Seoul and 735 from Pusan each month. The monthly demand at the sales centers is: A = 240, B = 480, C = 190, D = 375. Storage costs in Chicago are $60 per unit per month and in London, $38 per unit per month.
a. Draw a network representation of the transshipment problem.
b. Formulate an ILP model for this problem and solve the problem.
c. Determine the most economical monthly shipping schedule. Provide a table showing the routes and total costs.